High-Precision Deep Zoom


HD1 "Tartaglia"

My first high-definition fractal animation.


Unfortunately, the bottom line here is that high-definition video is just is not practical for this kind of animation of any significant length delivered over the internet. I have a lot to say about this below. It is so impractical that I ultimately decided, after two months of failed experiments, to downconvert this whole thing to 640x480 to more honestly represent the quality of the video that is in the files (unlike some other HD video sources). I have provided one 1200x900, 375 MB monster if anyone really wants to see it.

The MP4 files have been re-encoded with different settings and have much better quality, as well as supporting fast start download.

Download Options
MP4 File Formats:320x240 500 Kbps 18 MB preview quality Fast Start
640x480 2 Mbps 57 MB near DVD quality Fast Start
640x480 4 Mbps 109 MB true DVD quality fast start
1200x900 15-20 Mbps VBR 375 MB True HD quality
WMV File Formats:320x240 500 Kbps 12.8 MB preview quality
Vital Statistics
Date Generated:11-12 May 2008
Final Image Size:5.6e-31
Resolution:1200x900 (published at 640x480)
Video Length:2:44 of fractal, 3:28 total
Rendering Time:about 2 days
Method:Escape counts
Audio:"Chosen" by Technetium

The image I chose to zoom in to is an area where there are lots of tight spirals combined with fine fibers to try to showcase the higher resolution. The color palette was also chosen to be simple saturated colors to help evaluate color fidelity in the compressed images.

Most importantly, this animation is pretty cool in its own right, independent of whether it is in high-definition or not. The music ("Chosen" from the album Nocturnal by Technetium -- thanks for giving permission to use it!) works great with this video too. It usually takes me a long time to select music for these videos, but this one was an instant perfect match.

This project is also one more data point in my ongoing comparison of MP4 and WMV. I have encoded it into a whole lot of different formats for comparison. In this particular case, I actually like the 640x480 WMV file a little more -- it seems to have spread the compression artifacts out more evenly rather than accumulating them all into chunky blocks.

Niccolo Fontana Tartaglia

This animation is named in honor of Niccolo Fontana Tartaglia (1499-1557), an Italian mathematician who was an early pioneer in the development of the concept of what are now called "imaginary" numbers. He was a contemporary and eventual adversary of Gerolamo Cardano (in whose honor I have dedicated another video, DEHP-III). Tartaglia was one of the first (but not the first) to develop formulas for solving third-order polynomials ("cubic" equations), which, at the time, was akin to magic. His solutions frequently involved taking the square roots of negative numbers, an idea which seemed utterly preposterous in his day, since even the validity of negative numbers themselves was considered dubious by contemporary mathematicians. It turned out that Tartaglia's formulas gave reasonable answers anyway, since the terms with these square roots canceled each other out and add to zero. It was later found by Cardano that Tartaglia's formulas had been previously discovered by Scipione del Ferro, and Cardano's publicizing of this fact was the root of the animosity between the two.

"Tartaglia" is actually a nickname, arising from the fact he spoke with a stammer due to a facial injury. Although it is somewhat derogatory, it is the name by which he is known today.

High-Definition Details

If you are reading this far down, you must have some kind of interest in the issue of "high-definition" here. Please read on. I have much to say.

Why The Weird Resolution?

Since I'm not constrained to standard TV picture sizes, I had a choice to make about how big this animation should be. I chose 1200x900 because it fits nicely into a 1280x1024 computer screen with a little space for the player's title and status bars. It's higher resolution than 720 HDTV, but lower than 1080. I decided to stick with a 4:3 aspect ratio because the Mandelbrot set images fit best into a nearly square format. A 16:9 format doesn't make much sense when most of the visual effect is circles and other things that are basically as tall as they are wide. Some areas of the Mandelbrot set might work better in 16:9 (like the western antenna) but I didn't think this video would benefit much from it.

Some Notes on Bit Rates

I've published only constant-bit-rate (CBR) encoded files of this animation. I found that variable-bit-rate (VBR) encoding is essentially identical in quality to CBR encoding at the equivalent average bit rate, and that VBR tends to ruin the quality of simpler areas, like images with sparse texture and a gradient background -- the background tends to get severely banded and blocked. CBR encoding, both in MP4 and WMV, tends to provide a more esthetically appealing final product, although areas with lots of detail moving quickly are a bit more degraded. For this particular animation, all the CBR encodings look better than the VBR encodings at equivalent average bit rates.

