Here is an arrangement of boxes that appears to be fractal. |
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To quantify this, we measure the gaps and discover |
size | number |
16 | 1 |
8 | 2 |
4 | 4 |
2 | 8 |
1 | 16 |
|
A log-log plot reveals a straight line, |
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hence the power law relation |
number = 16⋅size-1 |
Now consider this arrangement of boxes. Does it look fractal? |
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The rigid structure of the first example, reminiscent of a
Cantor set, is absent here. |
However, this set has the same distribution of gaps as the
first. So power law scalings can help reveal fractal patterns. |
A similar example can be found in
self-similar distributions. |