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 their vivid and complex colors to create artwork of your own.

Fractals mathematically are sets of infinitely complex patterns that show recursion, meaning their 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 was able to do was that with computers, the brand new IBMs machines, he could finally illustrate to the theory.

What These Tools Do

This page directs you through two tools: the Fractal Explorer and the Fractal Composer. Full directions for both tools can be found here. These tools works best on desktop. Mobile visitors will be rerouted to the kids’ fractal explorer.

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

The Composer is a seperate canvas page that directs from the Explorer. Cut a piece out of any fractal using the Cutout tool in the Fractal Explorer, and it transfers directly into the Composer. 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.