Chaos Game

Pick a polygon, set a few rules, and watch the screen fill with fractal geometry one dot at a time. The chaos game algorithm works by repeatedly jumping halfway toward a randomly chosen vertex — a dead-simple rule that somehow produces the Sierpinski triangle and dozens of other intricate self-similar patterns. You can change the number of sides, adjust the jump ratio, restrict which vertices can be chosen consecutively, and swap in your own color scheme to see how each tweak reshapes the result.

There's real math underneath, but you don't need to know any of it to enjoy experimenting. Crank the restriction settings and a jagged triangle quietly reorganizes itself into something that looks hand-drawn. It's the kind of app that makes you want to keep changing one variable at a time just to see what breaks — or what accidentally looks great. Flocking Boids covers similar ground if you're drawn to simple rules producing complex emergent behavior.

Find it alongside other generative tools in interactive apps. A larger screen helps here because density increases with dot count and the fine structure of the pattern becomes visible only when you have the pixels to show it.