I’ve finished my next project. It’s called the Fractal Machine.
It’s a geometry tool that draws base-motif fractals from five inputs.
If you are unfamiliar with them, fractals are shapes that exhibit self similarity at different scales. This particular type of fractal is created by substituting every line with a shape called the “motif” a number of times.
The glyphs above show the controls working in isolation (at an angle of 60°), but the fractal machine’s complexity comes from the way in which they interact. Once these inputs are given, the fractal tries to dynamically resize itself in a way that highlights these relationships. So the length of a single line changes, but the overall size of the fractal and positions of analogous components should be relatively stable. Figuring out the trigonometry that made all this work turned out to be pretty fun.
I figure that some people will want to use this to explore human-scale geometric relationships, while other people will just want to turn on the animation, colors and trails and watch it like a music visualizer. Hopefully most people do a little bit of both and enjoy the way one builds into another. One of my favorite things about recursion is that it can let you see simplicity inside complexity.
If you want the quick tour, some shapes worth checking out include: The famous Koch Snowflake, something I’ve been calling the Koch Mirror, Sierpinski’s Triangle, Sierpinski’s Carpet, this great pentagon fractal, and this cube snowflake I found.
If you find yourself staring at this for a decent amount of time, you might like to know that you can press H to hide the controls and use the keyboard instead. I’ll leave you to work out what buttons do what.