Yes, we know. Another Mandelbrot app. The App Store has roughly as many fractal explorers as there are florets on a Romanesco broccoli — which, incidentally, is also a fractal, so at least we're in good company. We're not here to dethrone them. We just wanted our own fast, honest, no-nonsense way to fall down this particular rabbit hole, hand-built and tuned to run beautifully on your device — and we figured a few more people might enjoy falling in with us. No account, no ads, no data collection, no network access required — the entire render happens on your device.

To paint the Mandelbrot set, we go point by point across the plane: each point becomes C, written as x + i·y — x is the ordinary left-right coordinate, and i·y is the up-down one. We repeat a stupidly simple calculation — Z_n+1 = Z_n² + C, starting from zero — over and over, using that point's own fixed C the whole way through. For some points, the result stays small forever. For others, it rockets off to infinity.

Color each point by how fast (or whether) it escapes, and you get the Mandelbrot set: the dark, cauliflower-shaped body is "in" — those are the points where Z never blows up — and the storm of color swirling around its edge shows you how everything else falls apart. Zoom into that edge and you'll find spirals, seahorses, and tiny copies of the whole set again, and again. That endless, self-similar roughness is what mathematicians call a fractal — and it turns out to be everywhere: ferns, coastlines, lightning, blood vessels, broccoli.

An ambient, hands-free tour of the Mandelbrot set built for the big screen. AUTO explores continuously, swapping in a fresh palette every few seconds (smooth-generated, or a real vintage Fractint classic fetched live from our online library), and one button on the Siri Remote swaps the whole screen to the connected Julia set.

The Mandelbrot set as a real object in your room, sized and placed on any wall you like. Pinch to zoom the way you would on iPhone or iPad, then drag with one or two hands to shift the palette and its cycling frequency live, right in front of you. Control, Julia, Palettes, and the Online Library each open as their own independent window, free to arrange around your space — swap one to a full-screen Julia set while the Mandelbrot keeps exploring in another.

Fractals owe their name to Benoit Mandelbrot, a Polish-born, French-educated mathematician who spent much of his career at IBM. Building on ideas French mathematicians Gaston Julia and Pierre Fatou had explored decades earlier with nothing but pencil, paper, and remarkable imagination, Mandelbrot had something they never did: a computer. In 1980, using it to visualize this deceptively simple equation, he produced the image that now carries his name. Five years earlier, in 1975, he'd already coined the word "fractal" itself, from the Latin fractus — "broken" — to describe shapes that stay rough and irregular at every scale. His argument, laid out in a landmark 1982 book, was that nature simply isn't Euclidean: clouds aren't spheres, mountains aren't cones, coastlines aren't circles. The image you're about to lose an afternoon in has since been nicknamed "the thumbprint of God."

Prefer a direct download? DoomFracting 2.2 for macOS  ·  .dmg, notarized by Apple  ·  macOS 13 Ventura or later. The App Store copy updates itself; the direct build you update by hand.