This is a wonderful article. There is not nearly enough accessible material about higher mathematics written in English, such that most people can understand. I have a degree in Applied Mathematics, and Chaos Theory is something I have studied carefully. So allow me to elaborate and clarify with specific, and academically rigorous math terminology. Like any profession, math has it’s jargon. But math jargon, like math itself, is internally consistent.

Chaotic systems give rise to “Emergent Properties.” Emergent properties are the building blocks of emergence. Emergence is a concept, emergent properties are a characteristic. The defining feature of an emergent property is, that it is the result of an interaction between two items, neither of which contains any of the information (the DNA if you will) in the emergent property. The example I use is colliding rocks, making a sound. The sound isn’t “in” either rock, therefore it’s an emergent property.

Chaotic systems produce emergent properties, some are periodic, some random, and there are other classifications. I won’t go into that. But Chaos Theory isn’t as complicated as you might imagine. It’s just new, and people are still figuring out the right language to convey the central concepts clearly in layman's terms.

When teaching Chaos Theory I start by explaining that it can be thought of as a branch of logic. Binary logic is the logic of twos: yer or no, on or off. one or zero. Fuzzy Logic is the logic of threes: yes, no, and maybe (any three boolean operators will do). Chaos Theory is the logic of fours: yes, no, maybe, and exclusive-or (XOR). Beyond that comes Complexity Theory, and that’s as far as we’ve gotten. As the number of base variables in a logical system increases, so does chaos and complexity. Hence the progression of successive new math areas, and new mathematical theories.

Fascinating stuff :^)!!!