High-Precision Deep Zoom



A High-Def deep-zoom into the eastern cusp of the Mandelbrot set.

The eastern cusp of the Mandelbrot set has a lot of gorgeous spiral structures, and great deep zoom images abound here. It is a challenge for zoom animations because the images have so much sparkly noise here. This video was rendered with 9X oversampling using a median filter to reduce the sparkle noise, which, even after filtering like this, is still quite prominent.

This particular video contrasts the spike structure with the spirals that dominate the cusp regions. By approaching the spike of a mini-set, we can have both kinds of structures appear.

This is a true high-definition video at 1080x720 resolution (note that's only 720 rows, with a 1.5 aspect ratio giving 1080 pixels per row; this is not 1080p format).  See comments, below, for more information on some technical details of this video.

Half-Size Video

The 4 Mbps video is encoded in two formats -- the full-size 1080x720 and half-size 540x360. I was curious whether encoding at the same bit rate with a smaller frame size would affect the quality. You can view it at double-size in the video player to get the same final size on your monitor. Do you see a difference in quality? Maybe in playback smoothness?

Sample frames
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Video download options
Fast Download540x360 512 Kbps 21 MB fast start
High Quality Half Size540x360 4 Mbps 146 MB
High Quality1080x720 4 Mbps 146 MB
HD Quality1080x720 20 Mbps 711 MB
Fast Download540x360 512 Kbps 21 MB

The Fast Download files should play in real time over a reasonably fast internet connection. The larger files may not, depending on the speed of the internet connection. The high-quality and HD files will have to be downloaded and played back on your system.

Vital Statistics
Concept:Seattle WA Feb 2010
Date Generated:11-Jun-10 to 16-Jul-10
Final Image Size:1.6e-51
Resolution:1080x720 (3:2 aspect ratio)
Video Length:4:00 of fractal, 4:52 overall
Rendering Time:34.8 days
Method:Frame Interpolation
Noise Reduction:9X (3x3) oversampling with median filter
Audio:SonicFire Pro 5


Background of this project

This project was originally conceived during a visit to Seattle, WA. I had my old ThinkPad with a 100 MHz Pentium-III along, but I didn't need it during most of the day, so I let it sit in the hotel room and draw fractals (with that system, it takes all day to draw a single moderate-resolution deep zoom image!). This series looked good, so I decided to dedicate the quad-core system to rendering it. After a few tests, it became clear that the 9X oversampling was, unfortunately, going to be needed, so I postponed it for a while.


This is the first video project that has has rendering progress published on the website. The graphs below were on the main page as the project progressed, but they are moved here now that it's done. They show the number of frames completed versus time.

Overview as of Jul 5
Seattle Progress July 8
Detail Jul 8
Seattle Progress July 10
Detail Jul 10
Seattle Completion
Completion Jul 16

The total run time was 3,004,166 seconds, or 34.8 days, to create 7200 interpolated video frames at 1080x720 from 169 primary frames with 9X (3x3) oversampling.


The benefits of the 9X oversampling, and what exactly it means, are described in the technical page on anti-aliasing. That page also explains why I use a nonlinear filter -- the median filter -- to filter the supersampling data, rather than a linear filter like the mean filter.


Colorizing this video was done the same way as the previous animation, QBIX. This method keeps the count-to-color mapping constant in time (as opposed to dynamically adapting it to the changing fractal data), and a few data points based on the global distribution are used to create a single count-to-color map for the entire video.

The color palette uses a blend of saturated colors fading into white and black.  I used a few colors here that I don't typically use, especially bright bubble-gum pink, which I included here as a nod to the great work at TeamFresh does at their site HDFractals.com.

Frame Interpolation

With 9X oversampling, the rendering time is 9X longer, so some technique for speeding up rendering is important. Frame interpolation does that, without compromising the fidelity of the final video. This technique is described in detail in a technical page.

This project uses 170 master images, almost all of which are 2687x1794 pixels, to generate the final 7200 video frames at 1080x720.  Three of the master images are a few pixels smaller, and the final one is only 1640x1096.  Note that the end of the video says 169 master images were used; that is wrong--I forgot to count image 0!