| Review of self-similarity: a key to understanding fractals is the characterization that they are shapes made of smaller copies of themselves. Here we note some of the simple consequences of this property. | |
| Finding the rules to grow a simple fractal: first decompose the fractal into smaller copies of itself, then find rules transforming the whole shape into each smaller copy. The rules involve shrinking, rotation, reflection, and translations (motions). | |
| What the rules do: apply the rules for a fractal to the fractal leaves it unchanged. What happens if the rules are applied to some other shape? We shall see. | |
| Other examples: some variations on the simple examples allow us to grow fractal trees, ferns, and flowers. | |
| Try it yourself: here are two Java programs with which you can test your understanding of how to find the rules. | |
Much more information about growing fractals in this way can be found at http://classes.yale.edu/fractals/IntroToFrac/welcome.html.