Show Me!

If you really really want to see this animation in something close to a decent HD experience, or if you don't believe this was actually rendered in 1200x900 and want to see for yourself, do please try the insanely long full-size 1200x900 15 Mbps 375 MB true HD file.

Is It Worth It?

If you are looking at that 375 MB HD file and thinking to yourself "not worth it" I hear you. Although the bit rate is comparable to a top-notch HD 1080p television program (the VBR-encoded file has an average bit rate of about 15 Mbps), downloading this file probably isn't worth it. There is a little more detail, noticeably more in fact, especially in the tight spirals in the Julia sets, but the overall experience is not a whole lot better than the 640x480 4 Mbps CBR versions. The background color gradients still show a great deal of distracting banding artifact, and, despite the use of the anti-blocking filter in the encoder, areas of fine detail still have significant block artifact as well. 

But Isn't the Real HD Version Awesome??!!??

You have to get up beyond 20 Mbps bit rate to really see this video shine. I made one (a VBR encoding with an average bit rate around 48 Mbps) and it looks great. Unfortunately, that file is 1.3GB long -- yes, GIGAbytes -- and I just plain don't want to upload it. Even if I did, you probably wouldn't want to download it. And even if you did, there is a good chance you wouldn't be able to watch it unless you have a really fast computer and you defragment your hard drive after saving the file so that the file is not fragmented (yes, I have determined this makes a difference at super-high bit rates like this).

How Much Compression Are We Really Getting?

The uncompressed AVI files for this animation total 14.8 GB, which works out to around 720 Mbps, which is far more than any computer can play back in real time. The highest bit rate files that I can play back smoothly are around 50 Mbps sustained bit rate, which is about 7% the size of the original raw video files. The ones downconverted to 640x480 are at about 4 Mbps, a mere 0.5% of the original image bit rate.

Production Time

For this 210-second movie, it takes about 35 minutes to make a 500 Kbps 320x240 video, and over an hour to generate a 4 Mbps file at 640x480. The monster 1200x900 file took 3.5 hours to encode. This is on a 3.2 GHz Pentium-IV using Sony Vegas Pro 8.0.

We're Looking Out For You

Now, I could have played a trick here and encoded this thing at, say, 4Mbps (standard DVD quality), but kept the video resolution at 1200x900 and called it "High-Definition". The file would actually not be a whole lot larger, and many people would be fooled by seeing it come up at 1200x900 in their player. But HPDZ would never pull a stunt like that. Now, I do realize that so-called "high-definition" video is being offered over the internet, but it is bogus, almost to the point of being a lie. High-definition depends not just on the number of pixels in the image, but also on the bit rate of the video data. If an HD signal is compressed down to the bit rate of a standard DVD (around 4 Mbps) then it will look like a standard DVD, whether it's played back at 640x480 or 1440x1080.

So HPDZ encourages consumers to pay close attention to the quality of their high-definition products, whether those products are fractal animations or regular mainstream video. Most content distributors on the internet are compressing their product down well below the bit rate even for regular DVD. Even cable TV and satellite TV providers are compressing some their programming down to 8 Mbps or lower to try to squeeze more programming into their finite bandwidth space.

After going through all the experiments I've done over the past two months to try to get this little 3.5 minutes of video to compress to a reasonable size and still look good, I can understand why they are doing this, especially the internet-based providers. Very few home users have a service that can deliver 15 Mbps, and the vast majority are not going to even be able to sustain 4 Mbps reliably. Movies would have to be compressed to 1 or 2 Mbps to ensure reliably distribution over residential broadband. That content can be packaged into an HD format like 720p, but the picture quality will be so badly degraded it will look more like a VCD.

There should be a standard requirement for qualification as "High-Definition" for commercial labeling purposes. I believe it should be based on the modulation transfer function (both spatially and temporally) of the overall video signal delivered to the consumer end-point (the TV screen or computer monitor it's being watched on), including the compression, rather than on pixel resolution or bit rate alone. Otherwise the term "High-Definition" will deteriorate into meaningless as the word "organic" has for food labeling.

Business Model for Global Domination

High-definition DVD (Blu-Ray) burners and media are becoming less expensive, and I may offer some HD animations on disc for sale at a modest price (sorry, freebies are unlikely given the cost of media, shipping, etc.).