User Guide

What’s New in Version 3.0

Palette System: Steps, Resolution & Color Space

How palettes are defined

• Most non-[UW] built-ins are designed as compact gradients with about 5–25 color stops (control points), not hundreds of fixed colors.
• [UW] (Ultra-Wide) built-ins are also stop-based, using 768 steps and target a denser compiled result for ultra-smooth ramps.
• Custom palettes (including those imported from photos) may have any number of stops or explicit samples.

Native (compiled) LUT width

• At build time, those stop-based gradients are compiled into a native LUT:
  • Non-[UW] built-ins → 512-step LUT (wide).
  • [UW] built-ins → 768-step LUT (ultra-wide).
• This “512 vs 768” refers to the compiled LUT resolution, not the number of design stops.

Render LUT (what “1×1024” means)

• During rendering, every palette (whether compiled to 512 or 768) is resampled into a 1×1024 LUT for consistent precision and fewer rounding artifacts at deep zoom.
• Smooth mode interpolates between the 1024 taps; Exact LUT picks the nearest tap for discrete bands.

Wide Color (Display-P3) vs sRGB

• Display-P3 offers a wider gamut than sRGB for richer color on supported Apple displays.
• The current renderer and exports use an SDR 8-bit BGRA pipeline; Display-P3 is a wide-gamut color choice, not HDR output.
• For color-critical work, compare exports in a color-managed viewer and verify the result on the target display or print workflow.

First Run & Interface Tour

Welcome / Tutorial

A short, swipeable tutorial appears on first launch and is available any time.

• Show Welcome Now… — open the tutorial immediately.
• Show Welcome at startup — toggle whether it appears on launch.

Where to find it

• iPad: Tap the More (…) button in the top utility row.
• iPhone: Tap the More (…) button at top-right, then choose Welcome.

Free and Pro

Open More (…) and choose Upgrade to Pro to view the current monthly, annual, and lifetime purchase options. Purchases are tied to the App Store account; use Restore Purchases after reinstalling or moving to another device. Eligible legacy owners retain Pro access.

Navigation & Gestures

1. Pinch to Zoom. Two fingers to zoom smoothly.
2. Drag to Pan. One finger to move.
3. Double-tap to recenter + 2× zoom.
4. Single-tap Mandelbrot to Julia. In Mandelbrot mode, tap a point to open the Julia Set generated from that exact complex value.
5. Single-tap Julia to return. In Julia mode, tap once to return to the exact Mandelbrot view that created it.
6. Back. Return to the previous completed exploration state.
7. Forward. Move forward again after using Back.
8. Reset View. Returns to default framing.

Exploration History

Browser-style Back and Forward history is retained in Version 3. It is designed for trying a direction, comparing alternatives, and recovering a promising view without turning every experiment into a permanent bookmark.

What creates a history step

• A completed pan or pinch gesture
• A double-tap zoom, tap-to-Julia transition, or return to Mandelbrot
• A Fractal mode change, Coordinate Jump, bookmark load, or Reset

What is restored

Each state contains the center, zoom scale, iteration value and Auto setting, Mandelbrot or Julia mode, Julia constant and Mandelbrot return point, palette and palette name, contrast, 3D Look, and the active bookmark name when applicable.

How the history behaves

• Up to 50 states are kept for the current app session.
• Duplicate checkpoints are ignored.
• If you go Back and then begin a different exploration, the old Forward path is cleared.
• Palette or contrast adjustments do not create noisy standalone checkpoints; their current values are included when the next navigation step is recorded.
• Back and Forward are temporarily unavailable during an active gesture or capture.
• On an external keyboard, use Command-[ for Back and Command-] for Forward.

Fractal Modes

Use the Fractal selector in the top controls to choose the type of fractal being rendered. You can also create Julia Sets directly from the Mandelbrot Set by tapping a point on the canvas.

