Title: Smooth coloring of 2D Mandelbox slices Post by: Timeroot 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? :hmh:
Title: Re: Smooth coloring of 2D Mandelbox slices Post by: Timeroot on February 25, 2010, 07:04:38 AM For scale=3, @vary should be 0.455419.
Title: Re: Smooth coloring of 2D Mandelbox slices Post by: Timeroot on March 25, 2010, 12:41:13 AM ^bump
Has anyone else played around with this? :'( Title: Re: Smooth coloring of 2D Mandelbox slices Post by: reesej2 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.
Title: Re: Smooth coloring of 2D Mandelbox slices Post by: makc on March 25, 2010, 08:26:58 AM I assume you know this one (http://linas.org/art-gallery/escape/smooth.html) but wouldn't hurt to post it :D
Title: Re: Smooth coloring of 2D Mandelbox slices Post by: Timeroot 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. :sad1:
Title: Re: Smooth coloring of 2D Mandelbox slices Post by: David Makin on April 15, 2010, 04:14:34 AM Timeroot did you check the behaviour with different bailout values ? |