| One of the simplest ways to generate random fractals is a modification of a
Sierpinski gasket construction: |
| Start with the filled-in unit square, |
| remove the upper right 1/2 x 1/2 corner square, |
| then remove the upper right corner squares of the remaining squares, |
| and so on. |
|
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| Click the picture to animate. |
|
| Now instead of always removing the upper right corner,
at each stage select at random one of the four corners to remove. |
| Depending on the
sequence of random choices, different limiting shapes arise. |
|
| Click each picture to animate the steps generating that picture. |
|
| In what sense can we call these shapes self-similar? |
