ATON is a hopefully evolving classification theory. It aspires to unify knowledge around numbers and prefers naive methods. Some of the older posts are wrong but I'll keep them for the sake of continuity.

Saturday, March 25, 2006

H-Set

H-Set is like H-Fractal or the binary tree.

H0={}
H1=HH0={,{}}
H2=HH1={,{,{}}}
...
Hn=HH(n-1)

Where H is an inclusive-exclusive reflection operator.
It reflects the previous.

The number of states;

SH0=2^0=1
SH1=2^1=2
SH2=2^2=4
...
SHn=2^n

The Mandelbrot iteration;
z(n+1)=z(n)^2+c
is expanded in a H-Fractal;
z0=z0
z1=z0^2+c
z2=(z0^2+c)^2+c

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