SUPPORT / THE LANGUAGE OF EXPLORATION
The Mandelbrot Metal glossary. From your first bookmark to the math inside a GPU thread, find the words behind the image.
Start here: Orbit · SIMD · Taylor series · Infinity Engine · LUT · 3D Look · HUD
501 definitionsAbout the sources
Definitions cover current Version 3 behavior, general mathematics, historical engineering language, and future roadmap concepts. Older articles remain useful background; where descriptions differ, app-specific definitions follow the current technical materials and Revision 19 of the white paper. Planned features are identified as planned.
No matching terms. Try a shorter phrase, an abbreviation, or a different topic.
Also found as 3D Effects · 3D indicator
Optional relief shading derived from a two-dimensional fractal field. It adds perceived ridges and depth without creating a volumetric fractal or changing z² + c.
Read more: GPU Pipeline · User Guide
Also found as 3840 · 5760 · 7680
App presets with nominal longest edges of 3,840, 5,760, and 7,680 pixels, preserving the canvas proportions. They are still-image options, not claims of current video export.
Read more: GPU Pipeline · User Guide
Also found as application binary interface
The binary layout contract between compiled components. For shared Swift–Metal uniforms, field order, sizes, alignment, and padding must match.
Read more: Technical white paper · Revision 19
Also found as relative error
Absolute error measures the difference from a reference result; relative error scales that difference by a reference magnitude. Near zero, relative measures require special care.
Read more: Perturbation Rendering · Technical white paper · Revision 19
Also found as lost increment · precision wall
When a tiny increment rounds away on addition to a much larger value. The increment may be representable separately even though the resulting sum is unchanged.
Read more: Beyond Complex Numbers · Inside the Infinity Engine
Also found as numerical accuracy
Closeness to the mathematical result. Extra stored digits can help, but do not repair inaccurate inputs or guarantee a stable complete computation.
Read more: Technical white paper · Revision 19 · Inside the Infinity Engine
Also found as precision ladder · precision promotion
Selecting among bounded arithmetic representations as the work demands. Version 3 combines ordinary, compensated, and recovery paths; this is not arbitrary precision.
Read more: Technical white paper · Revision 19 · Perturbation Rendering
Also found as interactive quality · idle quality
Adjusting work according to interaction and rendering conditions. Preview responsiveness and completed-image fidelity are separate goals.
Read more: Technical white paper · Revision 19
A ratio comparing total or aggregate elapsed times for a corpus. It is not necessarily the arithmetic average of individual scene speedup ratios.
Read more: Inside the Infinity Engine
A field in which every nonconstant polynomial has a root in that field. Complex numbers have this property; real numbers do not.
Read more: Beyond Complex Numbers
Also found as jaggies · stair-stepping
Visible errors when fine spatial detail is sampled too sparsely, including jagged edges or misleading patterns. Extra samples can reduce it but cannot repair lost coordinates.
Read more: GPU Pipeline
Also found as padding · field offset
Rules governing where data sits in memory. Padding can place fields at required boundaries; mismatched offsets make GPU code read the wrong values.
Read more: Technical white paper · Revision 19
Also found as control image
An image computed with every relevant sample using the quad-single path, for comparison with adaptive routing. Agreement checks a related implementation, not an independent mathematical truth.
Read more: Inside the Infinity Engine
Also found as opacity · alpha channel
A channel describing opacity or coverage. BGRA and RGBA color formats include alpha in addition to three color channels.
Read more: Technical white paper · Revision 19
Also found as ambient fill
A baseline illumination term that keeps shaded regions visible. It is distinct from directional diffuse and specular contributions.
Read more: GPU Pipeline · Roadmap
Also found as holomorphic · complex differentiable
A function complex-differentiable throughout a neighborhood, where it has a convergent power-series expansion. This structure supports local derivative and Taylor analysis.
Read more: Beyond Complex Numbers · Perturbation Rendering
Apple's processor family, integrating CPU, GPU, and other components. Device capability and workload both matter when interpreting performance claims.
Read more: GPU Pipeline · Technical white paper · Revision 19
Accepting the previewed values in a tool. In Gradient Import, Apply saves the resulting palette after you choose its name.
Read more: User Guide
Also found as ≈
A symbol indicating approximation rather than exact equality. The full quadratic perturbation identity is exact algebraically, while a first-order truncation is approximate.
Read more: Perturbation Rendering
Also found as original app ownership
StoreKit's signed app-ownership information, including original acquisition details. The app uses verified ownership evidence in its Legacy Pro policy.
Read more: Technical white paper · Revision 19
Also found as multiprecision · variable precision
Arithmetic whose precision can be selected or expanded beyond a fixed hardware format, within resource limits. It is a research direction for references, not a description of the current public Infinity path.
Read more: Inside the Infinity Engine · Roadmap
Also found as phase angle · arg(z) · θ · theta
The angle of a nonzero complex number measured from the positive real axis. Angles that differ by a full turn describe the same direction.
Read more: Beyond Complex Numbers · 𝛑 and Fractals: Is There a Connection?
Image width divided by height. Coordinate fitting and capture presets preserve proportions rather than assuming every image has the same rectangular shape.
Read more: User Guide · GPU Pipeline
Also found as callback · completion handler
Work whose result arrives later. Generation and lifecycle checks prevent delayed results from updating a view or ownership request that is no longer current.
Read more: Technical white paper · Revision 19
Also found as attractor
A periodic orbit toward which nearby orbits converge. Attracting quadratic dynamics organize the interiors of Mandelbrot hyperbolic components.
Read more: Beyond Complex Numbers · The Mandelbrot Locally Connected Conjecture
Also found as Auto Iteration · Auto Iter · Auto
Automatic iteration policy responding to scale and renderer state. Its displayed proposal and the effective renderer count are distinct; deep-path policy can constrain or disable adaptation.
Read more: Technical white paper · Revision 19 · User Guide
Moving to an earlier entry in the temporary exploration timeline. It restores saved creative state; it is not the same as loading a permanent bookmark.
Read more: User Guide · Technical white paper · Revision 19
Also found as Export All backup
A separate saved copy used to recover files or move them between devices. Purchase restoration and a website download history are not substitutes for backing up personal work.
Read more: User Guide
Also found as legacy import · migration
Reading or upgrading earlier saved records without discarding their intended state. It does not mean an older renderer can reproduce every newer feature.
Read more: Technical white paper · Revision 19
Also found as escape radius · bailout threshold
A magnitude threshold beyond which escape is established for the applicable map and parameter. Radius 2 is sufficient for Mandelbrot's critical orbit; arbitrary Julia constants need a suitable bound.
Read more: Technical white paper · Revision 19 · Perturbation Rendering
Also found as color bands · quantization bands
Visible steps in a gradient. Source stops, LUT width, quantization, escape values, contrast, and display behavior can all contribute.
Read more: Palette System
Also found as relative magnification
A stored reference scale used to interpret magnification and restore navigation consistently. It is separate from the current scale.
Read more: Technical white paper · Revision 19
Also found as basin of infinity
The starting points whose iterates approach a specified attracting behavior. For a polynomial, escaping points form the basin of infinity.
Read more: What Are Fractals?
Also found as bounded batch
A group of work units submitted together. Smaller batches can create opportunities for cancellation and feedback, while every batch still has scheduling overhead.
Read more: Inside the Infinity Engine
Also found as export queue
Rendering several saved scenes through a managed queue. The roadmap treats it separately from the current single-image capture workflow.
Read more: Roadmap
Also found as timing corpus
A defined workload used to measure performance under recorded conditions. Device, build, view, settings, output size, and completion event belong with the reported result.
Read more: Inside the Infinity Engine · Technical white paper · Revision 19
Also found as BGRA8 · normalized eight-bit color
A four-channel format storing blue, green, red, and alpha in eight bits each, interpreted as normalized values. The app's active color output uses this format.
Read more: Technical white paper · Revision 19
A qualitative change in a dynamical system as a parameter varies, such as a change in the stability or period of an attracting cycle.
Read more: Beyond Complex Numbers
Also found as algorithmic complexity · O(width × height × maxIt)
Notation for how a workload grows. A worst-case pixel-iteration estimate explains scale, but real work also depends on early escape, sampling, recovery, and hardware.
Read more: Archived code review · October 2025
Also found as block-linear approximation
An acceleration approach that replaces a validated block of iterations with a local linear approximation. The roadmap treats it as research requiring validity checks and recovery.
Read more: Roadmap · Inside the Infinity Engine
Also found as Blinn Phong shading
A lighting model using a halfway direction to shape specular highlights alongside diffuse and ambient terms. It is discussed in the historical lighting review.
Read more: Archived code review · October 2025
Also found as copy pass
A GPU copy or transfer operation that moves existing buffer or image data. It does not recalculate fractal orbits.
Read more: Technical white paper · Revision 19
A saved description of a view and its rendering settings, not a finished picture. It can retain precise coordinates, mode, Julia parameter, palette reference, and appearance settings.
Read more: User Guide · Technical white paper · Revision 19
A collection of bookmark records distributed together. A JSON array and a ZIP of separate JSON files are different packaging forms.
Read more: Community Portal · Technical white paper · Revision 19
Also found as bookmark JSON v7
The portable bookmark version adding canonical Infinity center strings alongside numeric coordinates and optional residuals. Supported older versions retain compatible defaults.
Read more: Technical white paper · Revision 19
The frontier where every neighborhood meets both a set and its complement. Fine Mandelbrot detail concentrates near this mathematically intricate interface.
Read more: Beyond Complex Numbers · What Are Fractals?
Also found as non-escaping orbit
An orbit that stays within some finite distance of the origin for all iterations. Surviving a finite iteration budget alone does not establish boundedness.
Read more: Technical white paper · Revision 19
Also found as out-of-bounds access
A test that rejects positions outside a valid image or resource range. It is essential when rounded-up dispatch sizes exceed the actual data dimensions.
Read more: Technical white paper · Revision 19
A scaling exponent estimated from the number of boxes needed to cover a set as box size shrinks. Finite images provide estimates over a limited scale range.
Read more: The Coastline Paradox: When Math Meets the Infinite
Also found as divergent execution
When threads in one execution group follow different branches or need different iteration counts. This can reduce parallel efficiency even though the calculations remain independent.
Read more: Inside the GPU Engine of Mandelbrot Metal
Also found as MTLBuffer
A contiguous GPU-accessible data resource. The reference orbit uses a buffer, while image-like color and height resources use textures.
Read more: Technical white paper · Revision 19
Also found as build identity · version
A specific compiled revision used to identify test and benchmark conditions. Results from one build should not silently be attributed to a later one.
Read more: Technical white paper · Revision 19 · Inside the Infinity Engine
Also found as hyperbolic component
A Mandelbrot region associated with an attracting periodic cycle. Many visible bulbs attach to larger structures; their periods describe the cycle length.
Read more: Beyond Complex Numbers · The Mandelbrot Locally Connected Conjecture
A fractal family formed by taking absolute values of real and imaginary components before a quadratic update. It is a proposed additional family, not a current Mandelbrot mode label.
Read more: Roadmap
Eight bits of storage. A BGRA8 pixel uses four bytes before additional resource, staging, or encoding overhead.
Read more: Technical white paper · Revision 19
Also found as cache invalidation
Stored work reused to avoid recalculation, with rules for discarding it when inputs change. Orbit-free palette editing is planned work, not a current persistent escape cache.
Read more: GPU Pipeline · Roadmap
Also found as Metal layer
The display layer that supplies drawable textures for Metal presentation. It bridges GPU output and the screen's compositing system.
Read more: Inside the GPU Engine of Mandelbrot Metal
Also found as catastrophic cancellation
Loss of relative significant information when nearly equal quantities are subtracted or cancel. It can make a small reconstructed orbit unreliable relative to its reference.
Read more: Technical white paper · Revision 19 · Perturbation Rendering
Also found as exact center string · hexadecimal center
A standardized text encoding of a stored coordinate. It avoids discarding low-order state during serialization; the renderer still projects it into its working arithmetic.
