Welcome to Fractal Forums

Hello to everyone. Although JackOfTraDeZ posted a link to my site a few weeks ago in the "Fractal Website of the Month" board, I thought I'd officially say Hi to you all here as well.

www.hpdz.net (http://www.hpdz.net)

I focus mostly on generating deep-zoom animations of the Mandelbrot set. I am using custom software for this, and I am presently using a Core2-quad (Q6600) system to do the video rendering. New animations should be appearing every couple of weeks, or at least once a month.

I don't do much work with video processing that focuses on techniques that use the Mandelbrot set or other fractals only incidentally. I do use some special digital image processing methods, and am working on developing more, but these are always used as a tool to create better animations of the set itself, not as the focal point of the video.

So I hope you can take a moment to visit my site and stop by again once in a while. I'll keep working on getting better and better videos showing parts of the set nobody has ever animated before.

Hello and Welcome to the forum!

I enjoyed your site.  Someday I plan on doing such things, but I' still re-learning the basics of programming (things have changed quite a bit since I first learned to program - by Punching Cards!).

I hope to see more of you and your work around the forums...

hello and welcome, i always enjoy fractal animations, but my favorites are deforming fractals, rather than deep zooms...
also i do like interesting camera pathes....

welcome!!! O0

HPDZ,

I just found your website. Your adaptive coloring technique sounds a lot like the histogram based approach my program uses. I count the number of pixels at each iteration value in a plot, and create color tables where the color changes slowly for iteration values with a small number of pixels, and changes quickly for iteration values with a large number of pixels. I use a separate color value for each iteration count. I also optionally apply fractional iteration values to create smooth transitions between iteration values and eliminate banding.

Here's an illustration showing my histogram-based approach:

(http://www.pbase.com/duncanc/image/75494021/original.jpg)

And a link that includes a description:
http://www.pbase.com/duncanc/image/75494021/original (http://www.pbase.com/duncanc/image/75494021/original)

I haven't implemented animated zooms yet, and will need to figure out what to do about the colors changing between frames of an animation. One of the things I've thought about doing is to calculate the histogram for an entire animation, and use that single histogram to color the entire animation.

Regards,


Duncan C

hi duncan,

i can only say, simply try it with the single frame method, i believe it would make for an interesting effect ;)

 calculating the range over a whole animation leads to weird effects, especially in zoom animations,
because you are using this method exactly because of the problems defining a constant palette range a whole fractal type ;)  :police: :police: :police: :police:
 

Duncan,

Sorry for the long period of silence, and thanks very much for your great comments.

I am doing something similar to what you describe, although I have some variations on it. I generally use a rank-order method for mapping counts to colors. I tried the histogram-equalization method and like it a lot, but rank-ordering works just a little better. See http://www.hpdz.net/TechInfo_Software.htm (http://www.hpdz.net/TechInfo_Software.htm) (the Colorizing sectino) for a brief discussion and see http://www.hpdz.net/Anim_Technical.htm#Rank-Order (http://www.hpdz.net/Anim_Technical.htm#Rank-Order) for a short demonstration animation.

For animations, things get a lot more complicated. I describe some of the problems on the pages of the two latest animations I've made:

Canyon1 http://www.hpdz.net/Anim_Canyon1.htm (http://www.hpdz.net/Anim_Canyon1.htm)
MetaphaseVar1 http://www.hpdz.net/Anim_MetaphaseVar1.htm (http://www.hpdz.net/Anim_MetaphaseVar1.htm)

Basically there are two major problems for animations:

1. The fractal data is very noisy, so the histogram fluctuates a lot from frame-to-frame, whcih causes the color map to jitter unacceptably.

2. The fractal data spans a huge range over time, and the range changes with time. For one segment of the animation, the fractal data may be spread out over three orders of magnitude (i.e. the ratio of highest count to lowest count), while in another part, it may be squeezed into a very narrow spike on the histogram (high/low ratio maybe only 1.05 or 1.10).

In MetaphaseVar1 I demonstrate (but do not describe yet--it's pretty complicated and I haven't had time to write about it) a way of smoothing everything out so it looks nice. I am not sure I've achieved the optimal solution to this problem, and my technique is still evolving, but I think it looks pretty good so far.

I've recently learned of an approach that's used in some custom formulas for ChaosPro and/or UltraFractal. It does something very simple -- just scale the color mapping parameters by the magnification of the image. FractInt also has a method that seems to work well (see Descent on the UFVP web page, which is a rework of my Canyon1 zoom with FractInt). I will find out exactly what they're doing in a couple of weeks when I have time to look through the source code.