Zooming into a fractal
Posted May 21, 2010 6:53 a.m. EDT
You've probably seen fractals before, but if you're like me, you don't really know what they are. Never fear! I've done the foot work as a reporter and Googled it. From Wolfram Mathworld:
A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all scales, but the same "type" of structures must appear on all scales. A plot of the quantity on a log-log graph versus scale then gives a straight line, whose slope is said to be the fractal dimension. The prototypical example for a fractal is the length of a coastline measured with different length rulers. The shorter the ruler, the longer the length measured, a paradox known as the coastline paradox.
Well, check out this amazing video zooming into the complexities of a Mandlebrot fractal!