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Index › Discussion › Exhibition › Exploring a simple chaotic system
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Exploring a simple chaotic system (Read 1217 times)
Dan_Olner
Exploring a simple chaotic system
Oct 22nd, 2008, 12:39pm  
Hello

Here's an interactive version of the logistic map - an  equation used to illustrate how chaos can appear in even very simple systems.

http://www.personal.leeds.ac.uk/~gy06do/exploringchaos/

Sources linked to on that page. Note also - for anyone interested in this kind of thing - the question at the bottom. Chaos: a digital artifact or something out here, living and breathing in the meatworld?

Dan
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glenn
Re: Exploring a simple chaotic system
Reply #1 - Oct 23rd, 2008, 7:03pm  
link aint working!
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http://www.butterfly.ie
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Dan_Olner
Re: Exploring a simple chaotic system
Reply #2 - Oct 23rd, 2008, 7:14pm  
Wow, I somehow deleted all the files. Oops. Working again now, sorry!
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ramin
Re: Exploring a simple chaotic system
Reply #3 - Oct 25th, 2008, 12:03am  
it's cool. is it realy going into total chaos after the critical point has reached. scrolling up seems to strech the points out in a way that looks kind of systematic.
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Dan_Olner
Re: Exploring a simple chaotic system
Reply #4 - Oct 29th, 2008, 9:07am  
ramin wrote on Oct 25th, 2008, 12:03am:
is it realy going into total chaos after the critical point has reached. scrolling up seems to strech the points out in a way that looks kind of systematic.


It is systematic: it's entirely predictable given the initial conditions. That's what makes it, mathematically, chaos rather than randomness. It *looks* random, but it's not, it's deterministic.

It's when you're trying to apply this to real-world systems that it becomes a problem: the existence of chaos means that   -  e.g. for weather systems - we would have to know the initial conditions to an impossible degree of accuracy to make longer predictions. You can see how the degree of accuracy affects the predictability in this visualisation by changing the number of decimal places you're sweeping by.
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AtomBoy
Re: Exploring a simple chaotic system
Reply #5 - Nov 4th, 2008, 4:24am  
Very nice, thanks for sharing. It took me quite a while to realize it was meant to be interactive. An autopilot option might be fun. Also, do both lines have to be the same shade of blue? I am so allergic to math that I don't really understand their relationship to each other. I kept wondering why the moving stripe never jumped to the other line.

Are there any real world systems this relates to? I had read that some Lorenz attractors modeled dripping faucets.
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