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In my math studies I’ve been learning a little about the science of chaos, catastrophe theory, and fractal geometry. These are all approaches to handling random (or seemingly random) sequences, and they have all yielded many important applications for technology. Here is the basic gist of these terms, as I understand them from the textbook I’m reading.
“Chaos” refers to the point at which a pattern stops and a random sequence begins, in the context of equations that can represent, for example, factors in population increase and decrease.
“Catastrophe theory” shows that all sudden change events are combinations of seven basic changes or catastrophes.
“Fractal geometry” studies complex and nonlinear patterns, such as the shape of a coastline, which repeats the same shape over and over on different scales.