Self-similarity

Self-similarity refers to the interesting and counter-intuitive property of fractals which causes any part of them to reflect the structure of the whole.

In the Sierpinski gasket, for example, you can see how each of the three triangles that remain after the generator (the rule that says to remove the center triangle) is applied becomes, after the generator is applied an infinite number of times, a Sierpinski gasket as well.

One might be tempted to conclude that fewer triangular cutouts would be made in a part of the Sierpinski gasket than in the whole, but paradoxically, because the generation rule is applied infinitely many times, this conclusion cannot be drawn.

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