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From: park@usceast.UUCP (Kihong Park)
Newsgroups: comp.graphics
Subject: Re: Fractals, and Philosophy of Science
Message-ID: <3045@usceast.UUCP>
Date: 12 Jan 90 04:00:23 GMT
References: <119.256E54C5@uscacm.UUCP> <1247@becker.UUCP> <9144@cbmvax.commodore.com> <6780@lindy.Stanford.EDU> <9215@cbmvax.commodore.com> <12707@phoenix.Princeton.EDU>
Reply-To: park@usceast.UUCP (Kihong Park)
Organization: University of South Carolina, Columbia
Lines: 39

>Yes!  Mathematically speaking, the concept of fractal dimension is rigorously
>defined.  Chaos theory has some very specific results, as does complexity 
>theory.  Because of the hype surrounding fractals, one sees grandiose claims
>about the applicability of fractals to describing natural objects.  
>The problem with this is twofold:
>
>	a)	rarely are such descriptions analytically compared with
>		the objects they describe.  Pictures that are generated
>		with fractals are usually evaluated on purely subjective
>		criteria, which is error prone.

>	b)	descriptions say nothing about the processes that generated
>		the object in the first place.  Fractal mountains don't
>		react to erosion or gravity, fractals trees don't grow with
>		the wind etc....

This being the comp.graphics newsgroup, it is natural to emphasize fractals 
from the computer generation of images point of view. But there is a "physical"
aspect to the issue as well which lends the fractal approach to modeling
certain aspects of natural phenomena additional credence.
It is well known that cellular automata behavior can exhibit fractal 
structures in terms of the time-evolution of their global configuration 
patterns. Such properties are observed in some of the class 3 cellular automata
as empirically classified by S. Wolfram. An ensemble of simple elements
interacting with one another locally can exhibit complex global behavior. If
an analogy is made between such systems and certain natural phenomena, then
attributes such as erosion, friction, and gravity can be modeled within
such a framework by suitably modifying the CA transformation rules(modeling
fluid dynamics uses in essence such rules).
Moreover, A. Lindenmayer has developed grammatical systems(Lindenmayer systems),
the parallel realization thereof on a cellular substrate is regarded as very
good models of plant growth. The fact that plants do not grow unboundadly in
part due to gravitational forces can also be incorporated into the overall
framework. Similar observations are also applicable to cellular growth such
as the limbs of homo sapiens.
One should not loose sight that fractal object generation via simple iterative
functions systems(Barnsley), or probabilistic iterative automata(Culik), are
computational descriptions which do not exclude other forms of realization
as illustrated above.