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First, here is an example of a self-similar fractal whose
dimension we can't compute from the similarity dimension formula. |
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Derivation of the Moran equation. We re-express the
similarity dimension formula in a way that allows us to compute dimensions of fractals made of different size pieces. |
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Though it may not be obvious from its form, the Moran equation has a unique
solution. The proof of this uses a small amount of calculus. |
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Here are some examples of solving the Moran equation.
We give a numerical approach that always works, and an abstract approach that works for a special class of
fractals. |
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Exercises in computing the similarity dimension
using the Moran equation. |