Newsgroups: comp.graphics
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From: thomson@cs.utah.edu (Rich Thomson)
Subject: Re: fractals with dimension greater than 3?
Date: 4 Apr 91 09:47:45 MST
Message-ID: <1991Apr4.094745.13901@hellgate.utah.edu>
Organization: Computer Science Department, University of Utah, SLC, UT
References: <1991Apr4.163135.25063@leland.Stanford.EDU>

In article <1991Apr4.163135.25063@leland.Stanford.EDU>
	rick@hanauma.Stanford.EDU (Richard Ottolini) writes:
>I notice there are some geological phenemena that are scale-invariant in 3-D
>and over time.  Is this a fractal with dimension at least 3?

Probably more like it is a fractal with dimension between 2 and 3,
imbedded in 3-space.  For instance, the standard middle-thirds Cantor
set has dimension ln(2)/ln(3), which is somewhere between 0 and 1.
The standard Cantor set is imbedded in the real-line.

This is not to say that there aren't fractals with dimension higher
than 3, but they are imbedded in some space R^n, n > 3.

						-- Rich
Rich Thomson	thomson@cs.utah.edu  {bellcore,hplabs,uunet}!utah-cs!thomson
    ``Read my MIPs -- no new VAXes!!''  --George Bush after sniffing freon