Power Law Relations

Here is an arrangement of boxes that appears to be fractal.
To quantify this, we measure the gaps and discover
sizenumber
161
82
44
28
116
A log-log plot reveals a straight line,
hence the power law relation
number = 16⋅size-1
Now consider this arrangement of boxes. Does it look fractal?
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.

Return to Power Laws.