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Mandelbrot Metal is a next-generation fractal explorer for iPhone and iPad.
Built on Apple’s Metal GPU framework, it renders the Mandelbrot and Julia sets in real time with stunning clarity and smoothness. The app combines adaptive precision, vivid palette systems, ultra-deep zooming, and 3D lighting effects to bring the mathematics alive.
It turns one of the most complex objects in math into an immersive art studio — a place where you can explore endlessly, discover breathtaking structures, and capture or share the images you create.
• Artists: Create "wall-worthy" art with 8K export of images for print.
• Math/Science Folks: Explore the infinite complexity of the famous Mandelbrot set and Julia sets with the highest precision.
• Power Users: Turns your iPhone or iPad into a showcase of speed, precision, & stunning graphics.
• Casual Users: No expertise neded. Relaxing, fun, and easy to create beautiful visuals.
Mandelbrot Metal is built differently. Instead of relying on older CPU-based methods, it uses Apple’s Metal graphics engine to deliver true real-time fractal rendering. You get smooth 60 FPS zooming, clean detail, and instant feedback even at extreme magnifications.
When you go really deep, the app automatically switches to a high-precision multi-core CPU mode that keeps going long after other apps stall or lose accuracy.
It also has one of the most advanced color systems available in any fractal app:
Every bookmark is deterministic, meaning scenes render exactly the same on any device. And for creators, you can export images up to 8K with perfect gradients.
In short: It’s faster, deeper, more accurate, better colored, and easier to use than traditional fractal apps — designed for both artists and explorers.
See our comparison table for more information,
With Mandelbrot Metal's adaptive precision (32-bit, 64-bit, and 128-bit Double-Double math) plus perturbation rendering techniques, you can currently explore magnifications up to 10¹⁶× — that's ten-million-billion times deeper than the default view. Going forward, even deeper zooming is planned. (see Roadmap)
Yes. You can export captures up to 8K resolution, save them to Photos, copy them to the clipboard, print, or share directly to social apps. Mandelbrot Metal is designed to output professional-quality images. (See User Guide)
With release 2.0, Mandelbrot Metal supports both the Mandelbrot and Julia sets. Burning Ship is on the roadmap.
A Julia set is a close cousin of the Mandelbrot set — a fractal sculpted from the same simple rule, but viewed from a different angle.
Like the Mandelbrot set, every Julia set is built from the equation z → z² + c, where z and c are complex numbers. The difference is which number you hold still and which one you let vary:
In the Mandelbrot set, you start at z = 0 and ask: for which values of c does the sequence stay bounded? The answer, plotted across the complex plane, is the iconic Mandelbrot shape.
In a Julia set, you fix a single value of c and ask the opposite question: for which starting values of z does the sequence stay bounded? Every choice of c produces a brand-new Julia set with its own unique character.
In other words, the Mandelbrot set is a map of all possible Julia sets — every point inside it corresponds to a connected, intricate Julia set, while points outside produce delicate, disconnected "dust." This deep relationship is one of the most beautiful results in modern mathematics, and it’s what makes exploring the two together so rewarding.Add an answer to this item.
Same math, very different art.
The Mandelbrot set is a single, fixed object — there is only one Mandelbrot set. Julia sets, on the other hand, form an infinite family. Choose a slightly different value of c and the entire shape transforms — spirals tighten, dendrites branch, swirls fold inward, and dragon-like curves emerge.
Some quick visual cues:
Julia sets pulled from inside the Mandelbrot set are connected — a single continuous shape, often with mirror or rotational symmetry.
Julia sets pulled from near the boundary of the Mandelbrot set are the most ornate — spirals, seahorses, dragons, lightning, and lace.
Julia sets pulled from outside the Mandelbrot set break apart into Fatou dust — an infinite scattering of disconnected points (this is Fatou and Julia’s famous dichotomy theorem).
So while the Mandelbrot set shows you the global structure of the z² + c universe, Julia sets let you zoom into a single coordinate of that universe and watch what it looks like from the inside.