Read more: Technical white paper · Revision 19
Also found as Cantor dust · disconnected dust
A compact, perfect, totally disconnected set. Escaping parameters in the quadratic family produce Julia sets of this kind, often appearing as dust at finite resolution.
Read more: What Are Fractals? · Beyond Complex Numbers
The visible drawing area containing your fractal composition. Its display dimensions determine the Canvas capture size, but capture still performs a separate render.
Read more: User Guide · GPU Pipeline
Also found as Canvas capture
A capture using the drawable's current pixel dimensions. It still performs a dedicated complete render rather than saving a partially refined screen texture.
Read more: GPU Pipeline · User Guide
The command for rendering a complete PNG at a chosen output size. It snapshots the composition and renders separately from the live preview.
Read more: User Guide · GPU Pipeline
Starting the capture after choosing an output size. The app reports progress and opens the share sheet when the complete image is ready.
Read more: User Guide
Also found as rectangular form · x + iy
Writing a complex number using perpendicular coordinates, z = x + iy. Polar form describes the same number using magnitude and angle.
Read more: Beyond Complex Numbers
Also found as Cauchy Riemann
Relations between the partial derivatives of a complex function's real and imaginary parts. With suitable regularity, they characterize complex differentiability.
Read more: Beyond Complex Numbers
Also found as center coordinates · x and y
The complex-plane position at the middle of the view. The HUD displays a rounded summary while saved state can retain more precise components.
Read more: Technical white paper · Revision 19 · User Guide
Also found as horizontal slice · vertical slice
Extracting colors along the center row or column of an image. It is not an analysis of dominant colors throughout the whole photo.
Read more: Palette System · Introducing Photo2Palette: A Command-Line Tool
Also found as bounded scheduling
Ordering small regions from the image center outward and limiting work submitted together. It improves the order of feedback without guaranteeing a fixed completion time.
Read more: Inside the Infinity Engine
Also found as finite difference · gradient estimate
Estimating a derivative from values on opposite sides of a point. The relief pass uses neighboring heights to estimate slopes.
Read more: GPU Pipeline
Also found as sensitive dependence
Deterministic behavior in which nearby starting conditions can separate strongly over time. It is not the same as randomness or a random-number generator.
Read more: From Chaos to Beauty: How Simple Equations Create Infinite Art
Also found as runtime failure circuit
A policy that avoids an unusable rendering route after failure. The current design keeps valid slow frames; exceeding the 250 ms diagnostic target alone is not a failure.
Read more: Technical white paper · Revision 19
Texture addressing that holds coordinates outside the range at the nearest edge. It prevents a palette lookup from wrapping to the other end unless explicitly designed to do so.
Read more: Palette System · Technical white paper · Revision 19
Removing a whole managed library after confirmation. This is distinct from clearing a website search or selection.
Read more: User Guide
Also found as Download selected
Community Portal actions that reset the selected rows or package them into a ZIP. The ZIP contains bookmark JSON files, not rendered images.
Read more: Community Portal
Also found as command-line interface
A text-command interface used to run tools such as Photo2Palette. It supports repeatable scripted or batch workflows outside the app's graphical interface.
Also found as cyan magenta yellow black
A subtractive printing color model. The app exports RGB PNGs; a printer or managed print workflow handles conversion to an appropriate print profile.
Measured coastline length grows as a smaller ruler captures more detail. Ideal fractal models can have unbounded length; real coastlines have physical scale limits.
Read more: The Coastline Paradox: When Math Meets the Infinite
Also found as bookmark set
A named group of shared files on the Community Portal. Choosing a collection narrows the visible catalog without importing anything into the app.
Read more: Community Portal
Also found as wide gamut · wide color
The range of colors a space or device can represent. A wider gamut can include more saturated colors; it does not inherently reduce banding.
Read more: Palette System
Also found as color conversion
Interpreting and converting color values between defined spaces and devices. Check a finished PNG in its intended viewer because the app does not claim a validated ICC round trip.
Read more: Palette System
Also found as colour space
A specification relating numeric channels to colors, including primaries and an encoding. Choosing a wider gamut is separate from choosing more precision or higher brightness range.
Read more: Palette System
Also found as source stop · design stop · anchor
A position and color in a palette definition. The renderer constructs its lookup texture from these source values.
Read more: Palette System
A collection of encoded GPU operations submitted together. Its completion can be successful yet obsolete if a newer viewport has replaced the request.
Read more: Technical white paper · Revision 19
Also found as compute command encoder
An object that records resource bindings and operations into a command buffer. The compute encoder sets the kernel, inputs, and dispatch dimensions.
Read more: GPU Pipeline · Technical white paper · Revision 19
A Metal object used to create and order command buffers for GPU submission. Queueing work is separate from its eventual completion.
Read more: GPU Pipeline · Technical white paper · Revision 19
Also found as committed viewport · committed state
Accepting an interaction's resulting view as a rendering and history state. This is distinct from the transient image transform displayed during a gesture.
Read more: Technical white paper · Revision 19
Also found as community downloads
The website's shared bookmark and palette library. Downloads are separate from the app's local storage and do not automatically synchronize libraries.
Read more: Community Portal · Technical white paper · Revision 19
Also found as commutative
The property ab = ba. Complex multiplication is commutative; quaternion multiplication generally is not.
Read more: Beyond Complex Numbers
Also found as compact anchors
Retaining a smaller, evenly spaced set of source anchors from photo sampling. The documented Version 3 default is 64 anchors.
Read more: Palette System · Introducing Photo2Palette: A Command-Line Tool
Also found as high-low center · split center
A viewport center stored with leading components and small residuals. This helps navigation retain displacements that one ordinary number would round away.
Read more: Technical white paper · Revision 19
The study of repeated complex functions and their long-term behavior. Orbits, periodic cycles, Julia sets, and the Mandelbrot set are central examples.
Read more: Beyond Complex Numbers · The Mandelbrot Locally Connected Conjecture
Also found as Euler's formula · eⁱθ
The identity eⁱθ = cos θ + i sin θ connects complex numbers with rotation. It underlies polar notation and many cyclic color formulas.
Read more: 𝛑 and Fractals: Is There a Connection? · Beyond Complex Numbers
Multiplying two complex numbers multiplies their magnitudes and adds their angles. This gives the quadratic map both a growth and a rotation interpretation.
Read more: Beyond Complex Numbers
Also found as ℂ · a + bi · complex numbers
A number with real and imaginary parts, written a + bi, where i² = −1. Mandelbrot Metal maps each sample to a point in this two-dimensional number system.
Read more: Beyond Complex Numbers
Also found as Argand plane · parameter map
A plane whose horizontal axis is the real part and vertical axis is the imaginary part. Points represent complex numbers.
Read more: Beyond Complex Numbers
Also found as kernel · compute shader
A GPU function invoked across a grid of threads. The primary app kernel performs coordinate mapping, orbit work, coloring, and optional height output.
Read more: GPU Pipeline
A stage of GPU work described by a compute command encoder. The primary orbit-and-color pass and optional relief pass have different input and output responsibilities.
Read more: GPU Pipeline
Also found as concurrentPerform · dispatch queue
Managing multiple pieces of work that can overlap. Concurrent scheduling may use several CPU cores, but differs from the GPU's SIMD execution model.
Read more: Archived code review · October 2025 · Technical white paper · Revision 19
Also found as well-conditioned · ill-conditioned
How sensitive the mathematical result is to small changes in the input. A well-implemented algorithm still has difficulty when the underlying problem is strongly sensitive.
Read more: Perturbation Rendering · Inside the Infinity Engine
A statistical range derived by a stated method to express uncertainty about an estimate. A small descriptive benchmark is not automatically a confidence interval.
Read more: Technical white paper · Revision 19 · Inside the Infinity Engine
Also found as conformality · angle preserving
Locally preserving angles. A holomorphic map is conformal where its derivative is nonzero; the quadratic map's critical point is an exception.
Read more: Beyond Complex Numbers
Also found as connected set
A space is connected if it cannot be separated into two disjoint nonempty relatively open parts. Connectedness alone does not mean every two points can be joined by a path.
Read more: The Mandelbrot Locally Connected Conjecture · Milnor: Local Connectivity of Julia Sets
The set of parameters whose corresponding Julia sets are connected. For the quadratic family z² + c, this locus is the Mandelbrot set.
Read more: What Are Fractals?
Also found as compile-time evaluation
Evaluating expressions known at compilation or specialization time. A value shared by all threads is not automatically known to the compiler as a constant.
Read more: Archived code review · October 2025
Also found as contrast exponent · contrast slider
A nonlinear remapping of the computed value before color lookup. It redistributes visible tones and colors without changing the underlying fractal equation.
Read more: Palette System · User Guide
Also found as value stretch · stretch factor
Expanding sampled value differences around a midpoint. In photo import, it adjusts the resulting palette rather than adding geometric detail to the fractal.
Read more: Palette System
Approaching a limiting value or function as a sequence or series progresses. A useful approximation needs convergence or an appropriate error bound over the region used.
Read more: Perturbation Rendering
Also found as Go to Rect · Go to Rectangle
Entering a complex-plane rectangle and fitting it to the canvas. Decimal input is finite precision; a bookmark is preferable for transporting an already saved deep coordinate.
Read more: User Guide · Technical white paper · Revision 19
Apple's two-dimensional graphics framework used in palette construction and image conversion. Its color contexts matter when interpreting resulting RGB bytes.
Read more: Palette System · Technical white paper · Revision 19
Also found as central processing unit
The general-purpose processor that manages application state and rendering policy, builds the accurate reference orbit, and provides the deep fallback renderer.
Read more: GPU Pipeline
Also found as Deep Mode · DM
The established CPU deep renderer used when the preferred deep GPU route is unavailable or unusable. Older articles use DM for the earlier CPU-centered architecture.
Read more: Technical white paper · Revision 19 · Inside Deep Mode: How Mandelbrot Metal Pushes Beyond GPU Limits
Also found as Creating Art
The longer workflow guide to composition, iterations, palette selection, lighting, and finished capture.
Read more: Creating Art
The orbit starting at a critical point. For the quadratic family, the orbit of zero decides whether the parameter belongs to the Mandelbrot set.
Read more: Beyond Complex Numbers · Technical white paper · Revision 19
A point where a complex function's derivative is zero. For f_c(z) = z² + c, the finite critical point is z = 0.
Read more: Beyond Complex Numbers
Selecting a rectangular part of a source image. Cropping before Import Gradient changes which colors cross the sampled center line.
Read more: Palette System · Introducing Photo2Palette: A Command-Line Tool
Also found as comma-separated values
A plain-text table format useful for exported measurements or benchmarks. It is not the app's bookmark-sharing schema.
Read more: Inside the Infinity Engine
Also found as custom dimensions
A capture with explicitly chosen width and height. Larger dimensions increase output storage and work; the practical limit depends on the device and scene.
Read more: User Guide · GPU Pipeline
Also found as [C] · Custom
A palette created or imported by the user, usually marked [C]. Its definition must be available separately when a bookmark refers to it by name.
Read more: Palette System · User Guide
Also found as early termination
A condition that stops an algorithm or approximation when further work is unnecessary or unreliable. A perturbation cutoff and an escape bailout serve different purposes.
Read more: Archived code review · October 2025 · Perturbation Rendering
Also found as periodic color · hue rotation
A color progression designed to repeat, often with a smooth join between its ends. Repetition in color does not imply repetition in fractal coordinates.
Read more: 𝛑 and Fractals: Is There a Connection? · Palette System
Also found as anchor-based debounce
Waiting for a meaningful or settled change before repeating an action. In rendering policy, it can reduce excessive switching or redundant requests.
Read more: Archived code review · October 2025
Also found as ultra-deep zoom · extreme magnification
Viewing a very small complex-plane region at high scale. Useful detail depends on accurate coordinates, orbit evaluation, iteration budget, and output resolution.
Read more: Technical white paper · Revision 19 · User Guide
Removing an individual saved item. Keeping an exported backup is useful when you may want the bookmark or custom palette again.
