{"id":68,"date":"2014-01-24T07:46:48","date_gmt":"2014-01-24T07:46:48","guid":{"rendered":"https:\/\/existencia.org\/pro\/?p=68"},"modified":"2014-01-24T07:49:52","modified_gmt":"2014-01-24T07:49:52","slug":"the-logistic-map-in-action","status":"publish","type":"post","link":"https:\/\/existencia.org\/pro\/?p=68","title":{"rendered":"The Logistic Map in Action"},"content":{"rendered":"

Everyone’s heard of the logistic map:
\n\"x_{n+1}<\/p>\n

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<\/p>\n

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.
\n