Julia sets are rendered by the same Metal GPU pipeline that powers the Mandelbrot view — just with one parameter swapped.
For every pixel on screen, a Metal compute kernel maps the pixel’s position into a complex number z₀ and then iterates z → z² + c, where c is a single constant chosen by you. The iteration count it takes for z to escape a fixed radius (or to converge into the set) is fed through Mandelbrot Metal’s smooth-coloring formula and the unified 1024-tap render LUT to produce the final color — exactly the same path used for Mandelbrot rendering.
That means everything you already love about Mandelbrot rendering carries straight over:
The only thing that changes under the hood is the constant c passed to the shader, plus how the per-pixel coordinate is interpreted — z₀ instead of c. The mathematics, the precision strategy, and the color pipeline are otherwise identical.
Tap the Mandelbrot set — that’s your Julia coordinate.
Because every point in the Mandelbrot plane corresponds to a unique Julia set, Mandelbrot Metal lets you pick c by simply pointing at a spot on the Mandelbrot view. The app instantly switches into Julia mode and renders the Julia set for that coordinate.
You can:
A great starting move: zoom into a seahorse valley, mini-Mandelbrot, or dendrite tip on the Mandelbrot view, tap that location, and switch to Julia — you’ll see the local "personality" of that region expressed across the entire Julia plane.
Because the boundary of the Mandelbrot set is itself a fractal — and that boundary is where Julia sets are most sensitive.
Tiny movements of c across the Mandelbrot boundary can swing a Julia set from a smooth disk, to a spiral galaxy, to a lightning-bolt dendrite, to a cloud of disconnected dust. This extreme sensitivity is exactly what makes Julia exploration so addictive — you’re never more than a small nudge away from a completely new fractal landscape.
It’s also why bookmarking matters. A Julia coordinate that produces a stunning image can be a millionth of a unit away from one that looks ordinary, and Mandelbrot Metal’s deterministic bookmarks let you return to the exact spot every time.
Ultra-Wide palettes use 768 color steps for exceptionally smooth gradients and are labeled with [UW] in the palette library.
Unlike standard palettes, which are expanded into 512-step color ramps, Ultra-Wide palettes are defined with 768 pre-sampled steps, often derived directly from source images. This higher step count provides finer tonal resolution, making them especially effective for deep zooms, subtle lighting transitions, and regions where gentle shading reveals hidden structure.
During rendering, Ultra-Wide palettes are handled just like all other palettes — they are resampled into the renderer’s unified 1024-tap LUT (when High-Res LUT is enabled) to ensure consistent precision and smoothness across all palette types.
In short, Ultra-Wide palettes offer:
Learn more about how palettes work in the Palettes Guide.
The High-Res LUT (1024) setting controls the internal color precision used by the renderer when mapping fractals to color.
When enabled, Mandelbrot Metal renders using a 1 × 1024 lookup table (LUT) — a single row containing 1,024 evenly spaced color samples. Each pixel’s normalized escape value (from 0.0 to 1.0) is mapped into this table to determine its final color. In Smooth mode, neighboring entries are interpolated to produce continuous gradients.
Palettes themselves are defined at different resolutions:
Regardless of whether a palette originates as 512 or 768 steps, it is resampled into the unified 1024-tap render LUT before being used by the GPU.
What Happens When High-Res LUT (1024) Is Disabled?
When High-Res LUT (1024) is turned off, the renderer skips the 1024-step render LUT and instead samples colors directly from the palette’s native resolution:
In this mode:
This mode can be marginally lighter-weight and is useful for:
Why Enable High-Res LUT (1024)?
Using a unified 1024-tap render LUT:
In short, High-Res LUT (1024) standardizes palette rendering at the highest internal precision. Disabling it trades a small amount of color fidelity for slightly reduced processing overhead and more palette-native behavior.
Absolutely! You can scan gradients from your photos and other images in your Photos library by tapping the Import Gradient button . You're also able to exchange custom palettes with other users and with the community . Learn more about palettes.
