Power Law Relations

Weigh out different amounts of dried peas.
Wrap each amount in plastic wrap, in an approximately spherical shape and measure the diameters of the clusters.
One experiment gave the results on the left.
Plotting Log(mass) vs Log(diam), we see the points fall almost along a straight line of slope 3.0.
This data supports a power law relation of the form
mass = k⋅diam3
On the other hand, the peas pack tightly. Although there are spaces between the peas, the spaces are all about the same size.
There is no hierarchy of structures that characterize fractals.
Unlike crumpled paper, clusters of peas are not fractal.

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