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Fractal Math, Chaos Theory & Research => (new) Theories & Research => Topic started by: DarkBeam on July 07, 2011, 10:58:22 AM




Title: Weierstrass elliptic function looks like a fractal
Post by: DarkBeam on July 07, 2011, 10:58:22 AM
(http://img687.imageshack.us/img687/5250/weierstrass.png) (http://imageshack.us/photo/my-images/687/weierstrass.png/)

:D Other graphs can be seen here http://en.wikipedia.org/wiki/Weierstrass%27s_elliptic_functions

Too bad it's too complicate for me to understand; but I know that all differential eqns can be solved iteratively like fractals (example; the Lorenz equations). Can anyone find some stuff with those equations using some simple float funcs? :)

Luca


Title: Re: Weierstrass elliptic function looks like a fractal
Post by: DarkBeam on July 07, 2011, 11:09:27 AM
Another source; http://dlmf.nist.gov/23.3

Not very clear for me though :embarrass:


Title: Re: Weierstrass elliptic function looks like a fractal
Post by: JosLeys on July 07, 2011, 03:18:40 PM
For the Lorenz equations (ie differential equations) you need a Runge-Kutta method, which is pretty different from the iteration methods that one is used to in the field of fractals.


Title: Re: Weierstrass elliptic function looks like a fractal
Post by: DarkBeam on July 07, 2011, 07:29:28 PM
For the Lorenz equations (ie differential equations) you need a Runge-Kutta method, which is pretty different from the iteration methods that one is used to in the field of fractals.

Okay! But what equations do I need to reproduce the images? ^-^

I found some stuff in akl.ufm, a slow complicated function with two :o while cycles... Too complicated :dink: If I don't find a simpler version I better leave it alone :embarrass:


Title: Re: Weierstrass elliptic function looks like a fractal
Post by: JosLeys on July 07, 2011, 08:27:35 PM
Well if you apply the Runge Kutta method (see Wikipedia) to the Lorenz equations, all you are going to get is the Lorenz attractor as in this image...nothing else.


Title: Re: Weierstrass elliptic function looks like a fractal
Post by: Xenodimensional on July 21, 2011, 05:24:51 PM
that would make a killar slotcar (scaletrix) track... just sayin'  O0


Title: Re: Weierstrass elliptic function looks like a fractal
Post by: cKleinhuis on July 21, 2011, 05:54:11 PM
that would make a killar slotcar (scaletrix) track... just sayin'  O0

just if you accept that the start will never be reached again, and that you have an endless track :D
but you could play:"who stays longest on track" ;)