Smooth coloring of 2D Mandelbox slices

[Timeroot]

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? 

[Timeroot]

For scale=3, @vary should be 0.455419.

[Timeroot]

^bump

Has anyone else played around with this? 

[reesej2]

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.

[makc]

I assume you know this one but wouldn't hurt to post it

[Timeroot]

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. 

[David Makin]

Timeroot did you check the behaviour with different bailout values ?