Thursday, March 26, 2015

hereeeeee's the sausage!

i keep drawing "existence/sausages." sometimes you laugh, "there, crazy triff goes again."

well, i have a surprise for you:

here is a fractal curve: 

MinkowskiSausage


the number of segments after the nth iteration of the evolving figure is:

 N_n=4·3^n,

MinkowskiSausageLengths


(1)
and the length of each segment is given by:

 epsilon_n=(1/(sqrt(5)))^n,
(2)

the capacity dimension is: 

D=-lim_(n->infty)(lnN_n)/(lnepsilon_n)
(3)
=(2ln3)/(ln5)
(4)
=log_59
(5)
 approx 1.36521
(6)

(Mandelbrot 1983, p. 48).

what are you looking at?

a minkowski sausage! also referred to as the minkowski cover of a curve.

so, next time you see me drawing an "existence/ sausage" on the board to make a point, you know i can back it up.   

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