Examples for
One way of creating fractals is to start with simple shapes and repeatedly apply a rule that replaces parts of shapes with others. Many well-known fractals, like the Sierpinski gasket and the Pythagoras tree, can be constructed this way. Use Wolfram|Alpha to draw such fractals, get information about them and play with the parameters and number of iterations in their plots.
Investigate fractals generated by repeated iteration of rules on shapes.