Read more: User Guide
Also found as δc · Δc · parameter offset
The difference c − c₀ between a sample's parameter and the reference parameter. Keeping this small displacement separate avoids an early absolute-coordinate rounding loss.
Read more: Perturbation Rendering
Also found as δz · δₙ · orbit offset
The difference zₙ − Zₙ between a sample orbit and its reference orbit at an iteration. The perturbation recurrence advances this difference.
Read more: Perturbation Rendering
A branching, tree-like structure; mathematically, a dendrite is a locally connected continuum with no simple closed curve. Some Julia sets have dendritic form.
Read more: Beyond Complex Numbers · The Mandelbrot Locally Connected Conjecture
Also found as f′ · f prime · local sensitivity
The local rate of change of a function. For f(z) = z² + c, the derivative with respect to z is 2z; parameter sensitivity follows its own recurrence.
Read more: Perturbation Rendering · Beyond Complex Numbers
The same specified rules and inputs produce the same mathematical process. Finite implementations can still differ with arithmetic, build, device, or output settings.
Read more: Technical white paper · Revision 19 · How Mandelbrot Metal Stays Fast at Extreme Depths
Also found as repeatability
A test with controlled inputs and conditions. Repeatability within that setup does not promise identical exported pixels across devices, builds, and color conversions.
Read more: Technical white paper · Revision 19
A device-dependent Core Graphics color space. Its appearance relies on the drawing context and device interpretation rather than a universal, explicit RGB definition.
Read more: Technical white paper · Revision 19
An emulated extended-precision label used by a comparison app. The label alone does not establish native IEEE binary64 support or the same arithmetic as Mandelbrot Metal's CPU DD.
Read more: Compare Apps
Also found as 250 ms target
A reference timing used to observe performance. It is distinct from a correctness test, a promised frame time, or the conditions that activate fallback.
Read more: Technical white paper · Revision 19
Electrical breakdown through an insulating medium. Related growth models can produce branching, fractal-like structures such as discharge patterns.
Read more: What Are Fractals?
Also found as diffuse shading
A lighting contribution based on how the surface faces the light, producing broad shape cues rather than narrow highlights.
Read more: GPU Pipeline
Also found as DLA
A growth model in which wandering particles attach to a cluster, often making branching patterns. It is a separate process from quadratic complex iteration.
Read more: What Are Fractals? · Fractals in Nature
A GPU recovery route that evaluates a sample directly in quad-single when its reference is exhausted or unusable, reconstructing the parameter from its anchor and offsets.
Read more: Technical white paper · Revision 19
Submitting a grid of kernel invocations to the GPU. A dispatch specifies the work shape, while the kernel defines what each invocation does.
Read more: GPU Pipeline · Apple: threadgroup and grid sizes
Also found as Display P3 · P3 · Wide Color (P3)
A wide-gamut RGB space used in Apple color workflows. The app's P3 choice participates in palette construction and conversion; it is not an HDR switch.
Read more: Palette System
Also found as distance field
Estimating distance to a fractal boundary, often using orbit and derivative information. It is background rendering terminology, distinct from the app's escape-derived relief height field.
Read more: 𝛑 and Fractals: Is There a Connection? · Technical white paper · Revision 19
Small variations introduced to make quantization steps less conspicuous. Older blogs discuss it; it should not be taken as a promise of a distinct current user control or HDR output.
Read more: Inside the GPU Engine of Mandelbrot Metal
Also found as FP64 · binary64 · double precision
A 64-bit floating-point format with 53 bits of significand precision, roughly 15–17 significant decimal digits depending on the conversion or accuracy requirement.
Read more: Technical white paper · Revision 19
Also found as DD · two-Double expansion
A high and low Double whose unevaluated sum retains about 106 significant bits under suitable finite, well-scaled operation. The CPU uses it for the reference orbit.
Read more: Technical white paper · Revision 19 · Inside the Infinity Engine
Also found as DS · two-Float expansion
A compensated value represented as a high and low Float. It retains more significant information than one Float but is not a native 64-bit Double.
Read more: Technical white paper · Revision 19
Also found as 2× zoom
A navigation gesture that zooms in around a selected location. It is distinct from the single tap used for the Mandelbrot–Julia transition.
Read more: User Guide
Reducing sampled data to fewer output pixels. Supersampling can average several samples directly within one output thread without allocating a larger full-frame image.
Read more: GPU Pipeline · Inside the GPU Engine of Mandelbrot Metal
Also found as dots per inch
A printer's dot-density specification. It is often used loosely for image PPI, but printer dots and image pixels are different things.
Also found as CAMetalDrawable
A presentable image resource obtained for the display surface. Drawable dimensions are in pixels and can differ from the interface's point dimensions.
Read more: GPU Pipeline · Technical white paper · Revision 19
Also found as auto-numbering
Adding a numeric suffix when an imported name is already in use. A matching name alone is not evidence that two records have identical contents.
Read more: User Guide · Technical white paper · Revision 19
Apple's adjustable text-size system. Larger text and translated labels are part of interface layout and accessibility testing.
Read more: Technical white paper · Revision 19
Also found as z-plane · dynamical space
The plane of starting values z for one fixed function. A Julia image explores this plane, while a Mandelbrot image explores parameters.
Read more: Beyond Complex Numbers
Also found as analytic interior shortcut
Ending a sample's work as soon as a valid condition settles the required result, such as an applicable analytic interior test or escape test.
Read more: GPU Pipeline · Archived code review · October 2025
Also found as temporal interpolation
Changing how a parameter progresses over time, such as starting or stopping gently. It controls motion timing rather than the fractal recurrence.
Read more: Roadmap
Also found as effective iteration budget · Nmax · Nₘₐₓ
The finite budget actually used for the rendering request. It can differ from an earlier UI proposal or the configurable manual-control ceiling.
Read more: Technical white paper · Revision 19
An informal name for a Mandelbrot region whose curled forms resemble elephants. The app uses a bundled Elephant Valley composition for its first-install scene.
Read more: Technical white paper · Revision 19 · Creating Art
Also found as render-path qualification
Checks that a request and its resources are suitable for a rendering route. Export re-evaluates eligibility because its dimensions and pixel steps can differ from the live view.
Read more: GPU Pipeline · Technical white paper · Revision 19
Also found as exponential moving average
A weighted update that mixes a new value with the previous estimate. Iteration-policy smoothing can use different weights for increasing and decreasing targets.
Read more: Technical white paper · Revision 19 · Archived code review · October 2025
Palette stops carried inside a supported bookmark record. Import accepts this form; ordinary current export may instead identify the palette by name or index.
Read more: Technical white paper · Revision 19
Also found as hasProAccess
A verified access state granting a product tier or feature set. The app derives a shared Pro-access decision from current ownership evidence.
Read more: Technical white paper · Revision 19
Also found as error control
A quantitative limit on numerical error under stated assumptions. Runtime growth checks are useful safeguards, but should not be presented as certified error bounds.
Read more: Perturbation Rendering
Also found as pixel difference · image comparison
A stated allowance when comparing numeric or image outputs. Its meaning depends on the metric and reference; a visual match alone is narrower evidence.
Read more: Technical white paper · Revision 19
Also found as EFT
An arithmetic building block that returns a rounded result and its exact residual under required rounding and range assumptions. It does not make the entire renderer error-free.
Read more: Technical white paper · Revision 19
Also found as divergence · escaped sample
Growth of an orbit toward infinity. For Mandelbrot's critical orbit, crossing radius 2 proves escape in exact arithmetic; a fixed Julia parameter needs an appropriate escape bound.
Read more: Technical white paper · Revision 19
Also found as escape-time rendering · escape time
A rendering method that iterates each sample until escape or a finite budget is reached, then maps its measured behavior to a color.
Read more: Technical white paper · Revision 19 · Why Magnification and Iterations Are Linked in the Mandelbrot Set
The familiar geometry of distances, angles, lines, planes, and solid space. Fractal geometry adds tools for describing irregular structure across scales.
Read more: The Coastline Paradox: When Math Meets the Infinite · 𝛑 and Fractals: Is There a Connection?
Also found as working precision
The precision of actual arithmetic operations. A wide coordinate container does not automatically increase every calculation performed after loading it.
Read more: Technical white paper · Revision 19
Also found as exact palette output
Retaining all sampled photo colors as source stops. It is a separate choice from Exact LUT, which controls later construction of the rendering texture.
Read more: Palette System · Introducing Photo2Palette: A Command-Line Tool
A table-construction mode that selects the nearest source stop for each texel. Metal still linearly filters that texture; Exact LUT does not promise zero shader interpolation.
Read more: Palette System
Also found as cursor timeline · history stack
A temporary session timeline of committed views and appearance state. It supports Back and Forward; permanent discoveries should be saved as bookmarks.
Read more: User Guide · Technical white paper · Revision 19
Also found as exponent range
The power-of-two scale in a binary floating-point number. It determines range separately from the significand's ability to distinguish nearby values.
Read more: Technical white paper · Revision 19
Writing an image or structured record for saving or sharing. PNG artwork, bookmark JSON, and palette JSON have different purposes.
Read more: User Guide
Exporting a managed collection, such as custom palettes or bookmarks. Built-in palettes are not exported as a user's custom library.
Read more: User Guide · Palette System
Also found as external angle · ray landing
A curve outside a filled Julia or Mandelbrot set associated with an angle in a conformal coordinate. Landing asks whether the curve approaches a single boundary point.
Read more: The Mandelbrot Locally Connected Conjecture · 𝛑 and Fractals: Is There a Connection?
Also found as reassociation · contraction
Compiler choices that permit changes to floating-point evaluation for speed. They can affect rounding-sensitive expansion identities and require deliberate qualification.
Read more: Inside the Infinity Engine
Also found as Float fast path
The inexpensive Float perturbation attempt used for suitable Infinity samples. Rejected samples restart in a wider representation rather than making every pixel pay that cost.
Read more: Technical white paper · Revision 19
Also found as stable dynamics
The region where the family of iterates is normal, a precise complex-analytic notion of locally controlled behavior. Its complement is the Julia set.
Read more: What Are Fractals?
Also found as favorite star · favourite
Palettes marked with a star for easier access. Favorites are identified by palette name and shown ahead of other choices.
Read more: Palette System
A parameter associated with the limit of a period-doubling cascade. It is a classic example in the study of renormalization and universality.
Read more: The Mandelbrot Locally Connected Conjecture
Also found as tendril
A thin connecting or branching feature seen in fractal images. Its apparent thickness depends on resolution, sampling, iterations, and numerical precision.
Read more: What Are Fractals? · Creating Art
All starting points whose orbits stay bounded for a fixed c. The Julia set is its boundary, rather than the entire filled region.
Read more: Beyond Complex Numbers · The Mandelbrot Locally Connected Conjecture
Also found as black pixel · interior classification
A limited computation that detects escape or recognizes certain interiors. A black sample near the boundary may only mean that escape was not detected in the allotted work.
Read more: GPU Pipeline · Technical white paper · Revision 19
Arithmetic with a bounded set of representable values. Rounding and range limits remain even when several hardware numbers are combined into an expansion.
Read more: Technical white paper · Revision 19
Also found as finitely renormalizable
A dynamical condition in which the relevant sequence of nested renormalizations terminates. It appears in local-connectivity results, subject to their precise hypotheses.
Read more: The Mandelbrot Locally Connected Conjecture · Milnor: Local Connectivity of Julia Sets
Also found as linearization · linearised · linearized
Keeping the constant and linear terms of a local expansion. It describes small changes, but does not generally equal the full nonlinear recurrence used by Version 3.
Read more: Perturbation Rendering · Why Double-Double Precision Isn’t Enough for Deep Fractals
A value satisfying f(z) = z. Reapplying the function leaves that value unchanged.
Read more: Beyond Complex Numbers
Also found as InfinityFixed · canonical center
Coordinates stored at a fixed binary scale. The app's canonical center format has 1,152 fractional bits for transport and persistence, not 1,152-bit arithmetic throughout rendering.
