Fractals

(Big thanks to http://math.rice.edu/~lanius/frac/)

Above you see two pictures of what are called fractals.  Fractals are geometrical figures or patterns that show what happens when you repeat a process over and over.  Doing something over and over again is called an iteration.

Here's a couple of fractals you can make by hand:

• Jurassic Park Fractal (apparently used as decoration in the book Jurassic Park)

• Koch Snowflake and friends

Most fractals, like those at the top, are drawn on the "complex plane", a super-weird mathematical space consisting of complex numbers.  A complex number has two parts, 6-2i is a complex number for example.  If you take these complex numbers and plug them into equations over and over (there's that iteration thing again), watch to see how fast the numbers "explode", and graph the results - why, you get fractals.

Here's a link to a FREE demo of a fractal graphix program:

http://www.cygnus-software.com/downloads/downloads.htm#FractaleXtreme

Here's a link to some great fractal images, including images from nature:

http://sprott.physics.wisc.edu/fractals.htm