A note on Fractal Geometry

[Vaska]

David Casseres wrote:
>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.  

I've already thanked Juan [privately] for what seems to me an admirably
concise and precise description of some of the salient differences between
the two.  

>>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.

YEEEEES.  That was exactly what I'd suspected, but being an ignoramus could
only call it a hunch most vague.  Now that several people have given me a
few pointers and book titles, I feel I may even begin to get somewhere at
last!  
Juan and David: a big thank you to you both.  [And as for the gent who seems
to mind these effusions of gratitude, there's worse things in life, right?].

Vaska