The Mandelbrot set is one of the most iconic images in all of mathematics — an infinite world of swirling spirals, filigrees, and repeating patterns that reveal new structure no matter how deep you zoom. For decades, exploring it required a desktop computer and patience.

Now, with Mandelbrot Metal, you can dive into infinity right from your iPhone or iPad — in real time.

🔍 What Makes the Mandelbrot Set So Special

At its core, the Mandelbrot set is a simple formula:

z = z² + c (where z and c are complex numbers)

Repeated billions of times, that tiny equation generates one of the most complex and beautiful shapes in mathematics. Each point on the screen represents a complex number c, and, by testing whether that number “escapes” to infinity, we paint its destiny in color.

Every zoom reveals self-similar detail — miniature versions of the whole, twisted and transformed into unique landscapes. It’s a bridge between art, math, and computation.

📱 Exploring with Mandelbrot Metal

Mandelbrot Metal was built from the ground up to let you explore the Mandelbrot set with speed, precision, and artistry — powered by Apple’s Metal® GPU framework.

Here’s how to start exploring:

  1. Pinch & Zoom — Just like a map. Zoom into any region that catches your eye.
  2. Drag & Pan — Navigate smoothly through the fractal landscape with your fingertip.
  3. Auto Iterations — Let Mandelbrot Metal dynamically adjust detail as you zoom deeper.
  4. Precision Modes — Switch between GPU FP32, FP64, or Double-Double precision for extreme zooms (over 10¹⁶×).
  5. 3D Look Mode — Toggle depth shading to reveal the surface contours of the fractal.
  6. Color Palettes — Choose from over 130 curated palettes, including over 22 Ultra-Wide 768-step ones for extraordinary gradient smoothness — or import your own from any photo.
  7. Bookmarks & Sharing — Save your favorite locations, export them, and share or import bookmarks with other users.

Every gesture, every color, every zoom is calculated in real time — with no pre-rendering or delays. You’re seeing pure mathematics unfold live on your screen.

🧭 Visit the Community Portal

Want to explore breathtaking fractal scenes right away?

Visit the Mandelbrot Metal Community Portal, where you can download ready-to-explore bookmarks created by other users (and by us).

Each bookmark opens directly in Mandelbrot Metal — a perfect way to discover stunning regions or learn what makes certain coordinates visually striking.

🧠 Tips for Deeper Exploration

  • Start near the cardioid — the large black heart shape in the center. Zoom into its edges to find spirals and “baby Mandelbrots.”
  • Experiment with palettes — Ultra-Wide 768-step palettes are ideal for smooth gradients and subtle lighting transitions.
  • Try 3D Look — it highlights contour shapes that can be easy to miss in flat color.
  • Use Deep Rendering Mode — automatically activates at extreme zooms to ensure every pixel is accurate.
  • Share and import bookmarks — exchange discoveries with friends or download new ones from the Community Portal.
  • Capture your discoveries — export up to 8K resolution for fractal art prints or wallpapers.

⚙️ Behind the Scenes

Mandelbrot Metal combines GPU acceleration, multi-core CPU tiling, and perturbation theory to deliver scientific-grade precision in real time. It dynamically promotes precision as you zoom — from 32-bit floats to 128-bit Double-Double math — so you can explore to magnifications previously impossible on mobile.

Every frame is computed, mapped through your chosen color palette, and displayed in HDR / Display-P3 color on supported devices — revealing the full vibrance of mathematical beauty.

🌌 Explore Infinity

With Mandelbrot Metal, your iPhone or iPad becomes a window into the infinite. Whether you’re a mathematician, artist, or simply curious explorer, you can now experience the Mandelbrot set like never before — in your hand, in motion, and in living color.

Ready to begin?

👉 Download Mandelbrot Metal on the App Store