Path: utzoo!attcan!uunet!cs.utexas.edu!tut.cis.ohio-state.edu!pt.cs.cmu.edu!rochester!udel!princeton!phoenix!markv From: markv@phoenix.Princeton.EDU (Mark T Vandewettering) Newsgroups: comp.graphics Subject: Re: fractals as bad science Keywords: Fractals, ugh!, mathematicians, pure, applied, non- Message-ID: <11716@phoenix.Princeton.EDU> Date: 24 Nov 89 19:24:38 GMT References: <19544@pasteur.Berkeley.EDU> <1619@crdos1.crd.ge.COM> <3775@celit.fps.com> <5383@orca.WV.TEK.COM> <3842@puff.cs.wisc.edu> <1989Nov24.114609.8837@hellgate.utah.edu> Reply-To: markv@phoenix.Princeton.EDU (Mark T Vandewettering) Organization: Princeton University, NJ Lines: 77 After my last batch of flaming hate mail, I decided not to further stretch my bulging mailbox, but after a Thanksgiving turkey dinner, all seems better, so once more into the breach.... Excuse the confusing quotations here I have to sort them out myself.... In article <1989Nov24.114609.8837@hellgate.utah.edu> thomson@cs.utah.edu (Rich Thomson) writes: >In article <5383@orca.WV.TEK.COM> brucec@demiurge.WV.TEK.COM > (Bruce Cohen) writes: >] Am I to conclude that islands are constructed by some geological >] process of repeated subdivision? Of course not! All I have done is to >] produce a picture which looks (to me) like an island. Here we hit what I believe is the crux of the problem. Typical fractal mountains are not a model of physical terrain. They are a description of terrain. A model implies that some physical process is being estimated in order to produce behavior/appearance similar to something observed. A description is a qualitative "looks like" method. It says nothing about the physical processes which actually cause things like mountains to form. Researchers have noted that forces such as erosion play key roles in shaping the appearance of terrain. Some recent research papers have been written to demonstrate how fractals can be modified with forces such as erosion. These approaches are justifiably models, because they seek to provide a physical explanation for the formation of terrain. One might argue that beginning computer graphics wasn't modeling a scene, because there was little physical theory behind the generation of images. With the advent of radiosity and backward ray tracing, as well as improved surface descriptions, more and more computer graphics seek to model the interplay of light between objects in a scene. >Are we to conclude that at the subatomic level differential equations >represent the structure of the telephone wire? The example you've used >(random subdivision) may produce a similar structure, at a gross level, to >an island in the same way your differential equation provides a gross level >description of the spatial configuration of a suspended telephone wire. There is one small difference: caternaries have been discovered by a sound analysis of forces involved on the wire. The macroscopic properties of the wire are completely the result of relatively few forces, which can be analyzed analytically. No such basis has ever been demonstrated in fractal geometry. We rely on a qualitative and subjective approach (does this look right?) to model natural objects. >Another direction one can go with "fractals" is into the embryonic chaos >theory that has been worked out by people like Devaney in his book[2], or >start with Gleick's book _Chaos: The Making of a New Science_. You may >find out that self-similar curves (in particular, the Cantor Set) have more >relevance to the real world than what you thought. I would not recomment Gleick's book, as I think it causes far more confusion than it clears up. I don't believe that Gleick's understanding of fractals, chaos and non-linear dynamics is quite up to scratch. It was, however, my initial impetus to seek out other books and study the topic more, so it might be valuable in this regard. The bibliography is adequate at the very least. Devaney's book actually grinds into some of the theory, but I agree that it is at times difficult to read. I can't decide whether it is due to poor presentation, organization or what. Still, it seems moderately complete, and proves many of the theorems etc. just hinted at by Gleick. >show you how to generate all these "fractal" images without understanding >the ideas behind them. Personally, I feel it is more useful to study the >works of the emerging "chaos theory" and things like Rene' Thom's >catastrophe theory (as outlined in [3]). If you're looking for real-world >modelling applications using fractal methods, check out the course notes >from this year's SIGGRAPH course taught by Prusinkiwiecz (I hope I spelled >that right) and Hanan[4] Thanks for the bibliography.