Read more: Technical white paper · Revision 19
Also found as FP32 · binary32 · single precision
A 32-bit floating-point format with 24 bits of significand precision for normal values. Metal uses Float for the inexpensive Infinity tier and for expansion components.
Read more: Technical white paper · Revision 19
A representation using a sign, a significand, and an exponent. It offers a wide range, but spacing between nearby representable numbers depends on their magnitude.
Read more: Technical white paper · Revision 19 · Beyond Complex Numbers
Also found as expansion arithmetic
Representing one number as an unevaluated sum of multiple floating-point components, retaining low-order information that a single component would lose.
Read more: Technical white paper · Revision 19
Also found as fused multiply-add · fma(a,b,c)
Computing a × b + c with one final rounding. It is useful for recovering product residuals and building expansion arithmetic.
Read more: Technical white paper · Revision 19
Also found as pinch anchor
The canvas position around which a zoom gesture is applied. Preserving its coordinate helps the selected feature stay under your fingers.
Read more: Technical white paper · Revision 19
Returning to a later state after going Back. Starting a new branch of exploration replaces the previous forward branch.
Read more: User Guide · Technical white paper · Revision 19
Representing or analyzing signals through sinusoidal frequencies. It appears in the blog's discussion of π, cyclic patterns, and the mathematical language of color.
Read more: 𝛑 and Fractals: Is There a Connection?
Also found as frames per second · refresh rate
A rate describing displayed or rendered frames. A smoothly transformed preview can update rapidly while a newly computed deep frame takes much longer.
Read more: GPU Pipeline · Inside the Infinity Engine
A mathematical object or pattern with structure across scales, often described through scaling laws or a nontrivial dimension. Natural fractal-like patterns span a limited range of scales.
Read more: What Are Fractals? · Fractals in Nature
Also found as fractional dimension
A measure of how detail or covering requirements scale as measurement size changes. Different definitions exist; a fractal's dimension need not be a non-integer.
Read more: The Coastline Paradox: When Math Meets the Infinite · 𝛑 and Fractals: Is There a Connection?
Also found as Fractal Type · Mandelbrot Set · Julia Set
The control choosing the fractal family. Switching between Mandelbrot and Julia changes which parameter or initial value is varied across the canvas.
Read more: User Guide
Also found as full frame
The output image for one viewport and appearance request. A partially refined preview is not yet the completed requested frame.
Read more: GPU Pipeline
The access tier with the core renderer, built-in palettes, Canvas capture, and a limited personal bookmark allowance. Starter bookmarks are separate from those personal slots.
Read more: Technical white paper · Revision 19
Also found as progress percentage · rendering overlay
The fraction of the current requested image completed. The overlay ends after full current-frame presentation, not merely after the first tile or a reference orbit is ready.
Read more: Technical white paper · Revision 19
Also found as fused orbit and color
Combining orbit evaluation and color generation in the main compute work. Current Version 3 does not keep a persistent escape-value image for palette-only recoloring.
Read more: GPU Pipeline · Technical white paper · Revision 19
Also found as gamma adjustment
A nonlinear power-law adjustment. In photo import it modifies sampled HSV value; this creative control is distinct from an entire display's color-management behavior.
Read more: Palette System
Also found as generation token · render generation
An identifier for the current rendering request. Work from an older generation must not overwrite a newer view, even if its GPU command succeeded.
Read more: GPU Pipeline · Technical white paper · Revision 19
The study of size, dimension, and geometry for sets that may be irregular. It supplies tools for analyzing fractal boundaries beyond smooth curves and surfaces.
Read more: What Are Fractals?
Also found as first-run tour
The short introductory guide to navigation, colors, bookmarks, and capture. Opening it later should preserve existing exploration state.
Read more: User Guide · Technical white paper · Revision 19
Also found as glitch indicator · cancellation check
Checks for numerical symptoms such as excessive delta growth, cancellation, ambiguous escape, or non-finite values. They route difficult work to recovery.
Read more: Technical white paper · Revision 19
Also found as open bookmark
The action that loads a saved bookmark's composition into the renderer. Loading state can still require a new render to complete.
Read more: User Guide
Also found as graphics processing unit
A processor suited to large parallel workloads. Mandelbrot Metal uses it for many independent sample calculations, palette evaluation, relief shading, and presentation work.
Read more: GPU Pipeline
A pause while the GPU waits for resources, data, or synchronization. Buffering and scheduling can reduce some stalls but do not eliminate numerical workload.
Read more: Archived code review · October 2025
Also found as Metal-first
An architecture that assigns the large parallel pixel workload to the GPU while retaining CPU preparation and fallback. It does not mean all work executes on the GPU.
Read more: Inside the Infinity Engine
Also found as color ramp · colour ramp
A progression of colors along a normalized position. Gradients may be smooth or intentionally stepped.
Read more: Palette System
Also found as dispatch grid
The full collection of thread positions launched for a compute operation. Its dimensions are commonly derived from the output image or tile.
Read more: Apple: threadgroup and grid sizes
A loop that lets each GPU thread process several data positions separated by the dispatch grid's stride. It is a workload pattern discussed in the archived review, not the definition of a tile.
Read more: Archived code review · October 2025
Also found as stability margin
Extra working precision beyond a basic coordinate estimate, reserved for rounding and sensitivity. A rough bit-count formula is not a scene-independent correctness guarantee.
Read more: Inside the Infinity Engine
Also found as tile border · one-pixel halo
Extra neighboring samples around a tile used for operations such as relief gradients. Consistent full-image coordinates prevent seams between independently rendered tiles.
Read more: GPU Pipeline
A dimension defined through coverings at arbitrarily small scales. It can distinguish geometric complexity beyond the usual whole-number dimensions of lines and surfaces.
Read more: The Coastline Paradox: When Math Meets the Infinite · 𝛑 and Fractals: Is There a Connection?
Also found as high dynamic range
Imaging with a broader luminance range than standard dynamic range. It is distinct from wide gamut; the current documented app output is SDR, despite older blog discussions of HDR.
Read more: Technical white paper · Revision 19 · User Guide
Also found as High Efficiency Image Container
An image-container format commonly used for Apple photos. A photo must be available locally and decodable before gradient import can sample it.
Read more: User Guide
Also found as heightmap · escape field
A scalar value over the image used to infer local shape for lighting. It is a visualization resource, not a geometric mesh or a proof of physical depth.
Read more: GPU Pipeline
A practical rule that guides decisions without proving every case. Infinity's growth tests and relief probes are examples.
Read more: Technical white paper · Revision 19
Also found as high-resolution LUT · high res LUT
The color option selecting a 1,024-texel lookup row instead of 256. It controls table density, not output image dimensions or numerical orbit precision.
Read more: Palette System · User Guide
Also found as HQ Idle
An internal or historical quality-policy label for extra work after interaction stops. It appears in benchmark settings; the current user guide does not expose a manual SSAA switch.
Read more: Technical white paper · Revision 19 · User Guide
Also found as quadratic term · δz²
A term involving a second or higher power of a small change. Infinity retains δz² in its perturbation recurrence instead of dropping it through first-order truncation.
Read more: Perturbation Rendering
Also found as house icon · Full Mandelbrot Set · Reset
Returning to the full Mandelbrot overview. The current paper specifies that Home preserves palette and 3D Look, resets contrast, enables Auto, and records a reversible history transition.
Read more: Technical white paper · Revision 19
Also found as hue saturation value
A color model separating hue, saturation, and value. The photo-to-palette processing adjusts saturation and value before returning to RGB.
Read more: Palette System
Also found as heads-up display · readouts · overlay
The on-canvas summary of mode, center, scale, iterations, contrast, quality, palette, and color settings. Its rounded text is not the exact stored coordinate representation.
Read more: Technical white paper · Revision 19 · The Mandelbrot Metal HUD: Design, Meaning, and How to Read It
The color-family coordinate, often represented around a circle in HSV. Cyclic hue variation can generate repeating color progressions.
Read more: Palette System · 𝛑 and Fractals: Is There a Connection?
Using different thresholds for entering and leaving a state to avoid rapid oscillation. It helps keep precision or quality choices stable around a boundary.
Read more: Technical white paper · Revision 19
Also found as color profile
Metadata describing a color space for managed conversion. A Metal BGRA8Unorm texture alone does not carry an ICC profile or establish a verified color round trip.
Read more: Palette System · Technical white paper · Revision 19
Also found as library synchronization
A proposed way to keep scenes and palettes available across devices. Current portable-file sharing and Community Portal downloads do not provide automatic library synchronization.
Read more: Roadmap · Technical white paper · Revision 19
The standard defining common floating-point formats and operations. Its binary32 and binary64 formats underlie Float and Double; software expansions add their own implementation assumptions.
Read more: Technical white paper · Revision 19
Also found as iterated function system
A collection of repeatedly applied transformations that can generate a fractal attractor. It is another fractal construction, separate from iterating the single quadratic map.
Read more: Fractals in Nature
Also found as output dimensions
The number of pixels across and down an image. Increasing it changes sampling and storage costs; it is separate from zoom scale and arithmetic precision.
Read more: GPU Pipeline
Also found as Im(z) · imaginary component
The real coefficient b in a + bi. It is the vertical coordinate on the complex plane; b itself is not an imaginary number.
Read more: Beyond Complex Numbers
Also found as i · square root of minus one
The number i satisfies i² = −1. Multiplication by i rotates a complex number by a quarter turn.
Read more: Beyond Complex Numbers
Reading a supported file into a local library. Validation and compatibility rules apply; a named custom palette may need to be imported separately from its bookmark.
Read more: User Guide · Technical white paper · Revision 19
Also found as photo import
The Pro tool that samples colors from an image's center line, applies palette adjustments, and saves a custom palette. It does not turn the photo into a fractal.
Read more: Palette System · User Guide
Also found as in-place relief
Reading and updating the same resource where supported. The documented simulator relief path uses a separate output and copy-back for compatibility.
Read more: Technical white paper · Revision 19
Also found as high-precision reference image
A separately qualified calculation used to evaluate numerical correctness. Sharing the same code or error source can make a comparison less independent.
Read more: Technical white paper · Revision 19 · Roadmap
Also found as infinitely renormalizable
A dynamical condition with indefinitely nested renormalizations. These parameters require particularly delicate analysis of small-scale geometry.
Read more: The Mandelbrot Locally Connected Conjecture · Milnor: Local Connectivity of Julia Sets
Also found as Infinity
The app's deep Mandelbrot architecture: a CPU reference orbit plus GPU perturbation, adaptive recovery, bounded scheduling, and a CPU fallback. Its public computation remains finite precision.
Read more: Technical white paper · Revision 19
Also found as initial condition · z₀ · z-zero
The value from which an orbit starts. Mandelbrot membership uses z₀ = 0; Julia rendering varies the initial value across the image.
Read more: Technical white paper · Revision 19
Also found as iterate · recurrence step
One application of the update rule. An iteration count tells how many updates were evaluated; the iteration budget limits how many may be attempted.
Read more: Technical white paper · Revision 19 · User Guide
Also found as Set Max Iterations · maximum iteration cap
The selectable upper end of manual iteration control. It is separate from the current value and the renderer's effective policy; changing it does not itself add numerical precision.
Read more: User Guide · Technical white paper · Revision 19
Also found as manual iterations · iteration slider
The control setting how much orbit work to allow when Auto is off. More iterations can reveal later escape but cannot recover coordinate information already lost.
Read more: User Guide
Also found as camera path · saved-view path
A planned route between saved compositions, with timing and appearance choices. This is roadmap terminology rather than a current video-capture feature.
Read more: Roadmap
Also found as JPG · .jpeg · .jpg
A widely supported image format commonly using lossy compression. It is useful for photographs and previews but differs from the app's lossless PNG captures.
Read more: User Guide
Also found as JavaScript Object Notation · .json
A structured text format for objects, arrays, numbers, strings, and other simple values. The app uses it for portable bookmark and palette records.
Read more: Technical white paper · Revision 19
Also found as Julia c · juliaCX · juliaCY
The fixed complex parameter that defines a Julia scene. Bookmarks preserve it separately from that scene's viewport center.
