[chaoscope] Re: [image] Double Spiral (Follow on after Bug Report)
- From: Chaoscope <chaoscope@xxxxxxxxxxxxxx>
- To: chaoscope@xxxxxxxxxxxxx
- Date: Mon, 02 Aug 2004 15:29:47 +0100
Hi Anton, hello all,
Full marks for exploring why there are so many zeros - Are you a part time detective?
No, I think it's got something to do with the fact I was loosely involved in
Chaoscope development. :-)
If I am not mistaken, what you are looking at is a variant of the Rossler Attractor , Nice spirals
with fountains among other.
x=x + ax + by
y=y + cy + dz
z=z + ez + fyz
I've looked closely at your file, you have 7 parameters different from zero :P1,
P5, P8, P11, P18, P27 and P28. According to Sprott's equation in the manual, and
considering I've got it right, the simplified equation should be :
x' = ax + by + cz
y' = dx + ez
z' = fyz + gz
Polynomials aren't of the chaotic flow form (i.e. x' = x + dT(f(x)) ) like
Lorenz and Rossler.
The Rossler Attractor is defined by a set of three Differential equations
x = x - dT(y + z)
y = y + dT(x + ay)
z = z + dT(b + xz - cz)
So the gold was found with a map.
You found something better than gold, you came up with a new equation. Because
Sprott Polynomials offer all the possible variable combinations, excluding
zeroed parameters from the search is equivalent to excluding terms from the
equation.
Nicolas Desprez
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