• Mandelbrot Set: the default mode. Each pixel supplies the complex value c in z ← z² + c, starting from z = 0.
• Julia Set: renders a related family of shapes using the current view as the starting value z and a Julia constant c. Julia mode is useful for symmetrical, branching, and lace-like compositions.

Creating Julia Sets from Mandelbrot points

1. Start in Mandelbrot Set mode.
2. Single-tap any point in the fractal view. The app uses that point as the Julia constant c and switches to the matching Julia Set.
3. Explore, color, bookmark, or capture the Julia Set normally.
4. Single-tap again while in Julia mode to return to the exact Mandelbrot view, zoom, and iteration state where you started.

The HUD title updates to show the current mode. In Julia mode, the HUD also shows the active c value, and bookmarks remember the mode and Julia constant so a saved Julia scene reopens correctly.

Go to Rect (Coordinate Jump)

Enter exact bounds — minX, minY, maxX, maxY. The view aspect-fits without stretching and centers precisely.

Where to find it

• iPad: Floating toolbar (Row 2) ▸ Go to Rect.
• iPhone: Tap the top-left floating Go to Rect button.

Iterations & Precision

Default Iteration Cap: 50,000. Lower for smoother performance, or raise for extreme detail (slower renders). The cap persists across launches.

For Mandelbrot rendering, each pixel represents a complex number c. For Julia rendering, the view supplies z and the saved Julia constant supplies c. The app iterates z ← z² + c until escape or the iteration budget is reached.

Auto Iteration (recommended)

1. Enable Auto in the toolbar.
2. Zoom/pan; the app adjusts iterations to avoid artifacts at depth.
3. Pause briefly to let quality stabilize.

Manual Iteration

1. Disable Auto.
2. Use the calibrated, non-linear slider for fine control.
3. Watch the HUD for the current “effective” iteration budget.

Precision Promotion

Infinity Engine (Automatic)

The Infinity Engine is the Version 3.0 deep-Mandelbrot path. The CPU constructs one high-precision double-double reference orbit for a carefully selected point. Metal then evaluates nearby pixels as perturbations from that orbit using quad-single expansion arithmetic, with recovery logic for deltas that stop being trustworthy.

What happens during a deep render

• Reference construction: the CPU computes and validates the orbit data shared by the frame.
• Massively parallel evaluation: Metal processes the pixel deltas and escape calculations across the GPU.
• Recovery and fallback: unstable perturbations are recovered where possible; the established renderer remains available when the Infinity path cannot safely complete the scene.
• Full-frame completion: render timing ends only after the requested viewport is complete and presented, not when setup or a single kernel finishes.

Interaction while rendering

Pan, pinch, and double-tap immediately transform the last complete frame so the canvas stays visible. When the gesture settles, Version 3.0 renders the exact new viewport. At very deep scales, coordinate updates use expansion-aware math so movement is not lost to ordinary Double rounding.

The progress indicator reports completion of the requested image as a percentage. It represents full-frame progress—not rows, setup work, or a kernel-only timer. The render is finished when the complete target fractal has been assembled and presented.

Depth and precision

Version 3.0 raises the former 1×10¹⁶ product ceiling to a validated maximum of 1×10²⁵. Navigation stops there so the HUD, gestures, bookmarks, and renderer share one honest boundary. Practical detail within the range remains scene-dependent, and the engine is adaptive finite precision rather than a general arbitrary-precision implementation.

Iteration Cap (Advanced)

• Choices: 5,000 · 10,000 · 15,000 · 25,000 · 50,000 (default) · 75,000.
• Where: iPad → More (…) ▸ Set Max Iterations Cap · iPhone → More (…) ▸ Set Max Iterations.
• Lower when you want cooler/quieter operation and faster captures at modest zoom.
• Raise when exploring extreme detail (expect slower renders).
• Slider calibration: 0–50% → 0…300; 50–100% → 300…Iteration Cap. Right edge snaps to the current cap.
• Effective iterations: The HUD shows “Iterations: N (effective)” to reflect the active auto/manual budget and precision context.