Read more: User Guide · Technical white paper · Revision 19
Also found as Julia
For a fixed parameter c, the boundary of the filled Julia set: the starting points with bounded orbits under z² + c. The displayed colors also describe surrounding escaping points.
Read more: Beyond Complex Numbers · User Guide
Also found as Lindenmayer system
A rewriting system often used to model branching forms and plant-like patterns. It illustrates fractal-like growth outside Mandelbrot and Julia dynamics.
Read more: Fractals in Nature
Also found as Lambert · N dot L
A diffuse lighting model proportional to the nonnegative dot product of the surface normal and light direction. It produces broad surface-facing brightness cues.
Read more: Archived code review · October 2025
Also found as input response · first-refinement latency
Elapsed time until a specified event. Input feedback, first completed region, and the final frame measure different parts of the experience.
Read more: Inside the Infinity Engine
Also found as swipe actions
Direction-aware interface edges. Swipe actions are described this way so Export and Delete guidance can adapt to left-to-right and right-to-left layouts.
Read more: User Guide
Also found as GPU dd2 · historical deep label
A historical nested-Float GPU representation in the app. Its name should not be interpreted as two IEEE Doubles or as a promise of native FP64 computation.
Read more: Technical white paper · Revision 19
Permanent Pro access based on verified ownership from before the Version 3 boundary. It is an ownership entitlement, not a different renderer.
Read more: Technical white paper · Revision 19
Also found as backgrounding · foreground
The active, inactive, and teardown stages of an interface or app scene. Long work and callbacks must respect those transitions.
Read more: Technical white paper · Revision 19
Also found as light elevation
The orientation from which illumination is evaluated. The roadmap discusses expanded direction and elevation controls separately from current 3D Look behavior.
Read more: Roadmap · GPU Pipeline
Also found as high limb · low limb · component
One part of a multi-component representation. Expansion limbs carry successively smaller contributions; fixed-point limbs instead hold chunks of an integer representation.
Read more: Technical white paper · Revision 19
Also found as linear interpolation
Blending neighboring texel values according to the sample position. It smooths between LUT texels but does not imply scene-linear light values.
Read more: Palette System
Having a basis of connected neighborhoods around every point. This is a local topological property, not a conclusion that can be read reliably from a finite image.
Read more: The Mandelbrot Locally Connected Conjecture · Milnor: Local Connectivity of Julia Sets
The device's palette persistence format preserving a color-space label. Legacy bare stop arrays are interpreted as sRGB.
Read more: Palette System
Also found as locale · translated interface
Adapting text, formatting, and layout to a language and region. Number grouping and percentages may differ even when the stored numerical state is identical.
Read more: Technical white paper · Revision 19
Also found as log · log₂ · log₁₀ · ln
The inverse of exponentiation. Logarithms express zoom scales, drive iteration-policy curves, and help turn integer escape counts into smooth color coordinates.
Read more: Technical white paper · Revision 19 · Why Magnification and Iterations Are Linked in the Mandelbrot Set
Also found as pragma unroll
Replacing a loop with repeated operations to reduce control overhead or expose optimization opportunities. It can increase code size and does not automatically improve every workload.
Read more: Archived code review · October 2025
Compression that allows the stored image data to be recovered exactly. It does not undo numerical error in the render that produced the pixels.
Also found as lookup table · look-up table · 1D LUT
A sampled table mapping an input value to an output. The app's color LUT is a one-row texture sampled using a normalized escape coordinate.
Read more: Palette System
Also found as LUT resolution · 256 · 1024 · 1,024
The number of texels in the rendering lookup table. The current setting selects 256 or 1,024; more texels do not add more bits to each channel.
Read more: Palette System
Also found as epsilon · ε
A measure of floating-point spacing near one, with conventions that should be stated. It is useful for reasoning about rounding but does not bound every complete orbit's error.
Read more: Technical white paper · Revision 19 · Archived code review · October 2025
Also found as modulus · absolute value · norm · ∣z∣
The distance of a complex number from zero: for z = x + iy, its magnitude is √(x² + y²). Escape tests use this size.
Read more: Beyond Complex Numbers · Perturbation Rendering
Also found as cardioid
The large heart-shaped component of the Mandelbrot set, associated with an attracting fixed point. An analytic test can identify its interior without a full orbit loop.
Read more: GPU Pipeline · Technical white paper · Revision 19
The library interface for saving and opening views, sorting records, and importing or exporting bookmark files or packs.
Read more: User Guide · Technical white paper · Revision 19
The custom-palette library for importing, exporting, renaming where supported, and deleting user-created color definitions. Built-in palettes are protected.
Read more: Palette System · User Guide
Also found as Pro Account · Upgrade to Pro
The feature tier adding creative and workflow capabilities such as custom palettes, 3D Look, and larger captures. Free and Pro share the same underlying rendering precision.
Read more: User Guide · Technical white paper · Revision 19
Also found as 𝓜 · M · Mandelbrot
The set of parameters c for which the orbit of zero under z² + c remains bounded forever. A finite render approximates this classification.
Read more: Beyond Complex Numbers · Technical white paper · Revision 19
A three-dimensional fractal construction based on a spherical-coordinate power mapping. It is distinct from the complex Mandelbrot set and from relief shading.
Read more: Beyond Complex Numbers
Also found as infinity norm · ∥x∥∞
The largest absolute component of a vector. It is a different size measure from the Euclidean norm and appears in historical numerical cutoff discussions.
Read more: Archived code review · October 2025
The rate at which data can be moved through memory. Reference reads, texture access, and extra precision components contribute to a workload's data-transfer cost.
Read more: Inside the GPU Engine of Mandelbrot Metal · Inside the Infinity Engine
Also found as allocation profiling
Measuring memory use, resource lifetimes, and possible leaks. A raw pixel-size calculation alone is not a measurement of peak process memory.
Read more: Technical white paper · Revision 19 · Archived code review · October 2025
Also found as Metal API
Apple's low-level framework for GPU graphics and compute. The app uses compute work to turn a viewport into a fractal image.
Read more: GPU Pipeline · Technical white paper · Revision 19
Apple's support framework for integrating Metal drawing into apps, including MTKView. It handles part of the bridge between a GPU renderer and a platform view.
Read more: Technical white paper · Revision 19
Also found as mebibyte · kibibyte · binary memory units
Binary units: 1 KiB = 1,024 bytes and 1 MiB = 1,048,576 bytes. They differ from decimal kB and MB when reporting texture or image storage.
Read more: GPU Pipeline · Inside the Infinity Engine
Also found as baby Mandelbrot · mini-Mandelbrot · minibrot
A smaller Mandelbrot-like structure embedded in parameter space. Its surroundings and attachments can differ even when its central shape looks familiar.
Read more: Why the Mandelbrot Set Never Repeats · The Mandelbrot Locally Connected Conjecture
Also found as rectangle bounds
The minimum and maximum coordinates defining the rectangle supplied to Coordinate Jump. The app derives its center and an aspect-preserving scale.
Read more: User Guide
Also found as Mandelbrot Locally Connected Conjecture
The conjecture that the Mandelbrot set is locally connected at every point. Visual continuity or the absence of visible gaps is not a proof of this statement.
Read more: The Mandelbrot Locally Connected Conjecture · Milnor: Local Connectivity of Julia Sets
Also found as monotonic growth
Changing consistently in one direction, possibly with flat intervals. A nominally increasing iteration proposal may still be modified by quality or deep-path policies.
Read more: Technical white paper · Revision 19 · Archived code review · October 2025
Also found as More · ellipsis · …
The menu providing management, settings, and help actions. Available placement can differ between iPhone and iPad.
Read more: User Guide
Also found as GNU MPFR
A multiple-precision floating-point library with specified rounding behavior. The technical discussion considers such tools for higher-precision reference work; current public Infinity uses CPU double-double.
Read more: Inside the Infinity Engine
Also found as Metal Shading Language
The language used to write Metal shader and compute functions. The app's orbit and relief kernels are implemented in Metal source.
Read more: Technical white paper · Revision 19
Also found as MetalKit view
An Apple view that manages a Metal-backed drawing surface. The app embeds this canvas inside its SwiftUI interface.
Read more: Technical white paper · Revision 19
The family zₙ₊₁ = zₙᵈ + c for integer powers beyond the quadratic case. The roadmap proposes evaluating additional families with their own rendering limits.
Read more: Roadmap
Also found as λ · lambda
The derivative of a full return around a periodic cycle. Magnitude below 1 means attracting, above 1 repelling, and equal to 1 requires further analysis.
Read more: Beyond Complex Numbers
Also found as not a number · non-finite
NaN represents an invalid numerical result; infinity is also non-finite. These values are checked rather than accepted as trustworthy orbit state.
Read more: Technical white paper · Revision 19
A possible future interface designed for Mac displays, keyboard, pointer, and longer sessions. It is a candidate direction rather than an existing mobile-app capability.
Read more: Roadmap
Also found as nearest source stop
Choosing one nearest stored value rather than blending. Exact LUT uses nearest source stops while building texels; the later Metal sampler still uses linear filtering.
Read more: Palette System
Also found as indifferent cycle
A periodic orbit with multiplier magnitude 1. Linear information alone does not determine all nearby behavior.
Read more: Beyond Complex Numbers
Also found as lifetime Pro
A one-time product intended to remain owned rather than be used up. Lifetime Pro is distinct from recurring monthly or annual access.
Read more: Technical white paper · Revision 19
A system with repeating or oscillatory behavior governed by nonlinear equations. It is one example connecting dynamics, bifurcations, and complex behavior beyond fractal rendering.
Read more: What Are Fractals?
Also found as slider calibration
A control whose position does not increase the value at a constant rate. The app allocates extra travel to useful lower iteration or contrast ranges.
Read more: User Guide
Also found as dispatchThreads
A supported dispatch arrangement whose edge groups can be smaller than interior groups. The app uses a compatibility path where this arrangement is unsuitable.
Read more: Technical white paper · Revision 19 · Apple: threadgroup and grid sizes
Also found as normalized palette position
Mapping a computed quantity into a standard range, commonly 0 to 1 for lookup. This color operation differs from renormalizing arithmetic expansion limbs.
Read more: Palette System · Technical white paper · Revision 19
How an algorithm propagates rounding and other numerical errors. It differs from the conditioning of the mathematical problem being solved.
Read more: Why Double-Double Precision Isn’t Enough for Deep Fractals · Inside the Infinity Engine
Also found as zoom octave
A factor-of-two change, often expressed using log₂. Zoom-policy curves can describe depth in octaves relative to a reference scale.
Read more: Technical white paper · Revision 19 · Archived code review · October 2025
Also found as offline workflow
A design in which local work remains useful without a network connection, with synchronization handled separately. This is a principle in the library roadmap.
Read more: Roadmap
Also found as export render
Rendering to an image resource rather than directly to the live display. Every app capture uses a dedicated complete output render, including Canvas Size.
Read more: GPU Pipeline · User Guide
Also found as MIT license
Source code made available under a license specifying reuse conditions. Photo2Palette is the companion tool discussed as open source; this does not describe all app code.
Also found as trajectory · zₙ · orbit sequence
The sequence z₀, z₁, z₂, … obtained by repeatedly applying a function. Its escape or bounded behavior determines much of a fractal image.
Read more: Perturbation Rendering · Beyond Complex Numbers
Reusing a valid reference orbit and reusing per-pixel escape results are different optimizations. Current reference sharing does not imply instant palette-only recoloring.
Read more: GPU Pipeline · Roadmap
A result too large in magnitude for the working format, potentially producing infinity. Additional significand limbs alone do not guarantee a wider exponent range.
Read more: Technical white paper · Revision 19
Also found as color palette · colour palette
An ordered color definition mapped onto computed fractal values. The source definition, its rendering texture, and the final display conversion are separate stages.
Read more: Palette System
Also found as All · Standard · Ultra-Wide · Custom
Categories that narrow the palette picker. They describe the palette source and ownership, rather than selecting a different fractal equation.