Advanced users and programmers who are comfortable working in the terminal can use the command line interface (CLI) program photo2palette for more control over the import process.
Mandelbrot Metal makes it easy to share and exchange your discoveries. From Manage Bookmarks or Manage Palettes, simply swipe right on any item to reveal the Export button — or tap Export All to back up your entire collection. To import, tap the Import button at the top of the same sheet and select a file you’ve received via AirDrop, Mail, Messages, or Files.
Shared bookmarks include exact coordinates, zoom level, precision mode, palette, and rendering settings — so anyone who opens them sees the same fractal view you created. Shared palettes include the full gradient, color space, and name ensuring color consistency across devices.
All exported files are universal, meaning you can freely exchange them between your iPhone and iPad or share them with other users. This also makes it easy to back up your collections for safekeeping.
A community sharing portal is coming soon, where you’ll be able to upload, browse, and download bookmarks and palettes from other explorers — creating a global space for discovering, exchanging, and showcasing fractal art.
No personal data is ever included in shared files — only the rendering parameters needed to reproduce the image precisely.
Mandelbrot Metal runs on iPhone and iPad with iOS/iPadOS 18.6 or later. Performance scales with your hardware — the latest models render faster and capture higher-resolution images.
Not yet. Right now, Mandelbrot Metal is built for iPhone and iPad, but macOS support is under consideration for the future. However, if you have a Mac with Apple silicon, you can run the iOS/iPadOS versions on your Mac right now.
No. Rendering is fully on-device, powered by Apple’s Metal GPU framework. The only time you’ll need internet is for updates, optional beta feedback, or sharing online.
Fractal rendering is compute-intensive, but Mandelbrot Metal is optimized with adaptive iteration counts, GPU acceleration, and idle high-quality modes. On the latest Apple devices, you can explore for hours without overheating or rapid drain.
Yes. You can save bookmarks with full zoom/position/palette/contrast/3D and other rendering settings and return to them instantly. Exporting, importing, backing up, and sharing of bookmarks is also available. See "How do I share or back up my bookmarks and palettes?", below).
Mandelbrot Metal features full import/export support for both Bookmarks and Palettes, making it easy to share your favorite views and color sets between devices or with other users.
Bookmarks
Palettes
Import from Photos
You can also create new palettes from any image:
Whare are the Files Stored?
Exports are saved to the Files app under On My iPhone / Mandelbrot Metal (or iCloud Drive if enabled) with the prefix Bookmark- and extension .json.
You can open them from Files, Mail, or Messages and tap Open in Mandelbrot Metal to import.
Tips
Complex numbers are simply numbers with two parts: a real part (the normal numbers we use every day) and an imaginary part (a second, perpendicular direction). A helpful way to picture them:
Imagine a map...
A location like “3 miles east, 4 miles north” has two components, yet it describes a single point.
A complex number works the same way — the real part is like east-west, the imaginary part is like north-south.
Despite the name, “imaginary” doesn’t mean fake. It’s just the label mathematicians picked for this second direction. Once you allow that extra axis, problems that were impossible on the regular number line suddenly have simple, elegant solutions.
Add two complex numbers? You’re just moving around the map. Multiply them? You’re rotating and stretching — and that’s where things get interesting.
Complex numbers power everything from signal processing and quantum mechanics to computer graphics and the stunning geometry of fractals. In fact, the entire Mandelbrot set is created by repeatedly multiplying and adding complex numbers — the simple rule that unlocks infinite beauty.
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Mandelbrot Metal is a registered DBA (Doing Business As) of Michael Stebel Consulting, LLC, a Florida limited liability company.
Trademarks: Apple, the Apple logo, iPhone, iPad, Mac, macOS, iOS, Xcode, Swift, SwiftUI, and Metal are trademarks of Apple Inc.,
registered in the U.S. and other countries. All other product names, logos, and brands are property of their respective owners.