A piece of a fractal called The Mandelbrot SetA fractal is a figure with a fractional dimension. What does that mean? Well you'll just have to read my articles to get a better description! But consider these examples...

A tree has some fractal characteristics: it has a main trunk, which splits off into limbs, which split off into branches, then to twigs, then to leaves, and those leaves have a vein pattern which is similar in shape and function as the rest of the tree. Other familiar structures show fractal form, like highways, the human circulatory system, paintings, storm clouds, lungs, and even oriental rugs. While fractals are quite aesthetic, they also serve practical purposes. Sometimes the design for a task is a self-similar layout.

The Mandelbrot Set is the mother of all fractals. In short, it is an iterative equation that produces beautiful images. What is fascinating about this set is that whereas most fractals are self-similar, the Mandelbrot is anti-self-similar. What does that mean? It means that new images arise the more you zoom in. Every piece of the Mandelbrot shares a common artistically organic theme, but the actual designs are completely different. It is the ultimate embodiment of mathematical beauty.

Fractals don't just look good, they also have some very practical purposes. According to preliminary studies, fractals can predict weather reasonably well. If you were to take high-resolution pictures of clouds, then calculate the fractional dimension of that cloud, that number tells you whether it is storm-prone or not. The higher the dimension, the more likely it is to storm. Fractals have also been used in data compression. But more on all that later...

Page last updated: February 04, 2008