High-Precision Deep Zoom


Burning Ship 1 ("Wallis")

The first deep-zoom animation of the Burning Ship fractal


This video is a high-definition 1280x720 resolution, 12000-frame deep-zoom of the Burning Ship fractal. It is, to the best knowledge of HPDZ.NET, the first-ever deep-zoom animation of the Burning Ship fractal, and indeed is one of only a very few videos of this fractal in existence. This video magnifies the fractal image from an initial size of 3.0 to a final size of 2.35x 10-100, which is a magnification of 1.28x10100.

This animation begins with an overview of the large ship-like structure centered in the frame, then quickly moves sideways to the zoom point, pauses, then begins zooming into the sails of one of the ships in the Armada region off to the west/left. This fractal is famous for the tall, Gothic structures that appear in the sails of these little ships. This video explores depths of these structures never before seen.

In addition to the video captures below, some of the large primary images used to generate the animation are available for download. Click here or scroll down.

For a very brief explanation of the forumla for this fractal visit the Burning Ship still images page. That page also features some extreme-definition 3200x1600 pixel still images, views of various embedded mini-ships, some interesting structures in the sails, and images of higher-power versions of the underlying mathematical formula.

More details on this project and some explanation of the video encodings are below.

John Wallis

This project is dedicated to John Wallis, a 17th-century English mathematician who, among many other contributions, developed the geometrical interpretation of negative numbers and the number line, and initiated the concept of a geometrical interpretation of complex numbers. The number line with negative numbers to the left and positive numbers to the right, something we take for granted now, was quite a breakthrough at a time when negative numbers will still something dubious in the minds of many mathematicians. Even Wallis himself, despite his geometric analogy, believed for a time that the true nature of the negative numbers was that they were greater than infinity -- this seems ridiculous today, but think about what happens with 1/x as x goes to zero, and you will see why this seemed plausible.

Video Capture Images

This project has a lot more video frame capture images because it is much longer than most, and because there is just so much to see. Click on any image below for a high-quality full-size frame capture from the video.

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Burning Ship1 Video Image16 Burning Ship1 Video Image17 Burning Ship1 Video Image18 Burning Ship1 Video Image19 Burning Ship1 Video Image20
Burning Ship1 Video Image21 Burning Ship1 Video Image22 Burning Ship1 Video Image23 Burning Ship1 Video Image24 Burning Ship1 Video Image25


In order to conserve limited server hosting space, the larger versions of this video are only available as MP4 files.

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MP4 Files (QuickTime player)
Mobile Phone Viewing19 MB320x180300 Kbps FastStart
Fast On-demand Viewing62 MB640x3601 Mbps FastStart
DVD Quality255 MB640x3605 Mbps FASTSTART
Near HD Quality Download762 MB1280x72015 Mbps
True HD Quality Download2.0 GB1280x72040 Mbps INSANE Quality
WMV Files (Windows Media Player)
Mobile Phone Viewing19 MB320x180300 Kbps
Fast On-Demand Viewing57 MB640x3601 Mbps
DVD Quality271 MB640x3605 Mbps
Vital Statistics
Date Generated:11-13 Apr 2011
Initial Image Size:3.0
Final Image Size:2.35e-100
Magnification Ratio:1.28e+100
Length:6:40 of fractal, 7:04 total
Maximum Iteration Count:100,000
Rendering Time:28.6 hours (25.6 for primary fractal image calculation, 3.0 for interpolation of video frames)
Rendering System:Core i7 980X 4.0GHz overclocked
Method:Burning Ship fractal, exponential smoothing, interpolation from 407 primary images
Audio:Sonic Fire Pro


The 12,000 frames of this video were generated by interpolation from 407 primary images (directly calculated from the fractal data). Almost all of them are 4434x2497 pixels. The first two are a big bigger since the first 30 frames of the video are just the ship moving sideways, and that animation can be generated from a single large image. The final three primaries are a bit smaller because of the slowing down of the zoom. The primary images are blended together with 50% overlap on the leading and trailing segments. The weighted-averaging type of pixel interpolation was used.

This is the longest video published so far by HPDZ. In fact, I had to modify the software to accomodate a 5-digit frame file number, and some modifications were also necessary to support these much larger primary fractal images within the interpolation system.

All together, 30.4 GB of primary fractal data was generated. The 12,000 interpolated video frames add up to 41.2 GB. They were colorized and joined into 12 uncompressed 2.7 GB AVI files, which were then mixed with the soundtrack and compressed to the downloadable formats offered here.

The music for this project is a sequence of three SmartSound library pieces. None of the music I could find worked very well with a nearly 7-minute-long video, so I decided to use three separate tracks. I turned the intensity way way down because with such a long video, the music can start to get intrusive.

Exponential smoothing was used to achieve smooth gradients in the images. Although the function this fractal is based on is sort of like a second-order polynomial map, the absolute value operations mess up the mathematical behavior of the usual smoothing method (sorry, there's no technical reference on this site for exponential smoothing, unfortunately) creating bands of abrupt changes of counts in the images. The rank-order and histogram coloring methods can easily eliminate this effect in a still image, but the global rank-ordering method used for coloring videos cannot (the reason is very tedious), so the raw data of the videos needs to have smooth count gradients in every individual frame file.

Video Encodings

The "Insane" 30-40 Mbps encodings are becoming a standard for new videos on this site. The quality is really amazing, and it is getting easier to download (and upload!) files this large. The difference between these and the "Near HD" 15 Mbps files is that the lower bit-rate files have noticeably greater blocking artifacts in the gradient areas, and more moire in the areas with lots of fine lines close together. The 40 Mbps encodings here are distinctly not as good as the uncompressed raw video files, but those files have an effective bit rate of 664 Mbps and add up to 30.8 GB. They are just barely playable in realtime, demanding sustained hard-disk read throughput of about 80 M bytes/sec, and video system throughput that can keep up with that.

Primary Data Images

As with the MagnetDeep project, I have included here a sampling of the large primary images that are used for the interpolation. These are enormous uncompressed BMP files with different resolutions, but most are 4434x2497.

Note on Coloring

The coloring of these images is different from the video coloring. The same sequence of color gradients is used, but in the video, the fractal data is mapped into the color palette using a global set of data accumulated from all video frames. At present, the software cannot use the global data from a video to colorize an individual image file. There's nothing intrinsically impossible about this, but that ability needs to be written into the software, and that is definitely on the list of things to do on a free weekend. However, even if the exact color map that is used for the video were applied to these primary images, they would not be colored exactly like the corresponding video frames because the video frame images are a composite of overlapping primary images, and they are downsampled as well.