[chaoscope] Re: Chaotic solution map

  • From: Chaoscope <chaoscope@xxxxxxxxxxxxxx>
  • To: chaoscope@xxxxxxxxxxxxx
  • Date: Tue, 29 Jul 2008 23:36:43 +0100

Hi Laurent,

Congratulations for finding such a nice image during your first Chaoscope day!

in this tutorial : http://www.btinternet.com/~ndesprez/tutorials/search.htm
There is a map of chaotic solution for a given fixed parameters.

I find it very, extremly, wondermagically interesting.
Where can i find this tool to generate that kind of map ?

The map shown in the tutorial was created using homegrown code. However any fractal program which includes a formula compiler (like FractINT, ChaosPro or UltraFractal) would be sufficient.

Actually the Mandelbrot and Julia sets are traced the same way. In the case of the Mandelbrot set, both the real and imaginary parts of C (in Z => Z² + C) are the parameters mapped on the 2D plane just as are A and B parameters of Pickover on the map you mention. Values of C for which Z => Z² + C produces an attractor are inside the set. The attractor is never strange though, as far as I know anyway!

I haven't explored parameters mapping in depth yet. The difficulty lies in the fact that some attractors in Chaoscope have *many* parameters from which the user would have to pick just two, if we'd limit ourselves to 2D sets. I think it would be more interesting if we could trace sets with many more dimensions but then it becomes hard to render them.

Maybe Martin Pfingstl, author of ChaosPro, could tell us how difficult it would be to create such a map?

Kind regards,

Nicolas Desprez
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