## Fractals and Chaos

### Hey, that fern kind of looks fractal

As a matter of fact, that fern is fractal. The fern, something found in nature, exhibits fractal characteristics. What does this fractal order mean for chaos?

As we already know (hopefully), both fractals and chaos undergo iteration. The question that then arises is whether iterations of apparent chaos could cause some kind of fractal order. Well, to do this, let's play a little something called the chaos game. Random points will be placed, following a set of four rules depending on the size of a number. As always, a Java applet is here to demonstrate.

### What about a simpler game?

Okay, obviously that chaos game could only be done using the computer. You probably want one that you can play. First, you need a few materials. You need a pencil, a die, a ruler, and sheet of paper with an equalateral triangle with its vertices labeled A, B, and C.

Okay, start on any place on a side of the triangle and roll the die. If it is one or two, go halfway between your point and corner A and draw a small dot there (if 3 or 4 B and if 5 or 6 C). That is your new location. Roll the die again, and repeat the same process, except make the point halfway between your new location and the new corner based upon the die roll. After A hundred or so trials, you should get an image that approaches the following link. The design is called teh Sierpinski triangle and if you check, it is fractal in nature.

Last updated 8/9/99