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Image Threads / Re: Ducks/Kali
« Last post by pauldelbrot on Yesterday at 07:04:01 PM »
Down The Drain
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Downloads / Re: Infinity Fractal v1.0.13
« Last post by gerson on Yesterday at 05:00:17 PM »
Liked very much new improvements.

@Sabine62 "Can you also look at the issue I have with changing the size of the selection box with the mousewheel? "
I got the same problem so I simulate to set new coloring mode and it returns to work.
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@marcm200 "Since I am using the internal random number generator and have no idea what its distribution of numbers looks like,"
Maybe you could save the randon's number generated, and after load it to use with the other 2 algoritms and test if it give the same result.
I saw something about genetics and Particle Systems on softology's blog if you are interested. I don't know if refers to the same subjet of yours papers.
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Fractal Mathematics And New Theories / Re: Holomorphic Mandelbrot extensions
« Last post by marcm200 on Yesterday at 03:36:36 PM »
 uf237c2.jpg looks like it comes from a science fiction movie: A mother ship sending out probes into a supernova. Nice!

z <- z^2 + qw +c
w <- w^2 + pz +c
If I view this definition as program code, then the w-update uses the already updated z. Is that what's happening here (maybe part of the name "coupled"), or are those independently updated (stored in a temporary variable) ?

To search for interesting parameters: Maybe the genetic algorithm by Ashcroft ("Evolutionary exploration of the Mandelbrot set") might be of use. The suggested fitness functions on an escaping type fractal seem to have a preference for specific structures. So maybe they find a recurring interesting pattern in your formula system as well?

Of course then the "search for interesting parameters" becomes the "search for useful fitness funtions". I don't know if that's progress. But maybe worth a try. Ideally one would devise a genetic search algorithm that searches for "interesting formulas".
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Fractal movie gallery / Re: audiodriven freestyle fractal animation
« Last post by rontwd on Yesterday at 11:49:09 AM »
Lovely idea :)
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Characterizing monomial Mandelbrot sets with polygons that were derived from images calculated with the algorithm by Figuereido et. al. that comes with a mathematical guarantee (no point sampling).

Quadratic Mandelbrot: 1 exterior, 11 interior polygons: #1 and #5 are the period-2-bulb and the main cardioid. The others describe parts of different bulbs that - as far as I know - have not been described in total by a formula, nor in part.

Cubic: 1 exterior, 11 interior
Quartic: 1 exterior, 18 interior
Pentic: 1 exterior, 13 interior

The zip file contains the polygons as text files and can be used with the code I posted previously (https://fractalforums.org/programming/11/true-shape-based-cplusplus-oracle-for-the-int-exterior-of-julia-sets/2852/msg14804) as well as an image showing where the polygons lie.
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@sabine: Yes, this random genetics approach is quite appealing. And as I read your post, the bit strings reminded me of the Logo turtle which uses them to change directions (if I recall correctly).

But interestingly the Mandelbrot approach here is not exceptionally computationally expensive (just an 11x11 grid), I wonder if my 80's Amstrad could have handled it (okay, in hours to days, not in minutes, but nevertheless).
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Fractal Mathematics And New Theories / Re: Holomorphic Mandelbrot extensions
« Last post by gerrit on Yesterday at 07:14:52 AM »
One more, (p q) = (1,-1).
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Fractal Mathematics And New Theories / Re: Holomorphic Mandelbrot extensions
« Last post by gerrit on Yesterday at 05:51:24 AM »
for second inside is red.
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Fractal Mathematics And New Theories / Re: Holomorphic Mandelbrot extensions
« Last post by gerrit on Yesterday at 05:51:00 AM »
Two more of the coupled Mandelbrot formula with interactively selected p,q values.
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