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Topic: fractals
Replies: 2   Last Post: May 4, 1995 9:53 PM

 Messages: [ Previous | Next ]
 Ted Alper Posts: 51 Registered: 12/6/04
Re: fractals
Posted: May 4, 1995 9:53 PM

(I think my original post on this wound up only going to
the sender of the message to which I was replying. But the
reply could as easily have been to several of these messages.)

While there's nothing wrong with having some fun with fractals,
it may be a mistake to ascribe too much relevance to them.

Yakov Khurgin, in his book "Did you say mathematics?" -- translated
from the Russian by George Yankovsky and available quite cheaply
through Mir Publishers of Moscow -- cites the remarkable (and now
long-forgotten) studies of the shapes of leaves done by mathematicians
from Descartes (the jasmine curve x^3 + y^3 = 3axy) to German
mathematicians of the 19th century (with full-volume treatises on "The
Analytical Shapes of Leaves").

Something similar may be happening with fractal images. There is a vague
descriptive power to them (though the model is approximate --
after all, rivers and arteries and cauliflower only branch finitely
often, and the nature of the largest branches is qualitatively different
than that of the smallest ones), but that is not the same as
actually modelling something to the extent of capturing some
useful information or process.

None of which is to say fractals can't be pretty and raise some interesting
mathematical questions -- or that there aren't some substantial models
that use them (anyone actually know of one?). But they are not essential
to one's mathematical education in the way that, say, most of the
standard curriculum is. I know plenty of mathematicians who know
nothing about fractals; but all of them understand high school algebra.

Ted Alper
alper@epgy.stanford.edu

Date Subject Author
5/4/95 Scott Smith
5/4/95 Francis Fennell
5/4/95 Ted Alper