Free! What is a Fractal? A fractal is a never ending pattern that repeats itself at difference scales. Where do we find fractals? In nature fractals include branching patterns like trees, river networks, lightning bolts, blood vessels and spiral patterns like seashells, hurricanes, and galaxies. In math, like the Mandelbrot set, fractals are formed by calculating a simple equation thousands of times, feeding the answer back in to the start.