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Code Snippets / [DBP] - Bifurcation diagram plotter

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Neuro Fuzzy
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Posted: 17th Dec 2011 12:03 Edited at: 11th Aug 2012 11:39


The basic idea is that you start out with a number x. Lets say its .4. Then you assign x as x=x*(1-x) a bunch of times. After a hundred iterations or so the system obviously converges. If you generalize this equation to get x=x*r*(1-x), then as you vary r, you can see that sometimes x converges to a specific value, sometimes it switches forever in between two values, and sometimes it's so chaotic you don't know what's going on.

The bifurcation diagram of an iterative equation like that is the graph of all possible long-term values for varying r.

The magic happens in the "iterate number" function, so switch that one. Try commenting out the other functions that are there.

TheComet
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Location: I`m under ur bridge eating ur goatz.
Posted: 22nd Dec 2011 00:37
Hey, those graphs are oddly familiar with the mandelbrot set... Coincidence?



TheComet

Neuro Fuzzy
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Posted: 22nd Dec 2011 08:20
Funny you should say that, there's actually one thing about ratios of sides for chaotic series like these:
http://upload.wikimedia.org/wikipedia/commons/b/b4/Verhulst-Mandelbrot-Bifurcation.jpg
I have no idea why though...

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