Palettes & Color Controls

Using built-in palettes

1. Open Palette.
2. Choose from 156 built-in gradients — neutrals, warm/cool sweeps, neon, metallic — including 55 Ultra-Wide [UW] sets for ultra-smooth ramps at deep zoom.
   Design-wise, most non-[UW] built-ins use ~5–25 stops and compile to a 512-step LUT; [UW] compile to 768 steps.
3. Star favorites to pin them on top.

LUT Width (Wide vs Ultra-Wide)

• Ultra-Wide (768-step) palettes: extremely fine gradations; ideal for smooth lighting transitions and deep-zoom work.
• Wide (up to 512-step) palettes: punchier band separation; great for bold, graphic looks or teaching.
• Both respect your Exact LUT / Smooth choice and render through the same 1×1024 table.

Color parameters (Exact LUT, LUT 512/1024, Display-P3/sRGB)

• iPhone: long-press the Palette button to reveal Exact LUT, LUT 512/1024, Display-P3, and Dithering options.
• iPad: tap the Brush icon in the palette toolbar for the same options.
• Exact LUT shows discrete palette steps; Smooth blends between steps. Use the live preview to evaluate palette, color-space, and dithering choices on the current scene.

Importing Gradients from Photos · Pro

1. Tap Import Gradient and pick a photo.
2. Choose sampling mode (row/column/stripe).
3. Fine-tune in the editor and save.

Managing Custom Palettes · Pro

• iPhone: More (…) ▸ Manage Palettes to delete individual custom palettes (built-ins are protected). Swipe left to delete. iPad: More (…) ▸ Manage Palettes.
• Clear All: remove all custom palettes in one tap (built-ins remain).
• If you add a palette with a duplicate name, it’s auto-numbered (e.g., “Chrome (2)”).

Palette Filters & Custom Tag

You can filter the palette list by type using the filter bar: All · Standard · Ultra-Wide · Custom.

• Standard shows palettes that are not tagged [UW] or [C].
• Ultra-Wide shows palettes whose names end in [UW] and use 768 steps for extra-smooth gradients.
• Custom shows palettes you created or imported from photos. These are automatically tagged with [C] in the name.

Exact LUT & Step Markers

Exact LUT shows discrete palette steps (no smoothing). Optional Step Markers draw guides at each palette band for instruction or stylized art. Toggle both in the toolbar.

Contrast & Image Tuning

1. Adjust Contrast for midtone balance.
2. Use higher contrast for separation; lower for subtle shading.
3. Combine with palette tweaks for best results.
4. Non-linear slider: the first half concentrates fine control near ~2–3; the second half covers up to 10.0.

3D Look (3D Effects) · Pro

Adds realistic surface shading to bring out depth and form — great for revealing subtle ridges along filigrees and bulbs. The effect is computed from the fractal’s gradient field and shaded with a physically inspired light model.

How to toggle

• iPad: Toolbar (Row 1) — tap 3D Look.
• iPhone: Bottom toolbar — tap the 3D Look toggle.

Tips

• Palettes: Neutral or metallic palettes can emphasize the 3D relief; vivid palettes create stylized lighting.
• SSAA: For the cleanest shading, SSAA reduces stair-stepping on highlights.
• Export: 3D shading is fully preserved in captures (Canvas/4K/6K/8K/Custom).
• Export: 3D Look state is saved along with bookmarks.

Sampling & SSAA

SSAA (Super-Sampling Anti-Aliasing) renders multiple sub-samples per pixel and averages their sampled RGB component values for smoother edges and fewer moiré artifacts. Because the current textures are BGRA8Unorm rather than sRGB-decoded textures, this is not a guaranteed linear-light average.

• Levels: ×2, x3, up to ×4 (device-dependent).
• When to use: For stills, tight spirals, and fine filigree.
• Performance: Heavier than 1×. For maximum responsiveness, leave SSAA off while navigating and enable it before a final still.

