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Path: utzoo!watmath!clyde!bonnie!akgua!whuxlm!harpo!decvax!decwrl!Glacier!Navajo!fournier
From: fournier@Navajo.ARPA
Newsgroups: net.graphics
Subject: Re: fractal mountains
Message-ID: <161@Navajo.ARPA>
Date: Wed, 26-Jun-85 18:34:10 EDT
Article-I.D.: Navajo.161
Posted: Wed Jun 26 18:34:10 1985
Date-Received: Sat, 29-Jun-85 01:43:17 EDT
References: <241@kovacs.UUCP>
Organization: Stanford University
Lines: 25


*** REPLACE THIS LINE WITH YOUR FRACTAL ***
Indeed the triangular subdivision you mention is better than the
earlier one. It still has a big drawback though, in that the subtriangles
created will be recursively subdivided without any correlation with the
adjoining subtriangles. If you want to approximate fractional Brownian
motion (one of the random fractal processes), this is incorrect since
the 2-D version is non-Markovian, meaning that one side of the surface
cannot be computed knowing only the boundary. A better subdivision scheme
can be found in the Fournier/Fussell/Carpenter paper in CACM, June 1982,
or the Piper/Fournier Siggraph paper of 1984. Of course a rejoinder by
B. Mandelbrot and a reply can be found in the following CACM issue of
August (or July).
Several people are currently working on new schemes to generate 2-D 
approximations of fBm.
There will be a tutorial at Siggraph on fractals, with Loren Carpenter
and Benoit Mandelbrot together again for the first time.
This should be fun!
If anybody is interested in 3-D fractal (or approximations thereof), I can

If anybody is interested  in C code to generate 3-D fractal (and
the code is short indeed, but no display is included), mail to me.
It will take a few days, since I just got here and I have to bring
most everything up anew. Remember that 3-D here means the process
generate a volume, not a 2-D surface to be inbedded in a 3-D space.