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"I am also very interested in any ideas about alternative ways to render the branch cut ones. I'm sure that it's somehow possible to 'fix' the cuts but keep something of the richness of the amount of fractal detail it appears to resolve per rendered pixel.

Still have dreams of having the time and math skillz to do much more than play with the idea yet, but I am working on it! :)

Thanks heaps for posting, Michaelerule!!"
Dan Wills
"Apart from all that it's a fairly normal ultraFractal layer stack with iteration depths and coloring methods varying per layer. Always at the same location though, as I'm mainly interested in the actual fractal subject - not trying to dress it up with fancy coloring or composition tricks.

I fully recommend nova fractal exploration, I have found them just as you say, something like flame fractals/IFS and still very flexible in terms of coloring like other orbits fractals. Try phoenixDoubleNova for sure!!."
Dan Wills
"I never try to introduce detail (including cuts) from the coloring method, that seems kindof cheap and redundant to me. Unless you color using a coloring method that is itself fractal, it only adds a fixed amount of complexity.

Both of these approaches create an extremely chaotic area, usually on the 'inside' of the 'fractal lake'. Here things can get extremely and thoroughly detailed :D This and that is why I love them so much."
Dan Wills
"My other extremely branch-cut-rich stuff is, perhaps surprisingly, the good-old 'Mandelbrot fractal' formula, but using a negative, fractional (non-integer) exponent (power) rather than just the usual squaring. Using a fraction (eg -1.55555 rather than 2.0) makes the solution multivalued and introduces the cutting because of a limitation in the digital complex logarithm function (which isn't multivalued, of course, but limits itself to a single (closest) solution)."
Dan Wills
"Cheers mate! :)
Good questions indeed! :D
I will have to answer in a few parts because there appears to be a 512 character limit!

This one here is a 'phoenixDoubleNova' fractal, which is a great fractal formula implemented (by Damien Jones) as part of the nova 'family' of fractals in ultraFractal, (I think most of them are in dmj.ufm)."
Dan Wills
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