HUD & Readouts

• Mode: the HUD title shows the active fractal type, such as Mandelbrot Set or Julia Set.
• Loaded bookmark: after you open a bookmark, the HUD shows Bookmark: Name directly under the mode label until you load another bookmark or reset the view.
• Julia constant: in Julia mode, the HUD shows the active c value that defines the current Julia Set.
• Center: the rendering's center coordinates (x, y) as a complex number.
• Scale: magnification.
• Iterations: current iteration budget (shows “effective”).
• Contrast: current contrast setting.
• Quality: SSAA level, 3D mode, and the Infinity Engine indicator when those modes are active.
• Palette: name, LUT width, resolution.
• Color: Color space and LUT settings.

Bookmarks

Bookmarks save the principal inputs needed to reconstruct a scene: viewport, mode, iterations, palette, contrast, and visual settings. They are designed for repeatable exploration, although exact pixels and timing can vary with the app build, device, renderer path, and color management.

1. Tap the Bookmark button to bring up the Manage Bookmarks sheet.
2. Tap the "+" at the top of the sheet to add a bookmark.
3. Name and save. Stores fractal mode, Julia c value when applicable, center, scale, iterations (auto/manual context), contrast, palette, 3D Look, and precision context. The appropriate Version 3 renderer is selected automatically when the bookmark is reopened.
4. Tap a bookmark and press "Go" to reproduce the scene exactly. The HUD shows Bookmark: Name under the Mandelbrot Set / Julia Set label so you can see which saved view is currently loaded.

Sorting bookmarks

In Manage Bookmarks, use the Sort button (in the sheet’s top bar) to change how bookmarks are ordered:

Manage Bookmarks

• iPhone: More (…) ▸ Manage Bookmarks to delete individual bookmarks or Clear All. iPad: More (…) ▸ Manage Bookmarks.
• Sorting: Tap Sort to order bookmarks by Name, Newest, Oldest, Mode, Iterations, Palette, or Scale.

Bookmark & Palette Sharing

Share or move your bookmarks and palettes using the management sheets only.

Share / Import Bookmarks

• Open: iPhone → More (…) ▸ Manage Bookmarks · iPad → More (…) ▸ Manage Bookmarks.
• Export one: swipe right on a bookmark to reveal Export.
• Export all: tap Export All at the top of the sheet.
• Import: tap Import at the top of the sheet and choose a file.
• Duplicates: if a name already exists, the new item is kept by appending a number (e.g., “Chrome (2)”).

What’s shared (Bookmarks)

• View: exact center and zoom (scale).
• Fractal mode: Mandelbrot Set or Julia Set.
• Julia constant: Julia bookmarks include the saved c value, so imported Julia scenes reopen as the same Julia Set.
• Iterations: mode (auto/manual) and current value.
• Appearance: contrast, palette name, and 3D Look state.
• Precision context: the saved scene contains the information needed for Version 3 to select its appropriate renderer automatically.

Share / Import Palettes · Pro

• Open: iPhone → More (…) ▸ Manage Palettes · iPad → More (…) ▸ Manage Palettes.
• Export one: swipe right on a palette to reveal Export.
• Export all: tap Export All at the top of the sheet.
• Import: tap Import at the top of the sheet and choose a file.
• Duplicates: imported palettes with an existing name are auto-numbered (e.g., “Chrome (2)”).

What’s shared (Palettes)

• Gradient data: full palette steps (the LUT gradient), derived from your original design stops.
• Metadata: palette name, color space (Display-P3 or sRGB), and LUT resolution (512 or 1024).
• Color fidelity: files include the necessary info for consistent appearance on devices that honor the embedded profile.

