Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!eecae!netnews.upenn.edu!eniac.seas.upenn.edu!culmer
From: culmer@eniac.seas.upenn.edu (Charles Culmer)
Newsgroups: comp.graphics
Subject: Re: Fractals
Summary: Generation as the limit of an infinite random process
Keywords: Mandelbrot, Barnsly, different methods do same thing, Gleick
Message-ID: <8202@netnews.upenn.edu>
Date: 20 Feb 89 13:10:51 GMT
References: <153.23FF3228@muadib.FIDONET.ORG>
Sender: news@netnews.upenn.edu
Reply-To: culmer@eniac.seas.upenn.edu.UUCP (Charles Culmer)
Organization: University of Pennsylvania
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In article <153.23FF3228@muadib.FIDONET.ORG>
Mahesh.Neelakanta@f7.n369.z1.FIDONET.ORG (Mahesh Neelakanta) writes:
>
>  Has anybody done any work with fractals ? I am looking for some fast 
>algorithms with which I can plot an rotate them on a HP workstation 
>that I am using.  Any help will be appreciated.

This probably doesn't help you with your particular problems, but I'm
going to describe what little I know about fractal generation anyway.
The following is probably all somewhat wrong, but also somewhat right.
Is it Gleick or Glick?  Oh, well.

Mandelbrot defined or described how to generate fractals.
Barnsly discovered how to generate fractals as the limits of infinite
random processes.
Barnsly's approach is discussed on p. 236 of Gleick's recent book on
chaos, which is available everywhere including Crown Books (paperback
is $8.95, hardback is maybe $18.95).

Barnsly's approach works like this--

(1)  Select a finite set of rules for moving from the current pixel to
a new pixel (and turning it on).

(2)  From an arbitrary starting pixel, apply the rules randomly.

The recent Nova episode about chaos began with an application of this
technique to draw a triangle with inverted interior triangles removed,
kind of like the Cantor set.  The process required three fixed points.
For each fixed point, there was a rule that moved the current pixel to
the midpoint of the line joining the current pixel to that fixed point.

I want to draw Barnsly's fern, but I haven't figured out how to do it.
Gleick cites a paper by Barnsly, which probably presents sets of rules.
I don't know the answers to these questions--

(1)  Has Barnsly or anyone else proved the equivalence of the methods?

(2)  Is there a conversion algorithm in one or both directions?

Charles W. Culmer
culmer@eniac.seas.upenn.edu       Truth, justice, and the American way