A note on Fractal Geometry

[David Casseres]

Juan Cires Martinez sez

>1. Chaos Theory and Fractal Geometry, although related, are not the same.
>I'd recomend Mandelbrot's "The Fractal Geometry of Nature" as an
>introduction.

It is, of course, the horse's mouth.  But you have to take Mandelbrot 
with a grain of salt; he makes inflated claims for fractals as true 
representations of nature, seeming to ignore Juan's second point below.  
And his informal explanations of the math are too sloppy to be useful.  
But boy, does he have a lot of gorgeous pictures of fractals!

>2. Fractal objects are as ideal as spheres, lines and polygons.  And
>they are infinite.  Certain natural objects can be described APROXIMATELY
>using concepts from this geometry, like "fractal dimension".

This is very important.  Going back to Stoppard's idea about mathematics 
complex enough to represent natural objects like plants, the fact is that 
fractally-generated imitations of "organic" form are not very convincing 
at all, despite the usefulness of fractal concepts in understanding 
complex phenomena.



Cheers,
David