The Mandelbrot set is an image created by repeatedly applying a very simple rule (z → z² + c). Click anywhere on the image to zoom in on that point. Even as you zoom in, complex and similar patterns continue endlessly.
For each point c, we start with z=0 and repeatedly apply z → z² + c. If the magnitude of z stays bounded instead of growing without limit, the point is black (it belongs to the set); if z grows quickly, the point is colored according to how quickly it grows.