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![\"x_{n+1}](\"http:\/\/existencia.org\/files\/lj\/logistic\/equation.png\")
<\/p>\nEveryone’s heard of the logistic map:
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It’s elegant, it’s powerful (a classic for modeling ecosystems, e.g.), and it’s incredibly chaotic. As you change r<\/i>, its internal frequency doubles, and then redoubles over a shorter span, and then again and again, until it reaches an infinity frequency over a finite distance. So you get beautiful fractal pictures like the following, bursting with internal structure:
\n![\"Static](\"http:\/\/existencia.org\/files\/lj\/logistic\/static.png\")
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But they rarely tell you how you get the picture, or what it means. The closest you get is that these are “asymptotic” values– a meaningless statement for something that never settles down.<\/p>\n
So, I made an animation. In it, I just keep adding new points, each with a value of r<\/i> and an initial value of x<\/i>, and let them fly. Everyone’s heard of the logistic map: It’s elegant, it’s powerful (a classic for modeling ecosystems, e.g.), and it’s incredibly chaotic. As you change r, its internal frequency doubles, and then redoubles over a shorter span, and then again and again, until it reaches an infinity frequency over a finite distance. So you get beautiful fractal … Continue reading The Logistic Map in Action<\/span>
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