[microsound] Schroeder book

[Kim Cascone <kim@xxxxxxxxxxxxxxxxx>]

>  but all self-similar structures are inherently fractal (except
> degenerate cases).  For a self-similar curve comparable to the number
> sequence above, check the Koch curve.  It is a fractal because it has
> dimension log 4/log 3 (its dimension is a fractional value and not an
> integer).
another example would be the following:
create a real line: 0.0...1.0;
erase the middle third of the line excluding the points 1/3 and 2/3;
you have two remaining segments 0...1/3 and 2/3...1;
repeat ad infinitum by erasing the middle thirds of remaining segments;
after erasing n stages you are left with N=2^n segments with each being 
r=(1/3)^n long;
the dimension of the resulting fractal (or Cantor dust) is calculated 
by dividing the log 2/log 3=0.63;
theoretically, if you were to repeat this process infinitely you would 
be left with an infinite set of nothing

I paraphrased the example above from a book I started reading again 
while looking for info on projective geometry:
"Fractals, Chaos and Power Laws" - by Manfred Schroeder (who invented 
the infamous Schroeder reverb algorithm)
there are used copies of this book on Amazon for $12 -- it is the best 
money you'll ever spend...it is not a pop-science book and contains a 
lot of math so don't expect an armchair page turner...


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