Thursday, 20 January 2011
Benoit Mandelbrot (died 14.10.10) was the mathematician who disclosed many of the mysteries of fractal geometry. Fractals are geometric shapes which when magnified reproduce the same qualities over and over. Mandelbrot found a way to mathematically describe the shapes of natural forms such as mountains and coastlines, then he managed to measure them, leading on later to the basis for the Chaos theory in applied mathematics.
He wrote ‘clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightening travel in a straight line.’
In his essay’ How long is the coast of Great Britain’(1967) he explained it depended on the scale it was measured at, as you move in closer you find more and more, each bay had more bays.
Mandelbrot worked with IBM examining electronic noise which caused errors with IBM transmissions. He discovered the noise came in patterns and the more it was observed the more complicated the pattern became. When he examined it more he could see the ‘self-similarity’ of the patterns. Mandelbrot finally managed to produce a mathematical formula to represent these patterns,
Z = Z ² + C is now known as the Mandelbrot set.