Read more: Palette System · User Guide
Computing intermediate colors between sampled positions. Both source construction and texture sampling can affect the final transition.
Read more: Palette System
Also found as portable palette schema
The sharing format carrying a palette name, color-space label, and normalized stops. It has a different version history from local palette storage and bookmarks.
Read more: Palette System
Also found as palette button · brush menu
The interface for choosing a palette, inspecting previews, filtering its categories, and accessing related color options.
Read more: User Guide · Palette System
Also found as builtIn · customByName · embedded
A bookmark's way of identifying colors: a built-in index, a custom name, or embedded stops when supported on import. Current exported named custom palettes should be shared separately.
Read more: Technical white paper · Revision 19
Also found as drag
Moving the visible region without intentionally changing scale. The retained image follows the gesture, then a committed view is rendered.
Read more: User Guide
Also found as parallel computation
Doing independent work at the same time. Per-sample orbit evaluation offers extensive parallelism, while a reference orbit advances sequentially along its recurrence.
Read more: GPU Pipeline · Inside the Infinity Engine
Also found as c · complex parameter
The constant added at every step of zₙ₊₁ = zₙ² + c. Mandelbrot rendering varies c across the image; a Julia rendering keeps c fixed.
Read more: Technical white paper · Revision 19 · User Guide
The complex plane interpreted as choices of c. The Mandelbrot set lies in parameter space; each chosen c specifies a different dynamical system.
Read more: Beyond Complex Numbers
The stronger property that any two points can be joined by a continuous path lying in the space. It should not be used as the definition of connectedness.
Read more: The Mandelbrot Locally Connected Conjecture · Milnor: Local Connectivity of Julia Sets
Also found as Portable Document Format
A fixed-layout document format used for the technical white paper and downloadable guides. It preserves page layout rather than interactive app state.
Read more: The Tech in the App
Also found as p95 · p99 · latency distribution
A value below which a stated percentage of observations falls. Two timed runs per scene are insufficient to characterize reliable tail-latency percentiles.
Read more: Inside the Infinity Engine
A mathematical model of connectivity through occupied sites or links. Near critical conditions it can generate scaling and fractal structure.
Read more: What Are Fractals?
Also found as periodic orbit · cycle length
The smallest positive number of updates after which an orbit repeats. A fixed point has period 1; a two-cycle has period 2.
Read more: Beyond Complex Numbers
A bifurcation sequence in which attracting cycles pass through periods such as 1, 2, 4, and 8. Its repeated structure appears in renormalization theory.
Read more: The Mandelbrot Locally Connected Conjecture
Also found as period two bulb
The round component attached to the left of the main cardioid, associated with an attracting two-cycle. It has a useful analytic interior test.
Read more: GPU Pipeline · Technical white paper · Revision 19
Also found as saved state
Keeping data across launches. Permanent bookmarks and preferences differ from the temporary exploration history timeline.
Read more: Technical white paper · Revision 19
Also found as bookmark slot
A discovery saved by the user. Free's personal-bookmark allowance is separate from the supplied starter collection.
Read more: Technical white paper · Revision 19
Also found as delta orbit · perturbation orbit
Computing nearby orbits relative to a shared reference. For the quadratic family, δzₙ₊₁ = 2Zₙδzₙ + δzₙ² + δc is algebraically exact; finite arithmetic still introduces error.
Read more: Perturbation Rendering
The space of possible states of a dynamical system. In a fixed quadratic Julia problem, the complex z-plane is the phase space.
Read more: What Are Fractals?
The companion command-line tool for creating palette definitions from images. It supports source sampling and processing controls and can output portable JSON or developer Swift data.
Read more: Introducing Photo2Palette: A Command-Line Tool · Palette System
Testing on actual supported hardware. It checks performance, memory, heat, resource behavior, and other conditions that a simulator cannot fully establish.
Read more: Technical white paper · Revision 19 · Beta Tester’s Guide
Also found as π · 𝛑
The ratio of a circle's circumference to its diameter. It appears in angular, cyclic, and trigonometric descriptions of fractals, although z² + c does not require π.
Read more: 𝛑 and Fractals: Is There a Connection?
Also found as pinch to zoom · spread
A two-finger gesture that changes scale. Spreading zooms in and pinching together zooms out, with the gesture's focal point guiding the mapping.
Read more: User Guide
Also found as compute pipeline state
A prepared Metal object describing the compiled GPU function and execution requirements. It lets commands invoke the intended kernel efficiently.
Read more: Technical white paper · Revision 19
One output picture element. A pixel can combine several samples; it should not be confused with a source palette stop or a texture texel.
Read more: GPU Pipeline
Also found as MTLPixelFormat
The channel arrangement, bit depth, and numerical interpretation of texture elements. Color and relief use different formats because they store different kinds of data.
Read more: Technical white paper · Revision 19
Also found as sample spacing
The complex-plane distance between adjacent drawable pixel centers. It depends on scale and the display's pixels-per-point factor.
Read more: GPU Pipeline · Inside the Infinity Engine
Also found as Portable Network Graphics · .png
A lossless raster-image format used for finished captures. It stores pixels rather than the editable orbit and palette state of a bookmark.
Read more: User Guide · Technical white paper · Revision 19
Also found as UIKit point · logical point
A logical interface distance unit. A display can use multiple physical pixels per point, so gesture coordinates need conversion for the drawable.
Read more: GPU Pipeline
Also found as r exp(iθ) · r eⁱθ
Writing z = r(cos θ + i sin θ), or reⁱθ. Here r is magnitude and θ is angle; squaring squares r and doubles θ.
Read more: Beyond Complex Numbers
A finite sum of nonnegative integer powers with coefficients. For a fixed c, z² + c is a quadratic polynomial in z.
Read more: Beyond Complex Numbers
Also found as dropdown menu
A compact contextual panel of choices. The website's Support dropdown provides navigation to help pages, including this glossary.
Read more: User Guide
Also found as escape potential
A scalar function describing behavior such as escape growth outside a filled set. Potential-based analysis and coloring are broader concepts than the app's specific smooth escape coordinate.
Read more: What Are Fractals? · 𝛑 and Fractals: Is There a Connection?
Also found as pixels per inch
The density of image pixels at a chosen physical print size. Required pixels equal print dimensions in inches multiplied by the intended PPI.
Also found as significant precision
How much numerical detail a representation or calculation retains. Precision is distinct from exponent range, iteration count, image resolution, and color depth.
Read more: Technical white paper · Revision 19 · Beyond Complex Numbers
Executing instructions under a condition that enables or disables their effect for participating lanes. It is one way GPU code can handle conditional work.
Read more: Archived code review · October 2025
Also found as presented frame
Making a completed image available to the display. Kernel completion, the first refined tile, and complete-frame presentation are distinct events.
Read more: GPU Pipeline · Inside the Infinity Engine
Also found as print-ready artwork
The intended physical dimensions of a print. A high-resolution capture should be inspected at that size, with the destination's color and resolution requirements considered.
Also found as procedural palette
Generating color with a function rather than only reading a gradient texture. The documented shader includes HSV, Fire, and Ocean branches.
Read more: Palette System
Also found as performance profile
Measuring where execution time or resources are spent. A cost-model diagram suggests components to measure but is not itself a recorded profile.
Read more: Inside the Infinity Engine · Archived code review · October 2025
Also found as progressive refinement
Revealing completed regions while the remaining image is calculated. Infinity replaces an initialized preview with finished tiles before reporting whole-frame completion.
Read more: GPU Pipeline
Also found as pipeline state object
A prepared graphics or compute pipeline object. Creation and compilation costs are separate from the time spent running a kernel.
Read more: Archived code review · October 2025
Also found as precision restart
Re-evaluating a rejected sample from iteration zero in quad-single. Merely widening the current rounded Float state would not erase errors already accumulated.
Read more: Technical white paper · Revision 19 · Inside the Infinity Engine
Also found as binary128 · IEEE binary128
A distinct IEEE floating-point format with 113 significand bits. Four Float storage slots or a double-double pair do not automatically implement this format.
Read more: Technical white paper · Revision 19
Also found as QS · four-Float expansion
A software expansion of four Float limbs used for difficult GPU pixels and recovery. Its practical accuracy depends on normalization, operations, range, and reductions.
Read more: Technical white paper · Revision 19
Also found as quadratic recurrence · z² + c · f_c(z)
The function f_c(z) = z² + c. Repeating this simple rule generates the orbits used for Mandelbrot and quadratic Julia rendering.
Read more: Beyond Complex Numbers · Technical white paper · Revision 19
Also found as quality indicators · SSAA · 3D · Infinity
The HUD indicators describing active rendering features or paths. A quality label summarizes behavior; it does not specify the precision of every arithmetic operation.
Read more: Technical white paper · Revision 19 · The Mandelbrot Metal HUD: Design, Meaning, and How to Read It
Also found as bit depth
Representing a continuous range with finitely many levels. An eight-bit channel has 256 stored codes; a longer LUT does not change that channel depth.
Read more: Technical white paper · Revision 19 · Palette System
Also found as ℍ · quaternions
A four-component number a + bi + cj + dk with order-sensitive multiplication. Quaternion fractals and rotations are background mathematics, not the app's 3D Look renderer.
Read more: Beyond Complex Numbers
Also found as quick-two-sum
A shorter addition transform requiring a magnitude ordering between its operands. Using it without that precondition can invalidate its residual guarantee.
Read more: Technical white paper · Revision 19
Also found as height texture format
A texture format containing one 32-bit floating-point component per texel. The relief pipeline uses it to store height values rather than display colors.
Read more: GPU Pipeline
Also found as stale callback
An outcome depending on the timing of concurrent or delayed operations. Shared state and completion handlers need ordering and identity checks.
Read more: Technical white paper · Revision 19
Also found as rad · angular measure
An angle unit defined by arc length divided by radius. A full turn is 2π radians.
Read more: 𝛑 and Fractals: Is There a Connection?
Also found as Re(z) · real component
The a in a + bi. It is the horizontal coordinate on the complex plane.
Read more: Beyond Complex Numbers
Also found as rebase · reference-index reset
Changing the current perturbation representation, including resetting its reference index when appropriate. An in-kernel rebase does not mean the CPU rebuilds the shared orbit.
Read more: Perturbation Rendering
Also found as verified ownership
Checking trusted purchase evidence before deriving access. A local preference alone is not equivalent to verified App Store ownership.
Read more: Technical white paper · Revision 19
Also found as reconstructed orbit
Combining the reference and deviation, zₙ = Zₙ + δzₙ, for escape, color, or recovery decisions. Cancellation can make this combination numerically delicate.
Read more: Perturbation Rendering
Defining a process in terms of itself. Fractal writing often uses this word broadly; the app's orbit computation repeatedly applies a recurrence through iteration.
Read more: From Chaos to Beauty: How Simple Equations Create Infinite Art
A system accessibility preference requesting less motion. The app shortens or skips appropriate presentation effects in response.
Read more: Technical white paper · Revision 19
Reaching the end of the stored reference before a sample's useful computation is complete. The renderer needs a recovery route rather than reading beyond the buffer.
Read more: Technical white paper · Revision 19
Also found as Zₙ · Z_n
A sequence computed for a selected reference parameter, then reused by nearby samples. Infinity builds it on the CPU in double-double arithmetic.
Read more: Perturbation Rendering · Technical white paper · Revision 19
Also found as reference parameter · c₀ · anchor
The parameter chosen for the accurate shared orbit. Nearby sample parameters are expressed as offsets from this anchor.
Read more: Perturbation Rendering
Also found as reference caching
Reusing a compatible accurate orbit rather than rebuilding it for every request. Safe reuse depends on mapping, validity, and state compatibility, not just visual similarity.
Read more: Roadmap · Inside the Infinity Engine
Also found as regression testing
A check intended to catch behavior broken by a change. Passing the asserted cases is evidence about those cases, not a proof covering all possible fractal coordinates.
