“Mandelbrot’s insights imply that when viewed through a coarse-grained lens of varying resolution, a hidden simplicity and regularity is revealed underlying the extraordinary complexity and diversity in much of the world around us. Furthermore, the mathematics that describes self-similarity and its implicit recursive rescaling is identical to the power law scaling discussed in previous chapters. In other words, power law scaling is the mathematical expression of self-similarity and fractality. Consequently, because animals obey power law scaling both within individuals, in terms of the geometry and dynamics of their internal network structures, as well as across species, they, and therefore all of us, are living manifestations of self-similar fractals.”
“So, naturalists observe, a flea,
Hath smaller fleas that on him prey;
And these have smaller still to bite ‘em;
And so proceed ad infinitum.”
Cutely, this quatrain is quoted by Geoffrey West in SCALE.