## Mandelbrot Set

### Another name I can't pronounce

Before we go on, you need to understand the idea of a prisoner set. Basically, these sets have a function that if a number gets trapped in a pattern of numbers and is unable to escape to infinity, it becomes a prisoner.

The most notable person in the area of prisoner sets was a man by the name of Gaston Julia. His collection of Julia sets (appropriately named) were based upon the function f(z) = z^2 + c, in which changing the constant c produced a different Julia set. Now, some Julia sets were connected and others were not. Julia, however, had no way of determining whether a set was connected or not without iterating a series of points through that particular function.

### So when do we get to Mandelbrot?

When IBM researcher Benoit Mandelbrot discovered Julia's work, he was fascinated. During the 1970s, he developed a function for a prisoner set that determined whether or not a Julia set was connected or disconnected. If the number was in the Julia set. His prisoner set was named the Mandelbrot set, and aside from these pictures of the Mandelbrot set, you can check out this java applet to explore the set yourself.

### Okay, but if they are just numbers, how do the pictures come into play?

Did I forget to mention that we are in the complex number system? Basically, you can look at a complex number a+bi as coordinates (a,b) if it will help you understand this any better.

### Is the set fractal?

Well, there are indications of self-similarity if you go searching for it, but this is only near self-similarity. Moreover, the Mandelbrot set does not the requirement of non-integral complexity, so it is not a fractal. The complexity of the set is 2 dimensions.

Last updated 8/9/99