The Fractal Geometry of Nature

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   Many shapes in nature — a coastline, a snowflake, a lung — repeat the same pattern no matter how much you zoom in or out.

   The Fractal Geometry of Nature · 1982

   Natural forms are fractal: their jagged structure repeats identically at any scale of magnification.

   If you measure a country's coastline on a large map, you get one number. Measure it with a much smaller ruler, tracing every little bay, and the number grows. Mandelbrot called these shapes fractals: equally jagged at any scale. Their math can describe mountains, lungs, and even stock market prices.

   “Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.”

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