> You will, for a moment, have to think of fractals as having nothing to do with
> images - they do however have everything to do with self-likeness and finding
> patterns in what appears to be randomness.
> Now, the idea of fractal compression is not to be able to compress fractals
> which have been expanded - that is a relatively easy task. You don't just
> determine whether a data set has a rich fractal property by looking at it.
> The patterns found in the data are usually impossible for us to see just by
> looking at the raw data. To convince you of this, you could easily write a
> recursive formula which produces an image and then look at it and not be able
> to see any patterns in the result. Chaos theory deals with finding order in
> apparent randomness. ie. you could look at a data file and say, "no that's
> not a fractal, that's a sequence of words" but there are definitely fractal
> patterns in that data sequence.
I think you are giving fractal a bit of a loose definition. A fractal
isn't any pattern, but a pattern that is self-similar at different levels
of scale. Chaos theory deals with finding order in *apparent* randomness.
True randomness will not compress, and fractal compression will only work
on data that repeats at different scales. Unfortunately this is not a
feature of many data sets.
In the late eighties, scientists attempted to fit fractals to everything
in nature. Sometimes they discovered fractal geometry in "random"
effects, sometimes they didn't. The important point is they were
investigating *nature*. Few elements of data we deal with are natural,
with the exception of natural images, sounds (not music, it seems that
music designed along fractal concepts general ends up in elevators), and
stock exchange prices (think about it a second, and it is obvious they
recursive, a little longer and you can see they are fractals. Spend some
money to predict them, and you'll soon go broke). Documents, while
displaying patterns, are not fractal. Basically, gzip will always do a
better job on the written word them then any fractal algorithm.
> It is generally impossible to find one formula which will best compress a
> whole file. The file must be divided into sections each with their own
> fractal properties. By separating parts of the file, you can increase the
> level of compression because different parts of the file may have fractal
> properties very different from other parts of the file.
As you split up the file, you have to store more information to put the
pieces back together again. Because of this you start getting diminishing
returns on each split. The first is a big gain, but the twentieth may use
up more space then number nineteen.
> > Now this was from some researchers about two years ago, and things might
> > be better now, but I wouldn't go investing in a fractal compression
> > company just yet.
> Would have been good to invest 2 years ago.
> There are other researchers who were more successful then (I won't name
> > Sorry, this wouldn't work (IMHO). There are theoretical limits to how far
> > you can push lossless compression (which is what you want for data, not
> > images). An encyclopedia isn't fractal in nature (self similar at
> > different scales), hence would not compress using this technique.
> It's amazing isn't it. No-one can pinpoint the exact limit but we are always
> getting closer to it. Different data would have different limits ofcourse - a
> file full of 0's would have an obvious limit - or not so obvious! Think about
No, actually the limit was pin-pointed quite some time ago. I don't know
the details, and I'm a little to lazy to wonder down to the library for
the sake of an argument but it does depend on the data set, and it depends
on prior knowledge of the type of information being communicated (hence
the not so obvious limit on the file full of '0's).
> You are probably interested about how a fractal could compress an
> encyclopedia. You are probably thinking about how fractals would not produce
> the exact results and would cause misspelt words etc. This is not a problem
> however - it is possible to find a level of compression that will produce
> _exact_ results. For example, real numbers produced by the algorithm might be
> rounded up or down to an absolute value like an ascii character. If the lower
> character is wanted, the compressor would aim to produce a value less than 0.5
> higher than the wanted character.
Sorry, this is a case of the wrong algorithm for the job. If you look back
to what fractal compression is, you will see that it just won't work on
prose (unless artificially constructed). It relies on identifying patterns
and encoding them, not just any pattern, but *fractal* patterns. If the
patterns don't appear in the data - and that does not mean the data is
random - you won't get any compression, even if there are other patterns
that could be exploited.
Part of the magic of the fractal compression is that you can display your
image at some (nominal) resolution (of information, not image), then zoom
in as far as you like to see more detail. Think about what this would mean
to a word or sentence compressed in this manner. How can you print a
word at half it's resolution? You can't. Words and sentences are all or
nothing things, they have no similarity on different scale.
> Like I said before, you have to also forget about what people usually think of
> as fractals - pretty patterns. You are the first person I have heard who has
> said that an encyclopedia isn't fractal in nature. I am one of many who
> believe (like to beleive) that everything is fractal in nature and everything
> in nature is fractal and all of these fractals are derrived from super
> fractals... and there is one super-duper-fractal. It's hard to believe this
> becuase... well... it's hard to believe. The more you read about chaos
> theory, though, the closer that statement seems to be to the truth.
[I'm wincing as I say this] You're Wrong! [ouch! they hurt, I promise not
to say it again].
Fractals do not nature make,
nature does the fractals make.
The fact that fractals crop up in nature (quite often) does not mean that
everything in nature is a fractal. A crystal latice is not fractal, a
glass of water is not fractal, a gas is not fractal. A snow flake is, a
coast line is and so are most plants.
Before you consider everything to be a fractal, consider what a fractal
actually is. If you look at the definition of a fractal, you will see
that many things just don't fit in that category. And if it doesn't fit,
then it just won't compress very well.
Chaos theory describes a lot of things that were previously pushed to one
side as being to hard, that doesn't mean that everything is a part of
> It's all theory ofcourse.
> "Don't anthropomorphize computers. They hate that."
> Ryan Heise firstname.lastname@example.org
Scott Hopwood 'When all else fails, consult an oracle.
(02) 351-6098 Usually, the best place to track one down
email@example.com is at the bottom of a glass of red.'