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Welcome to Fractal Forums > Fractal Math, Chaos Theory & Research > General Discussion > Smooth coloring of 2D Mandelbox slices
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Author Topic: Smooth coloring of 2D Mandelbox slices  (Read 4675 times)
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Timeroot
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« on: February 25, 2010, 06:27:45 AM »
Hi. I was trying to get a working, smoothed coloring algorithim for 2D slices of the Mandelbox - this should also apply to all other escape-time IFS fractals that grow exponentially in size for large Z. (For the mandelbox, it grows like scale^iter.) I based my formula on these grounds, and said it should be #numiter-log(length). It didn't quite work, though, so I tried #numiter-@vary*log(length). It seems that there are certain values of @vary that work the best for different @scale values, but I can't figure out how they work. For scale=4, for instance, @vary should be set to 0.35995. Yes, that is the number of digits I found it to. For scale=2, @vary=0.721375. Does anyone have any idea how to find these values more simply?  huh?
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Timeroot
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« Reply #1 on: February 25, 2010, 07:04:38 AM »
For scale=3, @vary should be 0.455419.
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Timeroot
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« Reply #2 on: March 25, 2010, 12:41:13 AM »
^bump

Has anyone else played around with this?  cry
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reesej2
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« Reply #3 on: March 25, 2010, 02:25:20 AM »
I haven't, yet, but I'm intrigued. Judging from the values you've worked out, it looks like @vary decreases as scale increases. In fact, it looks like this is just change of base! e^(1 / @vary) is roughly 4 for scale = 2, roughly 9 for scale = 3, and roughly 16 for scale = 4. Try using log base scale^2 instead of plain old log, and leave out the "@vary" parameter entirely.
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makc
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« Reply #4 on: March 25, 2010, 08:26:58 AM »
I assume you know this one but wouldn't hurt to post it cheesy
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Timeroot
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« Reply #5 on: March 25, 2010, 11:56:20 PM »
Yeah... the general strategy is based on that, but the problem is that z doesn't grow so "cleanly", in a 2^(2^n) pattern. Rather, it goes up like scale^n, with occasional reductions by one, the rate of which is determined by the angle... it's a lot messier, overall.  sad
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David Makin
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« Reply #6 on: April 15, 2010, 04:14:34 AM »
Timeroot did you check the behaviour with different bailout values ?
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