Sunday, July 12, 2009

On Mandelbrot's Fractal Geometry of Nature

Why is geometry always described as “cold” Wind blown clouds and “dry?" One reason lies in its Stretched into wisps inability to describe the shape of a Water filled cloud, a mountain, a coastline, or a tree. Clouds are not spheres, Sinking into mountains are not cones, coastlines are not circles, and bark is not smooth, Penetration of nor does lightning travel in a straight line. More generally I claim that Mountain peaks many patterns of Nature are so irregular Sacred rite and fragmented, that compared with Euclid--a term Shrouded in a used in this work to denote all of standard Veil of fog geometry--Nature exhibits not simply a higher degree but an altogether different level of complexity. The number of distinct Act of Nature scales and length of natural patterns is for all practical purposes infinite. The existence Climaxing in of these patterns challenges us to study these Lightning bolt patterns that Euclid leaves aside as being “formless,” to investigate Water birth the morphology of the Mountain streams “amorphous.” Mathematicians have disdained this challenge, however, Pines ferns and have increasingly chosen to Condensate waters warmed flee from nature by devising theories unrelated In sunlit glades to anything we can see or feel……at first glance such Evaporate rise misbehavior looks most bizarre and even terrifying….contrary to rumors Reborn in that analysis is a dry subject, these fractals Wind blown clouds tend to be astonishingly beautiful.

(Text: Mandelbrot; The Fractal Geometry of Nature)