Again, take as initiator the line segment of length 1, but now the generator is the shape shown below.
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Click the initiator on the left to see successive iterates of the rule. These iterations give a sequence of shapes converging to a fractal, the Cantor set. Because the set is quite sparse, the animation shows steps of the Cantor set iteration in blue, and a more substantial shadow in red. |
Here is a picture of the Cantor set resolved to the level of single pixels.
Although so much has been removed that the Cantor set is hardly present at all, we shall find this fractal in many applications, including poetry.
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Return to Initiators and Generators.