High-Precision Deep Zoom



The first of a series of zooms into the "canyon" area.

This is the first video to feature my new adaptive color optimization. More on this below.

Sample frames
Canyon image 0Canyon image 1Canyon image 2Canyon image 3Canyon image 4
Canyon image 5Canyon image 6Canyon image 7Canyon image 8Canyon - final frame

The canyon is the area where the big main cardiod part of the M-set touches the first smaller circle to the left.  This area has a lot of cool shapes, and it is a very fun area to zoom in to. It's also called the "seahorse valley" because some structures in here resemble seahorses (although that's more on the eastern wall of the canyon, and this animation zooms into the western wall).

Zooming into this region poses a bit of a technical challenge because the images are always very close to the boundary of the set, so they have very high iteration counts. You'll notice I stay away from the deepest part of this canyon, where it seems to converge down to zero width. I'm working on some code to speed up this kind of animation, and upcoming videos in the Canyon series will utilize that improvement and take us closer to that vanishing point.

CanyonDeep1, produced in Feb 2009 (several months after this project), explores the little crevice to a modest depth of about 5e-20. That project turned out to be too difficult and it kind of got abandoned.

Metaphase is another canyon-type zoom, going down into the canyon of a mini-brot.

Video download options
MP4 Files:320x240 500 Kbps 14 MB Preview quality
640x480 4 Mbps 110 MB DVD quality
WMV Files:320x240 500 Kbps 12 MB preview quality

This is yet another data point in the ongoing MP4 vs WMV comparison. For this particular animation, I think WMV wins out. Maybe something about the shifting colors causes the MP4 codec to lose its mind -- there are nasty slicing artifacts at random times, even in some 20 Mbps (beyond HDTV quality) encodings I've made. The WMV files are a little more blurry overall, but they don't have the annoying slicing effect. They are also smaller for the same bit rate, although I've learned that with indexing information and different key frame rates and such, it's pretty hard to compare specs for file sizes.

The 8 Mbps WMV is really nice, if you have the patience to download it.

Vital Statistics
Date Generated:22-26 July 2008
Final Image Size:4e-41
Video Length:2:40 of fractal, 3:29 total
Rendering Time:92:36
Method:Escape counts
Adaptive color optimization


This video was colored with a radically new technique that generates an optimal, smoothed color mapping by analyzing the count data for each frame and adaptively mapping counts into the color space. Previously, I had been trying something like this that optimized the color palette frame-by-frame, but each frame's color map was independent of the earlier and later frames, so random noise in the counts caused the color palette to jump around too much, creating a very annoying effect.

The new method analyzes the entire animation first, then generates a mapping that smoothes out the random count spikes and also spreads colors out evenly over the count space. Unfortunately, since the fractal data varies wildly over the course of a single video, it's almost impossible to make use of a single, static color map and have good-looking animation, so this method changes the range of counts that map into the color space, and that means the colors have to shift throughout the animation. This can make the animation kind of annoying, and can introduce some bad temporal aliasing effects if not managed properly. Overcoming that problem was one of the major challenges in getting this to work well.

There is still some tweaking to do, but I think this gives great results from a region that would otherwise yield really flat images with large areas of one solid color.