> heard, fractal compression was very good at compressing scenes that had
> recursive patterns in them, i.e. fractals. The thing about fractals is
> they don't take much information to transfer them anyway. On images (or
> data) that doesn't have this property - including most data files your
> would which to move and most pictures, fractal compression works no
> better, and often worse then normal techniques.
?
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.
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.
> 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
names).
> 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
it.
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.
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.
It's all theory ofcourse.
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"Don't anthropomorphize computers. They hate that."
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Ryan Heise rheise@nospam.progsoc.uts.edu.au