Read more: Technical white paper · Revision 19
Also found as height budget · probe pattern
The iteration allowance used to derive a useful height field. A small CPU probe grid helps select it; this heuristic does not exhaustively inspect every output pixel.
Read more: GPU Pipeline
Also found as bump-like shading · surface relief
Lighting a surface inferred from a scalar height field. In the app, a second compute pass shades colors using completed neighboring height samples.
Read more: GPU Pipeline
Also found as relief depth · detail scale
Parameters controlling how strongly height variations influence apparent shape. The roadmap proposes broader controls; these change appearance rather than fractal coordinates.
Read more: Roadmap
Also found as reproduction record
A record of the exact rendering conditions, including state, build, device, arithmetic, LUT data, and output settings. It can capture more than a normal bookmark.
Read more: Technical white paper · Revision 19
Also found as rendering pipeline
The chain from view state through coordinates, arithmetic, orbit evaluation, color, optional lighting, and display or export. Correctness depends on the whole chain.
Read more: GPU Pipeline
Also found as expansion normalization
Reorganizing an arithmetic expansion to preserve ordered, suitably nonoverlapping limbs. This numerical operation differs from renormalization in complex dynamics.
Read more: Technical white paper · Revision 19
Also found as dynamical renormalization
Studying a suitable iterate on a smaller region as a new dynamical system. It explains nested quadratic-like behavior; it differs from normalizing floating-point limbs.
Read more: The Mandelbrot Locally Connected Conjecture
A periodic orbit whose multiplier has magnitude greater than 1, so sufficiently small perturbations grow locally.
Read more: Beyond Complex Numbers
Also found as representable pixel step
Whether a value can be stored distinctly in a chosen format. A nonzero stored step does not prove it survives addition to a large absolute coordinate.
Read more: Technical white paper · Revision 19
Also found as low part · rounding residual
A smaller remainder retained after a rounded leading result. Preserving residuals is central to compensated coordinates and expansion arithmetic.
Read more: Technical white paper · Revision 19
Also found as buffer index · texture index
Connecting a buffer or texture to the numbered input or output expected by a kernel. Correct data and compatible access permissions are both required.
Read more: Technical white paper · Revision 19
Also found as Restore
An explicit action to refresh verified App Store ownership. It does not restore deleted bookmark or palette files.
Read more: Technical white paper · Revision 19 · User Guide
Also found as retained image · gesture preview
The last completed image, temporarily transformed to follow a pan or pinch. It provides immediate feedback without claiming that new deep detail has already been calculated.
Read more: GPU Pipeline
Also found as Mandelbrot return view
The originating Mandelbrot state retained when entering Julia mode. It preserves a useful way back after exploring the linked Julia set.
Read more: Technical white paper · Revision 19
Also found as red green blue
An additive color model using red, green, and blue channels. Their numerical values only acquire a precise color meaning with a defined color space and encoding.
Read more: Palette System
Also found as RGBA · red green blue alpha
An eight-bit-per-channel arrangement in red, green, blue, alpha order. The photo-import working image uses RGBA8 before producing palette stops.
Read more: Palette System · Technical white paper · Revision 19
Also found as planned · research dependent · candidate
A sequence of proposed work, distinct from available features. Research milestones require qualification before a new precision or functionality promise is made.
Read more: Roadmap
The difference introduced when an exact value is replaced by a representable one. Repeated updates can propagate or amplify these errors.
Read more: Technical white paper · Revision 19
Also found as right-to-left layout
Interface layout for languages such as Arabic and Hebrew. Leading and trailing directions adapt with reading direction rather than always meaning left and right.
Read more: Technical white paper · Revision 19
The usable layout region that avoids system obstructions such as device cutouts and the home indicator. Toolbar placement respects it.
Read more: Technical white paper · Revision 19
Also found as SSAA×4 · SSAAx4 · subpixel grid
The pattern of sample locations inside a pixel. Ordinary renderer grids use totals such as 1, 4, 9, 16, or 25; four samples do not mean four times each image dimension.
Read more: GPU Pipeline
Also found as StoreKit testing
A testing environment separate from production purchases. Simulated purchase results do not by themselves prove production receipt recovery or migration behavior.
Read more: Technical white paper · Revision 19 · Beta Tester’s Guide
The intensity of color relative to gray in a chosen color model. Photo import can increase or decrease it in the sampled palette.
Read more: Palette System · User Guide
Also found as zoom scale · magnification
A measure of how much screen distance represents one complex-plane unit. The technical materials distinguish navigation points per unit from drawable pixels per unit and relative zoom factors.
Read more: Technical white paper · Revision 19 · Inside the Infinity Engine
Also found as dilation · scaling law
A property that remains unchanged, exactly or approximately, after rescaling. Statistical resemblance in nature should not be confused with exact mathematical invariance.
Read more: What Are Fractals? · Fractals in Nature
Also found as portable scene · self-contained scene
A complete composition description. The roadmap proposes a richer self-contained format including custom colors and full appearance; current bookmarks do not serialize every lighting parameter.
Read more: Technical white paper · Revision 19 · Roadmap
Also found as linear light
Color values proportional to light intensity. Averaging stored BGRA8Unorm components does not by itself establish physically linear light averaging.
Read more: Technical white paper · Revision 19
Also found as schemaVersion · file version
The agreed structure and version of a record. It tells an importer which fields and compatibility rules to apply.
Read more: Technical white paper · Revision 19
Also found as 1e25 · e notation · ×10ⁿ
Writing a value as a coefficient times a power of ten. It makes very large scales compact; displayed digits may be rounded.
Read more: Technical white paper · Revision 19 · The Mandelbrot Metal HUD: Design, Meaning, and How to Read It
Also found as content scale · pixels per point
The ratio between logical points and drawable pixels. Omitting it changes the effective sampling distance and can misstate zoom comparisons.
Read more: GPU Pipeline · Inside the Infinity Engine
Also found as standard dynamic range
The conventional output brightness-range category used by the documented app exports. SDR can still use a wide color gamut.
Read more: User Guide · Technical white paper · Revision 19
A familiar exploration region near the junction of the main cardioid and period-2 bulb, known for curling seahorse-like patterns.
Read more: Mandelbrot Metal 2.0: Tap Into Julia Sets · Creating Art
Also found as website search
The Community Portal field that filters bookmark entries by their searchable names and metadata. It operates on the website catalog rather than the app's local library.
Read more: Community Portal
Also found as bulk selection
Selecting the bookmark rows currently shown by the website's filters. A selection can be downloaded together as a ZIP.
Read more: Community Portal
Resemblance between structures at different scales. It may be exact, approximate, or statistical; familiar Mandelbrot motifs do not make every region an identical copy.
Read more: Why the Mandelbrot Set Never Repeats · The Coastline Paradox: When Math Meets the Infinite
Also found as deserialization
Encoding structured state into a file or reconstructing it from that file. Careful numerical representation prevents unnecessary loss of deep-coordinate information.
Read more: Technical white paper · Revision 19
Also found as series acceleration
Approximating orbit differences with a truncated series, potentially skipping repeated work within a validated range. It is separate from Version 3's full per-step quadratic recurrence.
Read more: Perturbation Rendering · Roadmap
A GPU program. In this app, compute shaders calculate fractals and relief; the term does not imply that every shader is a traditional triangle-coloring fragment shader.
Read more: GPU Pipeline
Also found as function constant · shader variant
Preparing a version of a shader for particular constant choices. It can remove unused branches, at a cost in compilation, variants, and resource management.
Read more: Archived code review · October 2025
Also found as share sheet · management sheet
A presented interface panel for a focused task. The system share sheet offers destinations for exported artwork or files.
Read more: User Guide
A parameter controlling the concentration of specular highlights in a shading model. It is discussed in the planned creative controls, not a guarantee of a current slider.
Read more: Technical white paper · Revision 19 · Roadmap
Also found as mantissa · significant bits
The digits carrying a floating-point number's precision. The exponent locates their scale; a large exponent range does not add more significant digits.
Read more: Technical white paper · Revision 19 · Inside the Infinity Engine
Digits conveying a number's precision rather than merely its decimal position. A compact HUD readout shows fewer digits than the canonical saved center may contain.
Read more: Technical white paper · Revision 19
Also found as Single Instruction Multiple Data
Executing the same instruction across several data lanes. Fractal samples share an update rule, making much of their computation suitable for this parallel execution style.
Read more: Apple: threads and threadgroups · Inside the GPU Engine of Mandelbrot Metal
Also found as simdgroup · SIMD-group
A group of GPU threads executing together. It is an execution unit within a threadgroup; its width is a hardware and pipeline property to query.
Read more: Apple: threads and threadgroups
Also found as lane
One participating position in SIMD execution, with its own data. Different escape times can leave some lanes inactive while others continue.
Read more: Apple: threads and threadgroups · Inside the GPU Engine of Mandelbrot Metal
Also found as float2 · float4 · vector type
Two- or four-component vector types. A float4 may carry four arithmetic limbs; its four storage components do not by themselves mean four independently scheduled pixel threads.
Read more: Technical white paper · Revision 19 · Inside the Infinity Engine
A development environment that runs an app with simulated platform behavior. Its GPU compatibility paths and timing are not substitutes for physical-device qualification.
Read more: Technical white paper · Revision 19
Also found as 4D slice · three-dimensional slice
Ways to inspect a higher-dimensional object: intersect it with a lower-dimensional space, or map it onto one. The selected method changes the visible structure.
Read more: Beyond Complex Numbers
Also found as continuous escape coordinate · fractional iteration
A logarithmic correction to integer escape counts that produces a fractional value. This reduces iteration bands before palette mapping.
Read more: GPU Pipeline · Technical white paper · Revision 19
Also found as Smooth
Constructing the lookup texture from a continuous gradient. This differs from the Exact LUT source-stop selection, while both textures use linear shader sampling.
Read more: Palette System
A small weighted image-neighborhood filter used to estimate horizontal and vertical gradients. It is background from an archived optimization suggestion; current relief uses central differences.
Read more: Archived code review · October 2025 · GPU Pipeline
Also found as Name · Mode · Newest · Oldest · Iterations · Palette · Scale
The ordering used to browse bookmarks. These options compare saved metadata, not necessarily how long each scene will take to render.
Read more: User Guide
Also found as stop count · palette length
The number and arrangement of colors in the source definition. It differs from LUT width, per-channel bit depth, and fractal-coordinate precision.
Read more: Palette System
Also found as specular · highlight strength
A concentrated lighting reflection that can make a surface appear polished. Its strength and shape affect the perceived material.
Read more: GPU Pipeline · Roadmap
A winding form around a center. Spirals recur throughout fractal imagery, but a visual spiral name does not specify a unique coordinate or formula.
Read more: Creating Art · 𝛑 and Fractals: Is There a Connection?
Also found as iPad multitasking
An iPad window arrangement with reduced available width. The app adapts controls so narrow layouts can still access the same actions.
Read more: Technical white paper · Revision 19
Also found as norm squared · ∣z∣²
The value x² + y² for z = x + iy. Comparing it with 4 avoids a square root in a radius-2 escape test.
Read more: GPU Pipeline
A widely used RGB color space and transfer encoding for web and screen imagery. It offers a smaller gamut than Display-P3.
Read more: Palette System
Also found as supersampling anti-aliasing · super-sampling
Evaluating multiple subpixel samples and averaging their colors to reduce jagged edges. The app selects sampling automatically; public Infinity currently uses one sample per pixel.
Read more: GPU Pipeline · User Guide
Also found as shared storage mode
An intermediate resource used to prepare or transfer data before final use. Shared CPU/GPU storage still needs correct ordering and lifetime management.
Read more: Archived code review · October 2025 · Technical white paper · Revision 19
Also found as obsolete completion
A tile or callback belonging to a superseded request. Generation checks and cancellation prevent it from presenting the wrong composition.
Read more: Technical white paper · Revision 19
Also found as Standard
A built-in palette outside the Ultra-Wide and Custom categories. Standard source definitions have varying stop counts; they are not all 512-step ramps.
