Economics is a science of fashions - Keynes and "pump-priming" at one time, Friedman and monetarism at another. The profession burns through new theories the way a teenager hops from one new date to another: It meets them, spends some time with them, examines them, finds what it thinks are flaws, and then drops them for a newer face.
In organic growth, such as lung airways, a process of iterative division is the logical outcome of the generic rules for animal development: A few instructions, executed simply and repeatedly
Fractal geometry is about spotting repeating patterns of this kind, analyzing them, quantifying them and manipulating them; it is a tool of both analysis and synthesis. The pattern can take many forms. It can be a concrete shape that repeats on successively smaller scales, as with the fern or cauliflower. It can be abstract, statistical pattern— for instance, the probability that a particular square in a grid will be black or white, or that a point in space will be occupied by a star or by vacuum. The pattern can scale up, scale down, and get squeezed, twisted—or both. The way the pattern gets used can be strictly defined by a precise, deterministic rule; or it can be left entirely to chance.