Mandelbrot Metal for iOS & iPadOS
Mandelbrot Metal for iOS & iPadOS
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    • What are Fractals?
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    • Home
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      • What are Fractals?
      • Beyond Complex Numbers
      • Perturbation Rendering
      • The Tech in the App
      • Roadmap
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      • User Guide
      • Beta Signup
      • Beta Tester's Guide
    • FAQ
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Get the App
  • Home
  • Gallery
  • Palettes
  • Tech
    • What are Fractals?
    • Beyond Complex Numbers
    • Perturbation Rendering
    • The Tech in the App
    • Roadmap
  • Support
    • Community Portal
    • User Guide
    • Beta Signup
    • Beta Tester's Guide
  • FAQ
  • Blog
  • Media
    • News
    • Reviewer Guide
  • Reviews
    • Code Review
  • About
Get the App

Mandelbrot Metal: Real-Time Fractal Power

Explore infinite complexity with GPU-accelerated rendering, deep zoom, and studio-grade visuals.

Mandelbrot Metal turns your iPhone or iPad into a showcase of speed, precision, & stunning graphics.

Mandelbrot Metal turns your iPhone or iPad into a showcase of speed, precision, & stunning graphics.

Mandelbrot Metal turns your iPhone or iPad into a showcase of speed, precision, & stunning graphics.

Mandelbrot Metal turns your iPhone or iPad into a showcase of speed, precision, & stunning graphics.

Mandelbrot Metal turns your iPhone or iPad into a showcase of speed, precision, & stunning graphics.

Mandelbrot Metal turns your iPhone or iPad into a showcase of speed, precision, & stunning graphics.

What Is the Mandelbrot Set?

The Mandelbrot set is one of the most famous images in mathematics and serves as a cornerstone of fractal art. It resembles a black heart-shaped figure surrounded by endless spirals and intricate patterns. What makes the Mandelbrot set special is that it’s generated from an incredibly simple formula, yet it reveals infinite detail upon fractal exploration. Zoom in anywhere on its edge, and new shapes emerge—spirals, lightning-like branches, and even miniature ‘baby’ Mandelbrots. This never-ending complexity exemplifies how generative art can stem from simple rules, showcasing an infinite variety that has made the Mandelbrot set a symbol of both mathematics and beauty. For those interested in experiencing this stunning fractal art, there are even iOS apps available that allow users to explore these captivating patterns.

Learn About Fractals

Where Math Becomes Masterpiece — Real-Time, Infinite, Shareable.

Whether you’re a student, an artist, or simply curious about the world of fractal art, this iOS app is the fractal explorer you’ve been waiting for. Dive into the wonders of fractal exploration and experience the beauty of generative art, including the mesmerizing mandelbrot set.

Key Features

iPhone screen displaying a beautifully intricate render of the Mandelbrot Set fractal.

Fractals Without Limits

Experience infinite depth brought to life by Metal-powered precision, perfect for fractal exploration. Zoom effortlessly — not just thousands, but up to 10¹⁶× magnification — while every frame renders in real time, showcasing stunning generative art. Each dive into the mandelbrot set reveals new worlds of self-similar beauty, from delicate spirals to infinite filigrees, computed with adaptive precision that keeps exploration smooth even at cosmic depths. This is where mathematics becomes art — and your iOS app transforms into a window into infinity.

Learn How it Works
Navigation in Mandelbrot Metal is smooth and responsive.

Smart Navigation

Pinch, pan, or jump instantly to iconic regions like Seahorse Valley or baby Mandelbrots, perfect for anyone interested in fractal exploration. The built-in HUD displays coordinates, iteration budgets, and palette info, allowing you to understand the math behind the stunning generative art as you delve into the mesmerizing world of the Mandelbrot set.

Learn More
iPhone displaying a colorful Mandelbrot fractal set 3D Look.

3D Look — Lighting and Depth Across Infinity

Mandelbrot Metal features an innovative 3D Look mode that transforms fractal color data into a luminous terrain, perfect for fractal exploration. Utilizing real-time lighting and height-mapped shading, this feature simulates surface contours, highlights, and shadows derived directly from the fractal’s geometry. What was once a flat color now becomes a sculpted landscape of peaks and valleys, showcasing hidden depth and form in even the tiniest details of the Mandelbrot set.


As you delve into smooth bulbous regions or navigate razor-sharp filaments, the 3D Look mode offers a fresh dimensional perspective on the infinite geometry of fractal art. This seamless blend of mathematics, physics, and art creates a continuous visual experience, making it a standout feature of this generative art iOS app.

iPad displaying an ultra-detailed zoom into the Mandelbrot set fractal set with color palette and it

Adaptive Precision

Experience GPU-powered rendering for stunning fractal art with Auto Iteration and a calibrated slider that ensures perfect detail every time. With adaptive precision (FP32 → FP64 → FP128 double-double), every zoom remains razor-sharp, making fractal exploration effortless — whether you're admiring wide views or diving deep into the complex intricacies of the Mandelbrot set. This functionality makes it ideal for generative art enthusiasts and those using the iOS app.