Read more: Palette System
Also found as starter collection
A curated scene installed once for exploration. Stable identifiers and matching checks preserve existing work and avoid reinstalling deleted starters after installation completes.
Read more: Technical white paper · Revision 19
Also found as pixel-step gate
An eligibility check on finite split pixel steps before selecting Infinity. It prevents taking a numerical path when its required displacement representation is unsuitable.
Read more: Technical white paper · Revision 19
Also found as transport precision
The information retained in saved or transmitted values. It is separate from the arithmetic precision used to generate a reference orbit or evaluate a pixel.
Read more: Technical white paper · Revision 19
Also found as StoreKit
Apple's framework for App Store products, verified purchases, subscriptions, and ownership. It is separate from storage for a user's artwork or bookmarks.
Read more: Technical white paper · Revision 19
Also found as xcstrings
Apple's structured localization resource for translated strings and variants. It supports the app's interface and guide localization workflow.
Read more: Technical white paper · Revision 19
Also found as denormal
A floating-point value below the smallest normal magnitude, represented with reduced relative precision. Infinity's public step gate requires suitable normal Float-sized split steps.
Read more: Technical white paper · Revision 19 · Perturbation Rendering
A calculation at a position within an output pixel. Each supersample can perform its own orbit and palette lookup before color averaging.
Read more: GPU Pipeline
Also found as monthly · annual
A time-limited purchase that grants Pro while eligible ownership remains current. It differs from a lifetime non-consumable purchase.
Read more: Technical white paper · Revision 19
Also found as normal vector
A direction perpendicular to the inferred surface. Lighting uses it to decide how strongly a point faces the light.
Read more: GPU Pipeline
Apple's programming language used for application state, policy, reference construction, export orchestration, and other CPU-side responsibilities.
Read more: Technical white paper · Revision 19
Also found as developer palette data
Source-code data emitted by Photo2Palette for developers. It differs from the portable JSON file normally imported through Manage Palettes.
Read more: Introducing Photo2Palette: A Command-Line Tool · Palette System
Apple's declarative interface framework used to compose the app's controls around its Metal canvas.
Read more: Technical white paper · Revision 19
Also found as rotational symmetry · reflection symmetry
A transformation that leaves a structure unchanged. An individual crop or color treatment may obscure symmetries of the underlying mathematical set.
Read more: Beyond Complex Numbers · 𝛑 and Fractals: Is There a Connection?
Also found as conflict resolution
A disagreement between independently edited copies of saved data. Planned synchronization needs explicit rules for edits, deletions, and recovery.
Read more: Roadmap
Also found as resource dependency
Ordering dependent operations so later work reads finished, valid data. Relief shading must read a completed height field rather than partially written neighbors.
Read more: GPU Pipeline · Technical white paper · Revision 19
Also found as single-tap · Julia linkage
Selecting a Mandelbrot location as the fixed Julia parameter c. A stored return snapshot lets the interface take you back to the originating Mandelbrot composition.
Read more: User Guide · Technical white paper · Revision 19
Also found as a₁,n · series coefficient
A multiplier of a power in a Taylor expansion. Orbit coefficients describe how the nth iterate changes when the parameter changes near a reference.
Read more: Perturbation Rendering
Also found as Taylor expansion · power series
A local expansion built from a function's derivatives: f(a + h) = Σ f⁽ᵏ⁾(a)hᵏ/k! where it converges. Truncating it gives an approximation with an error to control.
Read more: Perturbation Rendering · Why Double-Double Precision Isn’t Enough for Deep Fractals
Also found as shimmer
Unwanted changes between animation frames, potentially from sampling, numerical routing, or lighting. Future video workflows need to qualify consistency over time.
Read more: Roadmap
Also found as beta access
Apple's beta-distribution system for trying prerelease app builds. Beta testing and a published App Store release are different stages.
Read more: Beta Tester’s Guide
Also found as texture element · tap
One stored element of a texture. A one-row palette LUT contains 256 or 1,024 texels, which the shader samples to obtain colors.
Read more: Palette System
Also found as MTLTexture
A GPU resource arranged as texels, often an image or lookup table. The app uses textures for color, palette lookup, and temporary relief heights.
Read more: GPU Pipeline
Also found as shaderRead · shaderWrite · access permissions
Declared ways a texture may be used. A texture bound to a writable shader parameter needs compatible write usage even when a runtime branch skips writing.
Read more: Technical white paper · Revision 19
Also found as thermal state · sustained heat
A device reducing performance under thermal constraints. Sustained and repeated benchmarks need to consider heat and test order.
Read more: Roadmap · Inside the Infinity Engine
One invocation of a GPU kernel. The main fractal kernel typically assigns an output pixel to a thread, which may evaluate several subpixel samples.
Read more: GPU Pipeline
Also found as threadExecutionWidth
The number of threads in a compute pipeline's SIMD execution group. It informs efficient threadgroup sizing and should be queried rather than assumed universally.
Read more: Apple: threadgroup and grid sizes
A group of compute threads scheduled together, with facilities for cooperation and shared memory. It can contain more than one SIMD group.
Read more: Apple: threads and threadgroups
Also found as three-sum · five-term renormalization
Expansion primitives that combine several components and retain smaller residuals before reducing them to an ordered, fixed-length expansion.
Read more: Technical white paper · Revision 19
The amount of completed work per unit time. High throughput does not automatically imply low latency for one demanding frame.
Read more: Inside the Infinity Engine
Also found as tiled rendering
A bounded rectangular part of an image calculated as a work unit. Shared full-image mapping keeps neighboring tiles aligned.
Read more: GPU Pipeline
Also found as too long didn't read
A short overview before a longer technical explanation. It helps readers find the main idea without replacing the detailed assumptions and evidence.
Read more: Beyond Complex Numbers
Mapping a signal's tonal range into a displayable range. The blog uses the term descriptively for contrast; that does not establish a scene-linear HDR tone-mapping pipeline.
Read more: The Art of Color: How Mandelbrot Metal Turns Math into Art · Technical white paper · Revision 19
Also found as floating toolbar · utility row
A group of nearby controls for navigation or creative work. Phone and tablet layouts arrange them differently while using the same underlying state.
Read more: User Guide · Technical white paper · Revision 19
A notion of dimension defined through the structure of open covers rather than metric scaling. It differs from Hausdorff and box-counting dimension.
Read more: What Are Fractals?
Also found as comb space
A classical example illustrating how a space can be connected while failing local connectedness at some points. It helps distinguish those two properties.
Read more: The Mandelbrot Locally Connected Conjecture
Also found as verified transaction
A purchase record checked before granting access. Expired or revoked records should not be treated as current subscriptions.
Read more: Technical white paper · Revision 19
Also found as transfer curve
The nonlinear relationship between encoded color values and light-related values. It must be considered separately from gamut and storage format.
Read more: Technical white paper · Revision 19
Also found as in-flight buffers
Using multiple resource sets so CPU preparation and GPU work can overlap without overwriting data still in use. It appears in the archived renderer review.
Read more: Archived code review · October 2025
The error from omitting terms of an infinite series or approximation. It differs from rounding error introduced by finite numerical storage and arithmetic.
Read more: Perturbation Rendering
Irregular fluid motion with interacting structures at many scales. Fractal-like models can describe aspects of it; a Mandelbrot image is not a fluid simulation.
Read more: What Are Fractals? · Fractals in Nature
Also found as two-product
A transform returning a rounded product plus its residual. A suitable fused multiply-add can recover that residual when rounding and range conditions hold.
Read more: Technical white paper · Revision 19
Also found as two-sum
An error-free addition transform that separates a sum into a leading rounded value and a residual under its operating assumptions.
Read more: Technical white paper · Revision 19
Also found as user interface
The controls, labels, readouts, and interaction patterns through which you use the app. The same exploration state supports the phone and tablet layouts.
Read more: User Guide · Technical white paper · Revision 19
Also found as gesture bridge
Apple's interface framework supplying platform views and gesture handling. The gesture bridge maps touches into the actual Metal canvas coordinates.
Read more: Technical white paper · Revision 19
Also found as unit in the last place
The spacing represented by the least significant position at a given magnitude and format. A pixel offset smaller than that spacing can disappear when added to a center.
Read more: Beyond Complex Numbers · Inside the Infinity Engine
Also found as [UW] · ultra wide · 768-step
The palette category whose source ramps contain 768 stops. The tag describes the source, not a separate shader, a color gamut, or a forced 768-texel texture.
Read more: Palette System
A result entering the format's smallest-magnitude region, where precision may be reduced or the value may become zero. Deep pixel-step qualification must account for this.
Read more: Technical white paper · Revision 19
A memory architecture allowing CPU and GPU resources to share physical memory. Shared storage does not remove synchronization, bandwidth, or allocation limits.
Read more: Technical white paper · Revision 19
Also found as dispatchThreadgroups
A dispatch arrangement with a fixed group size, often rounded up to cover the image. Threads outside the valid image require bounds checks.
Read more: Technical white paper · Revision 19 · Apple: threadgroup and grid sizes
Also found as uniform buffer · MandelbrotUniforms
Parameters shared across a dispatch, such as mapping, dimensions, iteration limits, palette settings, and lighting. Swift and Metal must interpret their layout identically.
Read more: Technical white paper · Revision 19
Also found as edge case
A focused check of a small behavior, including unusual inputs or boundary conditions. Broader integration and device tests are still needed for the complete rendering workflow.
Read more: Archived code review · October 2025 · Technical white paper · Revision 19
Also found as universally unique identifier
An identifier used to distinguish records independently of their displayed names. Duplicate names can therefore be renamed without making identity depend only on text.
Read more: Technical white paper · Revision 19
Also found as HSV value · brightness
The V coordinate in HSV, based on the largest RGB component. It is not a physical measurement of scene luminance.
Read more: Palette System
The region of the complex plane currently shown, defined by center, scale, and drawable geometry. Appearance settings add the information needed to render a finished image.
Read more: GPU Pipeline · Technical white paper · Revision 19
Also found as screen reader
Apple's screen-reading accessibility feature. Meaningful control labels let actions be understood without relying on an icon's appearance alone.
Read more: Technical white paper · Revision 19 · Beta Tester’s Guide
Also found as true 3D fractal
A fractal object defined in three-dimensional space or inspected through higher-dimensional construction. It differs from 3D Look's lighting of a two-dimensional field.
Read more: Beyond Complex Numbers · Roadmap
Also found as help viewer
Apple's web-content framework used for the in-app HTML guides. Load and layout callbacks must coordinate correctly with SwiftUI state updates.
Read more: Technical white paper · Revision 19
Also found as Show Welcome at startup · Don't show again
Controls for whether introductory help appears on later launches. Reopening a guide is separate from resetting the current exploration.
Read more: User Guide · Technical white paper · Revision 19
Also found as peak memory · memory pressure
The resources needed during a computation. Tiling bounds part of the work, but export still needs final-image storage and may need conversion and encoding buffers.
Read more: GPU Pipeline · Technical white paper · Revision 19
Also found as puzzle techniques
A method of partitioning a dynamical plane into nested regions to study orbits and connectivity. It is a mathematical proof technique, not an app rendering option.
Read more: The Mandelbrot Locally Connected Conjecture · Milnor: Local Connectivity of Julia Sets
Also found as archive · bulk download
A container holding multiple files. Community bookmark ZIPs retain individual JSON filenames and contents for convenient download and extraction.
Read more: Community Portal
Also found as scale clamp · 10²⁵ · 1e25
The public Version 3 navigation boundary of 10²⁵ points per complex-plane unit. It is a product limit, not a guarantee that every location has resolved detail at that scale.
Read more: Technical white paper · Revision 19 · Inside the Infinity Engine
KEEP EXPLORING
This reference brings together the website’s technical explanations, app and testing guides, all 32 journal articles, the archived code review, and the 38-page technical white paper, Revision 19 (September 24, 2026). Entries link to their relevant reading; older posts and the archived review retain their original historical scope. Platform and mathematical references clarify selected definitions.
Glossary reviewed September 25, 2026. Looking for steps rather than definitions? Open the User Guide →