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.

Tuesday, October 24, 2006

Complex Normal Distribution

I called it CND but I haven't seen it defined. I just put complex variables in ND;

z=(1/c1*sqrt(2*pi))*e^((-1/2)*((z-c0)/c1)^2)





Where c1 and c0 are standard variation and mean. In the following c1 is the free parameter. A surprise here is that Mandel and Julia are similar in large scale. Although ND has that property of looking similar after a frequency transformation.

As before, restricting expansion also limits domain. I think I made a mistake with the expansion of CND. Fractal Explorer's Exp(z) does not give Taylor's expansion to a number. The expansion is not so trivial to calculate. Too many terms. I will keep the "expanded to 6" ones until I correct them. Currently I am trying to learn some Java.

Mandel
e^x expanded to 6
Sitting Buddha, hmm
















Julia
e^x expanded to 6
c1=(1.01,-1.11)
Doesn't it look like infinity sign?
Unfortunately the above Mandel
is not at the same c1, Mandel is below









Mandel
e^x to 6












Mandel
bailout=49













Mandel
bailout=324











Julia
bailout= 25












Mandel
bailout=25












Julia
bailout= 361












Mandel
bailout=361












Mandel
c0 free












Mandel
c0=(0,-1)
e^x expanded to 6
Mandel as mouth

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