The Logistic Map in Action
Jan. 23rd, 2014 11:43 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
jrisingEveryone'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 pictures like the following, bursting with internal structure:
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.
So, I made an animation. In it, I just keep adding new points, each with a value of r and an initial value of x, and let them fly.
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 pictures like the following, bursting with internal structure:
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.
So, I made an animation. In it, I just keep adding new points, each with a value of r and an initial value of x, and let them fly.
