User:Ind1v1dual/Zm=Zn2+c OR Zn+1 = Zn2 + c

2010-02-08T12:54:15Z

24.45.118.11: Okay this is what i got the image and the formula may not have been what most have speculated"

===Okay this is what i got the image and the formula may not have been what most have speculated" ===
all this has to do with the sequence of creation '''"of all life and matter" '''and brain waves, responses or how it works and what not but I think" the image wasn't a planet or galaxy collision but this mandelbrot set and that would mean the formula or expression is actually Zn+1 = Zn2 + c but see for yourselves if anyone is still interested" hey best i could do"
=== http://www.fractal.org/Life-Science-Technology/Publications.htm ===

===http://www.fractal.org/Life-Science-Technology/Publications/Fractal-Neural-Networks.htm ===

===Spatial Neural Networks Based on Fractal Algorithms
Biomorph Nets of Nets of ...===
Thomas Kromer,Zentrum für Psychiatrie,Münsterklinik Zwiefalten ,G

1 . Abstract and Introduction :
Biological central nervous systems with their massive parallel structures and recurrent projections show fractal characteristics in structural and functional parameters ( Babloyantz and Louren¸o 1994 ). Julia sets and the Mandelbrot set are the well known classical fractals with all their harmony , deterministic chaos and beauty , generated by iterated non - linear functions .The according algorithms may be transposed , based on their geometrical interpretation , directly into the massive parallel structure of neural networks working on recurrent projections. Structural organization and functional properties of those networks , their ability to process data and correspondences to biological neural networks will be discussed .

2. Fractal algorithms and their geometrical interpretation :
2.1 The algorithms of Julia sets and the Mandelbrot set:
Iterating the function f(1) : z (n+1) = c + zn2 ,(c and z representing complex numbers respective points in the complex plane), will generate the beautiful fractals of the Julia sets and the Mandelbrot set (Mandelbrot 1982 , Peitgen and Richter 1986) . According to the rules of geometrical addition and multiplication of complex numbers ( Pieper 1985) we can interpret function f(1) as describing a combined movement :
First , the term :" + zn2 " in f(1) describes a movement from point zn to the point zn2 . A lot of trajectories can connect these two points, one is the segment of the logarithmic spiral through zn . ( In a polar coordinate system we get a logarithmic spiral by the function f(2): r = aec*j . Geometrical squaring of a complex number is done by doubling the angle between the vector z ( from zero to the point z ) and the x - axis and squaring the length of vector z (2) . Doubling the angle j in f(2) will also cause a squaring of r . This proves point z2 lying on the logarithmic spiral through z .)
Second , the first term of f(1), " c " ( meaning the addition of complex number c ), can be interpreted as describing a linear movement along vector c .
Both movements can be combined to a continuous movement along spiralic trajectories ( according to Poincaré )from any point zn to the according point (c+zn2 ) = z(n+1).We get two different fields of trajectories , one with segments of logarithmic spirals arising from each point z n, the other as a field of (parallel) vectors c .We can follow the different trajectories alternately ( fig 2.1c ) or simultaneously ( fig 2.1d , 2.1e) . Various options to

visualize the developments are shown in figure ( 2.1 a-f )

God has used fractals to add interest and beauty to nature. He has somehow encoded the equations necessary to create fractal structure into the DNA of living things. He has created natural processes that produce fractal shapes in inanimate matter. Without fractals in our surroundings, our environment would appear bland and dull.

[http://fridaysunset.net/creation/beauty.html fridaysunset.net/ creation/beauty.html]

The Mandelbrot Set

A fractal of limitless complexity and great beauty

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