Universe-Mandelbrot Theory.

[Dark Mind]

Actually... I need to get this clarified in my own head before I post my actual theory...

 

Hang on...

 

Black Holes... Quazars... Super heated gas... Formation of our "universe"... Planetary Formation...

 

I'm getting there... I've got the picture in my mind... it's just not translating to a verbalized communcation form :). Weird. It was so clear a moment ago.

 

Oh well... I'll leave the thread here so I'm obligated to post again, but first I'm going to write it out so I can be understood :). Not going to make the same mistake as I did with this thread :D. :D

 

Be back... eventually...

[EWright]

Actually... I need to get this clarified in my own head before I post my actual theory...

 

Hang on...

 

Black Holes... Quazars... Super heated gas... Formation of our "universe"... Planetary Formation...

 

I'm getting there... I've got the picture in my mind... it's just not translating to a verbalized communcation form :D. Weird. It was so clear a moment ago.

 

Oh well... I'll leave the thread here so I'm obligated to post again, but first I'm going to write it out so I can be understood :D. Not going to make the same mistake as I did with this thread :). :)

 

Be back... eventually...

 

:D I'm sorry, but I don't believe that your theory, as you've described it thus far, jives with current observations. :D Back to the drawing board. :D

[Buffy]

Look the *entire* Mandelbrot set is described by:

 

z(n+1) = z(n)^2 + c

 

Who knows what you could do if you added a few more terms to the equation?

 

Computationally chaotic,

Buffy

[EWright]

Look the *entire* Mandelbrot set is described by:

 

z(n+1) = z(n)^2 + c

 

Who knows what you could do if you added a few more terms to the equation?

 

Computationally chaotic,

Buffy

 

Are you sure it's not c^2?

[Dark Mind]

In mathematics, the Mandelbrot set is a fractal that is defined as the set of points c in the complex plane for which the iteratively defined sequence:

 

does not tend to infinity.

 

The sequence is thus expanded mathematically as follows for each point c in the complex plane:

 

and so on.

 

If we reformulate this in terms of the real and imaginary parts (X and Y coordinates of the complex plane), looking at each iteration n, replacing:

 

• zn with the point xn plus yn times i. (zn: = xn + yni)
  
• c with the point a plus b times i. (c: = a + bi)
  

then we get

 

and

 

The Mandelbrot set can be divided into an infinite set of black figures: the largest figure in the center is a cardioid. There is a (countable) infinity of near-circles (the only one to be actually an exact circle being the largest, immediately on the left of the cardioid) which are in direct (tangential) contact with the cardioid, but they vary in size, tending asymptotically to zero diameter. Then each of these circles has in turn its own (countable) infinite set of smaller circles which branch out from it, and this set of surrounding circles also tends asymptotically in size to zero. The branching out process can be repeated indefinitely, producing a fractal. Note that these branching processes do not exhaust the Mandelbrot set: further upwards in the tendrils, some new cardioids appear, not glued to lower level "circles". The largest of these, and the most easily visible from a view of the entire set, is along the "spike" which follows the negative real axis out, roughly from real values of -1.78 to -1.75.

I love wiki :).

[maddog]

The whole notion of fractals can be a lot more than the Mandlebrot set. It is because

of the Complex Numbers are Algebraicly Complete and can form Analytic functions which

have no more than a countable number of residues (singularities). For this reason you

can form iteration on any Analytic Function and yield a Fractal. For instance, I have done

the following functions systems:

 

Z(0) = C where C is constant complex number for all of the following functions.

 

Z(1) = Sin^2 (Z0) + C

Z(2) = Sin^2 (Z1) + C

...

Z(n+1) = Sin^2 (Zn) + C

 

Z(1) = C1*exp(i*Z0+C0) + C0 where C0 = |C| & C1 = C*C† (C† complex conjugate of C)

Z(2) = C1*exp(i*Z1+C0) + C0

...

Z(n+1) = C1*exp(i*Zn+C0) + C0

 

etc... Make up your own functions. Just be sure that the root is an Analytic function over

some domain (no more than countable singularities). Thus all levels of derivatives will

exist. Viola´ ! You have a Fractal and an Iteration Function System. These are used

to approximate solutions to difficult differential equations (Dynamical Systems). Lots 'O

Fun!!! ;-)

 

maddog