The purpose of this lesson is to learn very simple methods to construct fractals, to do and practice some math, to appreciate the beauty of fractals, and finally to have fun with math. The lesson includes several Java applets for hands-on construction and interaction with simple fractals.
Lets start with definitions.
In very simple terms, fractals are geometrical figures that are generated by starting with a very simple pattern that grows through the application of rules. In many cases, the rules to make the figure grow from one stage to the next involve taking the original figure and modifying it or adding to it. The fractals' growth mechanism can be visualized very easily with a simple example. Repeat the exact same process recursively as many times as desired. It is interesting to note that Bertrand Russell wrote this in 1907, which applies so well to fractals, about 70 years before they were discovered by the Polish-born French mathematician Benoit B. Mandelbrot in the 1970's 1 .