High-Precision Deep Zoom


Cubic Burning Ship 1

The first deep-zoom animation of the Cubic Burning Ship fractal


The Cubic Burning Ship fractal is derived from the same basic formula as the Burning Ship fractal, but has the third power instead of the second power. The overall look of the two fractals is very similar. The Mandelbrot set of the Cubic Burning Ship looks kind of like a Klingon Bird-of-Prey, and this fractal is sometimes called the "Bird of Prey."

This video is a really nice high-definition 1600x900 resolution, 3900-frame deep-zoom with 9X oversampling for noise reduction. It is, to the best knowledge of HPDZ.NET, the first-ever deep-zoom animation of the Cubic Burning Ship fractal, and is, as far as I can tell, the only video of this fractal in existence. This video magnifies the fractal image from an initial size of 4.0 to a final size of 1.0 x 10-23.

The video pauses at two points before the end point. Images of these structures were published on the Burning Ship still images page previously. The first is a heart-shaped structure at a size of about 7.9x10-13. The next is an insectoid-looking things at a size of 1x10-19. The end point of the video is another insectoid structure at 1x10-23.

Video Capture Images

Click on any image below for a high-quality full-size frame capture from the video.

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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)
Extreme Quality Download739 MB1600x90040 Mbps INSANE QUALITY
HD Quality Download381 MB1600x90020 Mbps
DVD Quality78 MB800x4504 Mbps FASTSTART
Fast On-demand Viewing20 MB400x2261 Mbps FastStart
Mobile Phone Viewing7.8 MB400x226384 Kbps FastStart
WMV Files (Windows Media Player)
DVD Quality85 MB1600x9004 Mbps
Fast On-Demand Viewing22 MB800x4521 Mbps
Mobile Phone Viewing8.8 MB400x228389 Kbps

Note on Video Formats

I've tried to provide a good variety of download options to accomodate different needs. The smaller files can generally be downloaded fast enough to play as they download. The larger ones should be downloaded first, then played.

The 20Mbps encodings are quite good, but they both have perceptible compression artifacts, mostly extremely subtle blocking artifact in the gradients. The 40Mbps encodings are nearly perfect, essentially identical to the raw uncompressed AVI files. But the files are very large. Interestingly, the 40 Mbps WMV file, despite having a peak bit rate of nearly 60 Mbps and a slightly higher average rate of about 42 Mbps, actually looks worse than the 40 Mbps MP4 file during the opening fade-in, with very noticeable artifact. In fact, even the 20 Mbps MP4 version handles the fade-in much better than the 40M WMV version. Interestingly, the fade-out at the end doesn't have this problem.


Vital Statistics
Date Generated:12-14 Jun 2011
Initial Image Size:4.0
Final Image Size:1e-23
Length:2:10 of fractal, 2:36 total
Rendering Time:38.4 hours
Rendering System:Core i7 980X 4.0GHz overclocked
Method:Cubic Burning Ship fractal, exponential smoothing, interpolation from 96 primary images
Noise Reduction:9X oversampling, median filter
Audio:Custom Composition with ACID Pro


The 3,900 frames of this video were generated by interpolation from 96 primary images (directly calculated from the fractal data). They are all about 3700x2100 pixels, but they vary due to the translational motion at various points in the video. The primary images are blended together with 50% overlap on the leading and trailing segments. The weighted-averaging type of pixel interpolation was used.

As with the second-order Burning Ship video, exponential smoothing was used to achieve smooth gradients in the images.

Oversampling on a 3x3 grid was used for noise reduction, with a median filter.

Small erratum: The ending sequence of the videos say 95 primary images; it's actually 96. One of them is numbered "0" and I made the typical mistake of just looking at the number of the last one, forgetting about number 0.


The music is a custom creation with ACID Pro. It's not one of my best, but it gets the job done. I think I should have probably remixed it with a bit lower volume on the bass.

Primary Data Images

As with several previous porjects, I have included a sampling of the large primary images that are used for the interpolation. Ths file has 49 enormous uncompressed BMP files with different resolutions, mostly approximately 3700x2100 pixels.

The coloring of these images is different from the video coloring. This is explained in more detail on the Burning Ship video page.

Klingon Birds of Prey

I'm no authority on Star Trek canon, but a few details are worth mentioning about the "Bird of Prey" term.

First, there is also a Romulan BoP, although it looks distinctly different from the Klingon version and doesn't really resemble this fractal shape all that much. The main difference is the lack of the foreward bridge protruding from the main hull.

Interestingly, it's not clear what the actual size of the ship is supposed to be. Quite a few sites talk about details of scaling the ships, theorizing about energy consumption needed for structural integrity fields as ships get bigger. There's also a fair bit of work comparing movie images that have live persons and a ship to try to estimate how big the ships are.

It's also not known where the in-universe use of the term Bird of Prey originated, but it goes way back to the early episodes of the original series. It is believe, apparently, that the Klingons borrowed the term from the Romulans. The Romulan BoP actually has a bird painted on its ventral surface.

I wanted to put a picture of a BoP here, but I can't find one that is public domain, and it's not worth hassling with potentially upsetting someone about using their copyrighted image.