Re: attractors...

On 23 Feb 2006 07:03:49 -0800, marienkaferoe@xxxxxxxxxxx wrote:

Roger and Sebastiaan_

Thanks for your help. Today, we managed to use visual basic codes of
both lorenz and roessler attractors and jumped into rhino to see the
process in rhino -3d.

But, I still have questions.:) Because now we want to use excel for
attractors' differential equations to be able to control coordinates of
points and put this data to another software. Now, I'm searching for
possible ways of "converting a differential equation into a finite
difference equation".

In google groups I have found a topic"Converting a chaotic system into
a software program"But this topic is 6 years old and web-site addresses
written in the messages are old as well_may be you already know how to
convert Lorenz and Roessler equations into another type of equation
that excel will recognize...
The message below showed an ad hoc, heuristic method. You should find
the thread to get the nuances.

From: jmb...@xxxxxxxxxxxx (John Bailey)
Subject: Re: Chaos in new, simple, symmetrical 3D ODE
Date: 1997/02/19
Message-ID: <5edldl$2044@xxxxxxxxxxxxxxxxxxxxx>#1/1
X-Deja-AN: 219731946
References: <33019a72.13686640@xxxxxxxxxx>
<pecora-1402970723330001@xxxxxxxxxxxxxxxxxxx>
Organization: Frontier Internet Rochester N.Y. (716)-777-SURF
Reply-To: jmb...@xxxxxxxxxxxxxxx
Newsgroups: sci.math,sci.fractals,sci.nonlinear


In article <33019a72.13686...@xxxxxxxxxx>,
Arne.Dehli.Halvor...@xxxxxxxxxxx (Arne Dehli Halvorsen) wrote:

A new, simple attractor has been discovered which exhibits rotational
symmetry around the axis x, y, z

(This means that in its definition, x is to y and z
as y is to z and x
as z is to x and y)

The definition:

dx/dt = -ax-4y-4z-y*y
dy/dt = -ay-4z-4x-z*z
dz/dt = -az-4x-4y-x*x

If you convert the three symmetrical differential equations to
an analogous difference equation form, you can get striking
chaotic behaviour with a spread*** (I used Microsoft Excel)

ODE form
dx/dt = -ax-4y-4z-y*y
dy/dt = -ay-4z-4x-z*z
dz/dt = -az-4x-4y-x*x
dz/dt = -az-4x-4y-x*x
Difference equation form
x(new)=Ax(old)+Bsum(old)+Cy*y
y(new)=Ay(old)+Bsum(old)+Cz*z
z(old)=Az(old)+Bsum(old)+Cx*x
sum(old)=x(old)+y(old)+z(old)
Typical values for constants: A= 1.03, B= -0.09, C= 1/1000

Plots and and the Excel can be found at
[THE OLD URL GIVEN HERE NO LONGER WORKS]

Really exciting to be able to play with totally new stuff!!!!
John
.