Fractal Art Generator, Explorer and Composer

The Beauty of a Fractal

Fractals are mesmerizing, alien but familiar. They echo the shapes found in our physical world, but repeated in odd dimensions. That is what fractals literally are, odd dimensions, or as Benoît Mandelbrot wrote, rough. This fractal art generator lets you play with the vivid and complex colors to create artwork of your own.

Fractals mathematically are sets of infinitely complex patterns that show recursion, meaning the basic shape repeats again and again. Zoom into the edge of a shape and you find yet another shape, same structure, smaller scale.

Mathematicians have a word for this: self-similarity. Magnified snowflakes, coastlines, ferns, in the fractal universe, they keep on repeating. In the real world they stop, of course, but graph the rule mathematically and they go on forever.

The word fractal itself comes from the Latin fractus, meaning broken or fractured. Benoît Mandelbrot coined it in 1975, though the underlying field had been emerging for a century. What Mandelbrot saw was that computers, his brand new IBMs, could finally catch up to the theory.

What These Tools Do

This page directs you through two tools: the Fractal Explorer and the Fractal Composer. The directions can be found here. This tool works best on desktop, for those on mobile, the tool will reroute to the kids’s fractal explorer.

The Fractal Explorer lets you generate 20 different fractals, each listed below the tool button. Each one has its own controls: colour palettes, iteration depth, zoom, angles, particle counts. The escape-time fractals (Mandelbrot, Julia, Burning Ship, Newton) are zoomable and pannable, scroll to zoom, drag to pan. The others regenerate when you adjust their settings.

The Composer is a canvas tool that sits alongside the Explorer. Cut a piece out of any fractal using the Cutout tool in Fractal Explorer, and it transfers directly into the Composer via shared browser storage. From there you can arrange pieces, layer them, rotate and scale them, draw over them with the built-in brushes, and finally export the whole composition as a PNG.

Together they work as a generative art studio.