Fractals and Chaos

Fractals are the signature of chaotic systems. In a chaotic system, tiny changes in the starting point lead to wildly different outcomes — the famous butterfly effect, where a hurricane's track hinges on conditions too small to measure.

Weather and population swings behave this way because they run on feedback loops that amplify small causes into large effects. In 1963, Edward Lorenz mapped the first such system, and the shape it traced turned out to be a fractal.