Understanding Chaos: Chaos can ensue when rules lead to unpredictable results. Typically, when say “2+2″ it equals “4”. But what if the next time you did it, 2+2 = 5? This is what chaotic systems are like. They often (maybe always? I haven’t looked deep enough yet) show up in a horseshoe map. Here’s the significance of a horseshoe map: It is similar to stretching out a ball of multicolored clay, folding it back towards itself (a horseshoe) and then mushing it together. That’s one iteration. If you do 8 iterations, do you know how the multicolored ball will look? Can you predict it ahead of time? With identical multicolored balls and identical movements, you can *learn* what each iteration will do. But you can’t predict it just by the simple rules you are applying. [stretch, fold, squish]

Understanding Chaos: Chaos can ensue when rules lead to unpredictable results. Typically, when say “2+2″ it equals “4”.

But what if the next time you did it, 2+2 = 5?

This is what chaotic systems are like. They often (maybe always? I haven’t looked deep enough yet) show up in a horseshoe map. Here’s the significance of a horseshoe map: It is similar to stretching out a ball of multicolored clay, folding it back towards itself (a horseshoe) and then mushing it together. That’s one iteration.

If you do 8 iterations, do you know how the multicolored ball will look?

Can you predict it ahead of time?

With identical multicolored balls and identical movements, you can *learn* what each iteration will do. But you can’t predict it just by the simple rules you are applying. [stretch, fold, squish]

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