Path: utzoo!utgpu!news-server.csri.toronto.edu!rpi!zaphod.mps.ohio-state.edu!swrinde!elroy.jpl.nasa.gov!ncar!gatech!prism!ar12
From: ar12@prism.gatech.EDU (REGISTER,ANDREW H)
Newsgroups: comp.compression
Subject: Re: Number theory compression ?
Summary: fractals are kind-of like that
Message-ID: <25894@hydra.gatech.EDU>
Date: 9 Apr 91 20:34:17 GMT
References: <1991Apr4.150053.29873@linus.mitre.org> <1991Apr5.064220.18509@dde.dk> <4931@pink1.UUCP>
Organization: Georgia Institute of Technology
Lines: 23

In article <4931@pink1.UUCP>, beville@motcid.UUCP (Anthony T. Beville) writes:
> For any given sequence of bits longer than some number,  
> merely (!) find a matching sequence deep within the bowels 
> of pi or sqrt(2) or some fraction or whatever, and represent
> that sequence with a greatly reduced number of bits.  
> 

As best I can tell, this is the kind of thing that goes on when you play the 
fractal game (as Barnsley calls it).  The generation of a picture is based
on a set of attractors each with a strength, a probability and a affine (I 
think I spelled that correctly) transformation that is basically a scale and
a rotation.  I would be pretty sure that you could represent an irrational number
based on a set of linear (ie. not 2-D) attractors.  As such, you could then
compress a number like PI (no flames please) accurate to an infinite number of bits just
by describing the attractors.  I know of no work in this area but the trick is
to find just the right attractors!  If you claim to know how to do that, you can
get a lot of money from venture capitalists.  All the work I have seen is in the
image compression arena.
-- 
Andy Register  Internet: ar12@prism.gatech.edu   Bitnet: aregiste@gtri01.bitnet

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