> On Fri, 19 Jul 1996, Scott Hopwood wrote:
> > Yes, I can imagine compressing data fractally (I don't have to visualise
> > it), however I still don't see how that negates the argument I have been
> > putting forward. You can't use fractal compression effectively on data
> > that isn't fractal in nature. All the examples you have given me
> > (including that game) are specific instances where fractal compression is
> > appropriate. Using fractal compression in these instances is a good
> > example of choosing the correct algorithm for the application. However,
> > that does not mean that fractal compression is the general answer for all
> > your compression needs.
> I agree that a particular fractal compression software will not produce very
> good results on some blocks of data. This is because it can't find the
> fractal property in the data - that is basically what you are saying - except
> you are also saying that if the software can't find the fractal property, then
> it is not there. Would you agree that fractal compression software can be
> improved to find more fractal properties in given data in the future?
ONLY IF THE DATA CONTAINS FRACTAL PROPERTIES ORIGINALLY. And then, only
if we are willing to loose some of the data during the process. You imply
that ALL data is fractal in nature, I think this is basic flaw in your
argument. If you can somehow prove to me that everything has a fractal
component to it, then I will agree that you can perform lossy compression
on it. Why lossy? Because the difference between the original image, and
the fractal image is the components of it that are not fractal (or that the
processing can not find).
Let me give you an example. One of the most commonly given examples of
fractals in nature are coastlines. If you take a coastline and double the
scale, it still looks like a coastline. But what happens when you scale
down to the level of a beach? It looks nothing like a coastline. Here is
where it's fractal nature breaks down. The beach, and everything smaller
than it are the non-fractal components of the real coastline. Any fractal
approximation won't contain that sort of detail.
So what has this got to do with data files? Well, it all depends on what
we reguard as important. In an image, size matters, descrepencies matter,
details don't. If we loose some of the non-fractal detail in an image it
doesn't seem to make much difference. It still looks almost the same. For
a data file things are very different because everything can be important.
The flipping of a single bit can turn a working system into a waste of
space. It can turn a customer into a employee, and can declare a living
person to be dead.
In short, loosing *any* information can be problematic. (Yes, I know that
we can perform consistency checks, and store redundent data. But it's
much better not to loose the information in the first place.)
> > Again it boils down to the issue that not all things have a fractal
> > nature. I'm not saying this out of blind faith, but because I have some
> > idea of what it means to say "X is fractal". If you can point out to me
> > how a dictionary is fractal, then I will admit that it can be compressed
> > well. If you can't then I will have to retain the opinion that it won't
> > be.
> Before fractal image compression was invented, do you think that anyone would
> have thought that Pavaroti was a fractal?
Thats as incorrect as saying "before jpeg compression, who would have
thought that Pavaroti was a quad tree?". The fractal image is an
approximation of the original image (it's lossy). It happens that our
visual system ignore the artifacts introduced through the conversion
process, which is why it is so good for compressing images. Paveroiti
isn't the fractal and the image isn't the fractal. The image does however
have fractal components.
> You would require an extremely fast chip to take that picture or you would
> have to keep the camera still for a while and hope nothing moves. Maybe
> beyond 2000 we will have the technology.
The problem is the mechanics of the input, not the processing. The CCD's
used today automatically pixelate an image, what I would like to see is
something that don't use an intermediate pixelation between images
capture, and fractal generation.
Scott Hopwood 'When all else fails, consult an oracle.
(02) 351-6098 Usually, the best place to track one down
firstname.lastname@example.org is at the bottom of a glass of red.'