Here is an arrangement of boxes that appears to be fractal. 

To quantify this, we measure the gaps and discover 
size  number 
16  1 
8  2 
4  4 
2  8 
1  16 

A loglog 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
selfsimilar distributions. 