Compute the similarity dimension of a strictly self-similar fractal with a replacement ratio of 5 and a scaling ratio of 4. Round to the nearest thousandth.

Question
Similarity
asked 2021-03-07
Compute the similarity dimension of a strictly self-similar fractal with a replacement ratio of 5 and a scaling ratio of 4. Round to the nearest thousandth.

Answers (1)

2021-03-08
Formula used:
The similarity dimension of a strictly-similar fractal is given by
\(\displaystyle{D}=\frac{{{\log{{N}}}}}{{{\log{{r}}}}}\)
Where N is the replacement ratio of the fractal and ris the scaling ratio.
Calculation:
We have, N = 5 and r = 4. Now, use the formula for similarity dimension D of square fractal to calculate it as shown below.
\(\displaystyle{D}=\frac{{{\log{{5}}}}}{{{\log{{4}}}}}={1.161}\)
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