The simplest fractals are constructed by iteration. For example, start with a filled-in triangle and iterate this process:
For every filled-in triangle, connect the midpoints of the sides and remove the middle triangle. Iterating this process produces, in the limit, the Sierpinski Gasket.
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Click the picture to iterate. |
The gasket is self-similar. That is, it is made up of smaller copies of itself.
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We can describe the gasket as made of three copies, each
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"Big gaskets are made of little gaskets, |
The bits into which we slice 'em. |
And little gaskets are made of lesser gaskets |
And so ad infinitum." |
Return to Scene Four.