## [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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