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-- Mike Condron

Happy Holidays to all!

This month there is no new animation. Things have been really busy, and the little time I've had available for fractal work this month has gone into technical improvements to the software. There's some great stuff coming, but this month I just have not been able to get a video put together.


Here's a quick summary of what's been going on. For more details, see below, or visit the newly updated Technical section of the website.


CanyonDeep is a project that has been planned for several months. It will be very computationally demanding even though it won't be a very deep zoom. Much of the work done on the software in the past few weeks has been in preparation for it. I have a very rough plan for the zoom end-point of this animation now.

Software Improvements

Frame Interpolation

This is a somewhat controversial technique for making more efficient use of image data while rendering animations. CanyonDeep is not feasible without this approach. I first added this to my software several years ago but abandoned it for various reasons. Most of the effort since November has been focused on getting this working again and on some major improvements to make it work better.

Histogram Equalization Coloring

This is a method for determining which color gets assigned to each value of fractal data. It tries to balance the use of colors based on the distribution of values of data. I had tried this years ago and decided to take a different approach (rank ordering), but am revisiting it now after some suggestions on a fractal discussion forum have made me reconsider whether this might have some advantages. Please see the Technical-Colorizing and Technical-Animation pages for more details on this.



CanyonDeep will be a modestly deep zoom into the canyon part of the set (aka the Seahorse Valley), which we've previously explored a bit in Canyon1 and Canyon2. CanyonDeep will actually not be very deep itself in terms of its final frame magnification, and it will have a quite different plan from the previous two. Canyon1 and Canyon2 both zoomed into the cusp just a little bit, then moved off to one side and zoomed way deep down into some interesting structures. CanyonDeep will zoom way down into the cusp first, so deep that it will just look like a single-pixel wide line for a moment, then it will move off to one side and zoom in to something for a short span.

Since this video will include a huge number of points very close to the boundary of the Mandelbrot set, this is a vastly more computationally demanding plan than the previous two Canyon animations. That is why I've been working hard to make sure that the software has everything I can think of to speed up the process. Last month we talked about improvements in the high-precision math and about using the rectangular decomposition method of rendering. I thought those would be enough, but I've had to dust off another old trick, and some people aren't going to like it.

The problem with this project is that most of the test images I've made of reasonable endpoints are taking about 60-90 hours to render ... just a single frame! This is not because they're at super-deep magnifications, but rather because the iteration count has to be turned up so high to get an image. The average count number is in the tens of millions, which is a hundred to a thousand times higher most of the other videos I've made, even the ones that zoom to beyond 1e100. This is because the image is so close to the edge of the set, much closer than any other video I've tried to make.

The solution -- the only solution I can see -- is to use frame interpolation to render this animation.

Frame Interpolation

This technique has been around at least since 1988 and was described in Peitgen & Saupe, The Science of Fractal Images. Some commercial fractal programs do this, and many (but certainly not all!) of the existing fractal animations use this method.

I've written a fair amount about this on the Technical-Animation page of HPDZ.NET, including a discussion of whether this is really "cheating" or not.


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