There is actually a very simple reason as to why things like fractals, fibonacci sequences, hexagonal and pentagonal-heptagonal tasselations happen in nature.
Those things build upon what has come before. They iterate. Iteration is how nature works. Iteration builds on past results and builds on top of them. If the rules remain largely the same (thermodynamics, kinetics, statistical and quantum mechanics), then the next result will have some characteristics of past ones. But the inherent randomness of it all will change things ever so slightly. This is why we never truly observe perfect structures in nature, but we observe patterns–probability distributions.
This is the way evolution works, it’s the way organisms develop, it’s how culture, language, science, maths and art evolve. Building upon previous groundwork and mixing it up a little bit upon the next iteration. Every so often, those random mix ups build up to give something radically different. Whose baggage is hidden behind many layers, but is still evident to the keen eye.