Visit the Gallery
iPhone displaying a Mandelbrot fractal set and the Mandelbrot Metal bookmark menu.

Bookmark Your Favorites

Never lose your place in infinity during your fractal exploration. Save any zoom as a bookmark within this iOS app and return instantly, or mark your favorite fractal art discoveries, like the mesmerizing mandelbrot set, for quick access later. 


Bookmarks serve as presets that save coordinates, zoom, iterations, palette, and contrast, ensuring that the bookmarked image looks exactly the same each time you load it. 


This feature is perfect for building your own library of generative art and infinite wonders.

Learn More
iPad screen displaying a Mandelbrot set fractal with a palette selection menu open.

Rich Palette Library

Unlock the full spectrum of fractal beauty with Mandelbrot Metal’s powerful palette system, perfect for your fractal art and generative art projects. Choose from 140+ professionally crafted palettes, including 40+ Ultra-Wide (768-step) LUTs for ultra-smooth ramps, or wide (256-step) sets for punchier bands. Import colors from any photo — in HDR & P3 color, fine-tune gradient stops, and save your custom schemes to the library. With gamma-aware interpolation and lookup table (LUT) rendering, every color blend remains smooth and precise, even in the deepest zooms essential for fractal exploration. Whether you want mathematically accurate gradients or bold artistic expression, Mandelbrot Metal puts the colors of infinity at your fingertips, all within an intuitive iOS app that enhances your experience with the Mandelbrot set.

Explore Palettes
Colorful fractal pattern with blue and gold spirals on a dark background.

High-Resolution Capture

Transform your fractal exploration into stunning finished works of art. Export crystal-clear images at resolutions up to 8K, perfectly suited for large prints, presentations, or sharing online. Save directly to your photo library, copy to the clipboard, or share instantly with friends. Each capture preserves the vivid colors and intricate detail of your zoom, ensuring that your generative art masterpieces look as breathtaking on the wall as they do on your screen, including stunning depictions of the Mandelbrot set.

User Guide
iPad screen showing Mandelbrot Metal with the manage bookmarks sheet open.

A Fractal Community Is Forming

With powerful tools for importing and exporting palettes and bookmarks, you can now share your work between devices, safeguard your creations, and connect with others through your iOS app. The Community Portal extends that connection — a vibrant network where fractal art, generative art, science, and imagination converge, allowing for deeper fractal exploration and discussions around concepts like the mandelbrot set. 


Try the Community Portal preview.

iPhone displaying a very deep zoom into the Mandelbrot set using Mandelbrot Metal

Performance Modes

On the latest iPads and iPhones, Mandelbrot Metal delivers impressive interactive rates for fractal exploration at tens-of-thousands of iterations — without compromise. Experience the beauty of generative art as you balance speed and quality with GPU/CPU modes that utilize all available cores, super-sampling anti-aliasing, and low power options. The screenshot opposite showcases a deep zoom into the mandelbrot set at an astounding magnification of 21,022,541,715,612x, featuring 8,210 iterations and leveraging Chihuly [UW], one of the 36+ Ultra-Wide 768-step palettes available in the palette library.

Technology
The heads up display (HUD) in Mandelbrot Metal.

Live Learning

Experience fractal exploration like never before. With head-up display (HUD) overlays and real-time feedback, the Mandelbrot Metal serves as an educational tool that enhances your understanding of the mandelbrot set and how fractal art unfolds at virtually infinite scales, making it a unique generative art iOS app.

Get it on the App Store
A spectacular fractal produced using Mandelbrot Metal

Why Mandelbrot Metal Is Different

Mandelbrot Metal stands apart from traditional fractal exploration tools in three essential ways:


GPU-First Rendering Architecture


The core iteration loop operates entirely on Apple’s Metal compute framework, rather than relying on the CPU. This design enables sustained real-time navigation through fractal art, stable frame pacing, and immediate visual feedback even in regions of high complexity.


High-Precision Deep Zoom Engine


When GPU precision reaches its limits, Mandelbrot Metal transitions to a multi-core double–double precision CPU pipeline. Tiles refine progressively, ensuring the UI remains responsive, and magnifications of up to 10¹⁶× are maintained with computational accuracy — avoiding any approximations or interpolations commonly found in other generative art applications.


Modern Color Pipeline


Featuring over 137 curated palettes, 768-step Ultra-Wide LUTs, dithering, HDR/Display-P3 support, and deterministic bookmarks, this iOS app eliminates banding, preserves microstructure, and guarantees reproducible outputs across devices.


In practice, Mandelbrot Metal renders deeper, faster, and more accurately than traditional fractal apps, while producing cleaner gradients and higher-fidelity color. Its architecture embodies modern GPU compute principles rather than relying on legacy CPU-bound fractal visualization, and that difference is immediately evident in both performance and image quality.

More about the tech
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Mandelbrot Metal

The app where math becomes art, powered by Metal®

© 2025 Mandelbrot Metal - All Rights Reserved.

 

 

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, 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.

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