Examples for

Shape-Replacement Fractals

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.
Shape-Replacement Fractals

Investigate fractals generated by repeated iteration of rules on shapes.

Draw fractals based on replacement of shapes:

Sierpinski gasket
Haferman carpet

Draw fractals by repeatedly adding smaller figures:

H fractal
ice fractal
Pythagoras tree

Plot a fractal based on removal from an original shape:

Cantor set

Plot a curlicue fractal:

curlicue fractal
More examples