FRACTALS
M
ore than seven hundred years after Fibonacci, the American mathematician Benoit Mandelbrot (1924-2010) used recursion in a different way. He had never learned the alphabet and had never memorized the multiplication tables past the fives, but he wondered what it would mean to measure the size of a cloud and how you would do it. In pursuing this question, Mandelbrot would invent an entirely new branch of mathematics. Instead of applying recursion to numbers, he applied it to equations that generate geometric patterns. The computational process was so complicated it would have been impossible without computers. The result was the Mandelbrot Set, which generates a special kind of recurring patterns Mandelbrot named fractals (from the Latin word for fragments). When we look at things through a microscope or a telescope, they usually look entirely different at different scales or magnifications. Fractals, however, look similar at different scales. The crystals that make up a snowflake, for instance, resemble the snowflake itself. The veins of a leaf look like tree branches. A whirlpool is made up of smaller swirls containing still smaller swirls. Broccoli flowers are made up of tiny buds that resemble the whole flower. Understanding how objects change or remain the same at different scales is an important key to understanding a vast number of different kinds of things. Scientists now use fractals to uncover patterns in everything from the weather to the stock market.
SFI | 2011