The Chaos Game

  In chaos theory, there is a feedback iteration where choosing a random point reproduces random outputs among the following iterations. But over a long enough period of time, it doesn't appear to be so random. The shape the points make after thousands of iterations becomes a fractal- specifically the Serpinski Gasket. This called the Chaos Game. A better explanation with illustrations can be found at the Boston University math department here. 

A Sierpinski Gasket showing the outcomes of rolled dice over an infinite series of iterations. Mysterious gaps in the "landing zone" result in a classic fractal structure.

 It is one example of the connection between chaos and fractals; how seemingly random events inevitably lead to order within a larger structure. This could be applied to nature through the Bayes Theorem of probability, where the likelihood of an iteration having a given output is predictable over the course of time but not at the beginning. It serves the wave-particle duality of nature as tiny variations within a structure ultimately lead to the same result. It is the probability of particles forming an entity that lend it reality. Like the chaos of a fractal, any initial condition iterates to the same body plan, as if it was already there. That's where waves converge on particles, with the particles serving the plan and the waves serving the force. Together they create a probability distribution that "fractalizes" nature in real time.