In TML subject 2188, Mark Cook writes:
> In TML subject 2186, [email removed] (Brent L. Woods) writes:
>
> > What's the data capacity of a holocrystal? [ ... ]
>
> [ ... ]
>
> Given these boundary conditions (pixel depth, image dimensions, and
> number of frames per second), we can estimate the amount of storage
> neccessary for 5 hours of continuous visual data. Figure 24-bit pixels
> in a 1024x1024 image, scanned 60 times per second, and you end up with
> 1,509,949,440 bits of data per second. Multiply that by the number of
> seconds in 5 hours (18,000) and you get 2.7179 x 10^13 bits of data.
>
> [ ... ]
Whoa! A holocrystal holds 5 hours of HOLOGRAPHIC video. I think the
parallel soundtrack is nothing compared to the fact that this data is
3-D. The picture is likely to be 1024x1024x1024. Multiply that number
by another 3 orders of magnitude to get 2.7831 x 10^16 bits (3,240,000
Gigabytes) if the data is uncompressed.
>
> Regarding the compression of image data, I offer only one tantalizing
> point. Recent date compression reseach has demonstrated that very
> complex natural images (a fern, a tree, a mountain skyline) can be
> reduced to a single factal equation for storage, and then reproduced
> in total detail, with no loss of resolution. Optimists suggest that,
> eventually, more sophisticated methods will be found which allow ANY
> image to be stored in fractal form. This form of compression results
> in a storage space reduction several magnitudes of order smaller than
> the original image. The current drawback is that discerning the correct
> storage fractal is very hit-and-miss, and deriving it is extremely
> time-consuming. Some images fail to be fractally compressed.
>
Actually, fractals are really just the beginning. There are many amazing
compression techniques which are just being developed now. For instance,
you can time-compress pictures for a tremendous savings, and without
using nearly as much CPU time as fractalizing would take. For example,
you might fractally draw a picture once, then move regions of the picture
from frame to frame. Any compression technique like this would incorporate
a way to patch the new frame, so that you can optimize between drawing new
parts of the picture and moving the old ones.
You could also get even better compression ratios with 3-D fractal
expansion (although not enough to out-weigh the fact that the picture is
3-D as opposed to 2-D). There are many other compression techniques, too.
For instance, you could take advantage of things such as locality of color,
which might let you use 8 bits instead of 24 bits (or something like that)
to represent colors).
We could also probably assume that maximum compression is available, no
matter how much processing power is needed. Computers are bound to be
pretty fast by that time (even hand-comps).
The question remains -- how much compression can we get? Uncompressed,
the images might take 3 million billion bytes. I can't tell you how
much all of the compression techniques give you, but lets assume that
fractalizing gives you a 32 K to 1 savings, time-compression gives you
a 128 to 1 savings, and various other methods such as color-compression
give you a further 32 to 1 savings. Wow! Already down to 25,920,000
bytes! Of course, this is a very rough estimate, but entirely feasible.
Also, this would be an AVERAGE. You could get better or worse
compression depending on what you're recording. Hopefully, compression
techniques will have advanced enough to cover just about all cases by
then.
> [ ... ]
>
> I don't know about you, but I always assumed that these crystals were
> about half the size of a standard domino. Considering that modern
> high-density 3.5" floppy discs can already hold over 1 Mb. of data,
> This only represents a 2 order of magnitude improvement in data storage
> density, which doesn't seem at all unreasonable to me.
>
Well, 3 1/2" CD-ROMs can hold 250 MB of data. Assuming they use the
outer 3/4" band to store data (remember that they are only 1 3/4" in
radius), they have about 6 1/2" of surface ares. A square inch of
surface area would thus hold 40,330,000 bytes of information. If you
think of it as a square of bits, thats 6350 bytes per side, or 20,000
bits per cm. Well, that's 8 x 10^12 bytes (7450 Gigabytes, or
6.4 x 10^13 bits), for a 1x2x4 cm chunk, assuming that all else is the
same as today except we use 3-D crystals instead of 2-D disk storage.
In any event, that's 300,000 times the size I (optimistically)
estimated as required for storage. You could assume that the (usable)
crystal is 1/40 of a cm on a side. Or, you could assume that data
compression techniques are much less efficient.
One thing you DON'T want to do, however, is to assume that you can
store 3,240,000 Gigabytes on a crystal. You can't. Compression simply
lets you store video, which, if uncompressed, would take 3,240,000
Gigabytes to store. Pure DATA compression is an entirely different
matter, and in most cases can't come anywhere near the ratios that you
can get with video.
>
> If we assume that one of these 5-hour holo-crystals is 1x2x4 cm., then
> the total number of them in a cubic meter of crystal would be 100 x 50
> x 25, or 125,000. If we assume that each crystal can hold 2.7179 x
> 10^13 bits of data, before fractal compression, then you have 3.3974 x
> 10^18 bits of storage per cubic meter. Since volume of a sphere is
> stated as 4/3 pi R^3, where R (in this case) is 50,000 meters, the
> total volume of a 100 Km. diameter sphere is 5.2360 x 10^14 cubic
> meters. Multiply that by the storage capacity per cubic meter, and
> you have a total storage capacity of 1.7789 x 10^33 bits.
>
Again, remember that fractal and other video compression methods do not
apply to pure data. You might be able to get this kind of storage, but
take data compression out of the picture.
Using my CD-ROM model, I got 8 x 10^18 bits (931,000,000 Gigabytes)
per cubic meter, for a total of 4.19 x 10^33 bits (4.88 x 10^24
Gigabytes) for the entire sphere. You could probably increase this
with data compression as well, but probably on the order of 2 to 10
times, not the same level that you can get with video.
In any event:
o There is more data to store than you thought. I'm pretty sure that
the intention was for the images to be 3-D.
o I think that data compression may be able to more than make up for
it (but who knows).
o Don't take fractal compression into consideration when considering
how much data a crystal can store. This merely means you can store
more video using the same amount of data.
- - --------------------
Jerry Williams
[email removed]
#include <std.disclaimer>