Infinite Self-Similarity

A fractal is a shape that looks similar at every scale. Zoom into a coastline and you see the same jagged pattern at one mile as at a hundred miles. Broccoli florets resemble the whole head. Tree branches mirror the shape of the full tree.

Benoit Mandelbrot coined the term in 1975 and showed these shapes are not just curiosities — they describe how nature actually builds. Clouds, mountains, river networks, and blood vessels all follow fractal geometry far better than the smooth shapes of classical math.