Settings

Capture & Export

1. Frame your scene.
2. Optionally enable SSAA and/or 3D Look for a still.
3. If you are at deep magnification, wait for the Infinity Engine render to complete.
4. Tap Capture (center-bottom on iPhone).
5. Select resolution: Canvas is included in Free; Pro adds 4K, 6K, 8K, and Custom (aspect-fit preserves framing).
6. Export PNG using the selected sRGB or Display-P3 setting. Final color tagging depends on the UIKit image/graphics context, so verify color-critical output in your target workflow.
7. If Photos access is restricted, use the Share Sheet to save to Files or send to another app.
8. 3D Effects: Captures include 3D shading exactly as seen on canvas.

Perturbation Rendering

At extraordinary Mandelbrot magnifications, the CPU computes a double-double reference orbit and Metal evaluates nearby pixels as deltas using quad-single expansion arithmetic. Recovery logic handles deltas that leave the trustworthy perturbation range, and an established fallback path remains available. Julia uses its direct Julia renderer for the active c value rather than the Mandelbrot reference-orbit path.

Troubleshooting

Image looks coarser while moving

• During panning/zooming the app prioritizes frame rate: it may temporarily lower iterations and sampling. For the cleanest stills, stop moving and enable SSAA for capture.

At ultra-deep zoom, it takes time to “finish”

• Expected: the Infinity Engine must build a reference orbit and complete the requested full-frame Metal render.
• Render time varies sharply with the scene, iteration budget, SSAA level, drawable size, device, and thermal state.
• Use the on-screen rendering state as the completion signal; a setup or kernel-only time is not the time to a fully presented fractal.

Colors look different in other viewers or on another device

• Exports use the selected sRGB or Display-P3 graphics setting. Color tagging depends on the UIKit image/graphics context, so verify color-critical files in the viewer and workflow you plan to use.
• Exports are SDR. For cross-device consistency, compare sRGB and Display-P3 output in a color-managed viewer and choose the version appropriate for the target display or print workflow.
• Exact LUT vs Smooth palette modes can shift apparent hues slightly. Match the mode when comparing.
• Prefer in-app Export over OS screenshots for color-critical work.

Very deep zoom shows speckles or noise

• Let Auto Iteration settle at moderate depths; at ultra-deep, wait for the Infinity Engine to present the target view after interaction stops.
• Enable SSAA for still frames to reduce aliasing; use Smooth palette mode and an Ultra-Wide palette when you want gentler gradients.
• Adjust the Maximum Iteration Cap (5,000 · 10,000 · 15,000 · 25,000 · 50,000 (default) · 75,000) — lower for cooler/quieter operation, higher for extreme detail.

FAQ

Are all non-[UW] palettes 512 steps?

Clarification: Design-wise, most non-[UW] built-ins use about 5–25 color stops. At build time, those stops are compiled into a 512-step native LUT. Palettes marked [UW] compile to 768. Regardless of native/compiled width, the renderer then resamples the palette into a 1×1024 LUT for display (with Smooth or Exact LUT behavior).

How does the iteration slider work?

It’s calibrated: 0–50% → 0…300; 50–100% → 300…Maximum Iteration Cap. If the cap ≤ 300, it’s linear. The right edge snaps to the current cap exactly.

When does the Infinity Engine activate?

Automatically for Mandelbrot views that benefit from the deep reference-orbit path. Renderer selection is based on the scene and device rather than a user-facing threshold or toggle.

Is Version 3 arbitrary precision?

No. Version 3 combines a CPU double-double reference orbit with Metal quad-single perturbation and recovery. The validated release range extends through 1×10²⁵, but the implementation remains adaptive finite-precision computation.

Why doesn’t every deep view render instantly?

Reference construction and a full-resolution, high-iteration GPU pass still require real work. Performance varies by bookmark and device; the completion time is measured through presentation of the entire target frame.

Do captures match the canvas?

Canvas capture matches the completed viewport. Pro high-resolution exports render to the selected output size. At deep magnification, let the target frame finish before capture.

Glossary