Category:Definitions/Similarity Dimensions
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This category contains definitions related to Similarity Dimensions.
Related results can be found in Category:Similarity Dimensions.
Let $S$ be a self-similar fractal embedded in a space of dimension $d$.
Then $S$ can be assigned a similarity dimension $D$, such that $0 \le D \le d$ as follows:
Let there be $N$ similarity mappings with scale factors $r_1, r_2, \ldots, r_N$ that map $S$ to itself.
Then $D$ satisfies the equation:
- $\paren {r_1}^D + \paren {r_2}^D + \cdots + \paren {r_N}^D = 1$
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