Fractal Theory and Benoit Mandelbrot
Overview
In 1975 Benoit B. Mandelbrot (1924- ) wanted a word to describe the strange group of mathematical sets he was studying, and looked for inspiration in his son's Latin dictionary. The term he created was "fractal" to describe sets that modeled such diverse phenomena as cloud boundaries, stock market prices, plant growth, and even the distribution of matter in the universe. Mandelbrot's attempts to make the mathematical, scientific, and business communities, as well as the general public, aware of fractals have led some critics to see him as obsessed, both with fractals and his own place in history. While practical uses of fractals have been few, these unusual mathematical sets have left their mark on many areas, from financial analysis to Hollywood special effects.
Background
In the late nineteenth and early twentieth centuries a number of mathematicians described strange mathematical sets that seemed to defy logic. One such set, the Koch curve—named after Nils Fabian von Koch (1870-1924)—is constructed by taking a line segment and replacing the middle third of the line with the other two sides of an equilateral triangle. The result has four line segments, each one-third the length of the original line.
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