Processing 1.0 _ALPHA_ - attractors: Lyapunov exponent

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   attractors: Lyapunov exponent

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Topic: attractors: Lyapunov exponent (Read 2089 times)

Sjeiti

attractors: Lyapunov exponent
« on: Mar 7^th, 2005, 5:02pm »

Hi...

I have a problem that one of you math-wonders might be able to explain to me. I've been fooling around with attractors and the like and so far I have this:
http://www.sjeiti.com/p5ref.html?lorenz15&code/lorenz15.jar&code /lorenz15.pde&800&600&lorenz15&:
(ps: / renders image,... / again returns to the viewing state)
To get better randomisations (re-randomize when iterations diverge to infinite, or converge to a single point) I will need to calculate the Lyapunov exponent (http://mathworld.wolfram.com/LyapunovCharacteristicExponent.html).
The problem is that I don't really speak math so those formulas look like abracadabra to me.
So I have an x, y and z value. Next iteration I'll have new x, y and z values. What to I do with those numbers to get the Lyapunov exponent?

thanks...

http://www.sjeiti.com/

st33d

Re: attractors: Lyapunov exponent
« Reply #1 on: Mar 10^th, 2005, 12:43pm »

I haven't been able to approach chaos math as yet. It took me long enough to grasp a four dimensional object. But I've recently been made aware of a great maths magazine which had a great article about chaos theory.

http://plus.maths.org/issue9/features/lyapunov/

It's fairly easy going on the brain and is pretty much the only article I've read that put things a lot simpler for me. They also have another great article about maths and art that's worth a read.

http://plus.maths.org/issue33/features/dartnell_art/index.html

I could murder a pint.

Sjeiti

Re: attractors: Lyapunov exponent
« Reply #2 on: Mar 12^th, 2005, 12:36am »

That is a very nice site indeed.

I have also found an easy explanation on how to use that Lyapunov exponent here: http://members.xoom.virgilio.it/rovedi/lyapunov_exponents.htm

There are some cool formula's on this page: http://www.btinternet.com/~ndesprez/manual/attractors.htm
and here: http://astronomy.swin.edu.au/~pbourke/fractals/

The attractor thing I'm building is updated. It creates real smooth images at a processor clogging amount of 50 million iterations.
http://www.sjeiti.com/p5ref.html?lorenz15&code/lorenz15.jar&code /lorenz15.pde&800&600&lorenz15&:

Now let's see if I can do these: http://astronomy.swin.edu.au/~pbourke/fractals/quatjulia/
They look great but sound really freaking complicated.

http://www.sjeiti.com/

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