String Theory

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Offline FractalDave

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« on: September 15, 2018, 12:55:18 AM »
String Theory



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Silly math - 4D iteration (all variables complex):

    w = sqr(w+z)
    z = sqr(z)
    w = w + cw
    z = z + cz

Render is part of the Mandy.
The meaning and purpose of life is to give life purpose and meaning.

Offline gerrit

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« Reply #1 on: September 15, 2018, 03:56:09 AM »

Silly math - 4D iteration (all variables complex):

    w = sqr(w+z)
    z = sqr(z)
    w = w + cw
    z = z + cz

Render is part of the Mandy.
Nice. So this is a 3D slice of the 4D parameter space?

I wonder what Pauldelbrot's Mandelbrot foam would look like in 4D -->3D. Formula is
\(
w_{old} = w\\
w = c_w w/z\\
z = z^2 + w_{old}^2 + c_z
 \)

Offline FractalDave

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« Reply #2 on: September 16, 2018, 12:14:36 AM »
Part if the 3D slice of the 4D Mandy for the iteration of Pauldelbrot's foam:

  func test4(complex &z,complex &w, complex &cz, complex &cw)
    complex w2 = sqr(w)
    w = cw*w/z
    z = sqr(z)+w2+cz
  endfunc

zstart is (1,0) and wstart is (1.5,0) in this case.

Offline gerrit

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« Reply #3 on: September 16, 2018, 03:29:26 AM »
Part if the 3D slice of the 4D Mandy for the iteration of Pauldelbrot's foam:

  func test4(complex &z,complex &w, complex &cz, complex &cw)
    complex w2 = sqr(w)
    w = cw*w/z
    z = sqr(z)+w2+cz
  endfunc

zstart is (1,0) and wstart is (1.5,0) in this case.
Cool. Critical point for this map is \( z_0 = \sqrt{-cw/2},\ \ w_0=i z_0 \).

Offline FractalDave

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« Reply #4 on: September 19, 2018, 10:34:23 AM »
Using s=(1,0.001) as the set up value, critical start value used is z=sqrt(-0.5*c) and w = flip(z).

The 0.001 imaginary part avoids a thin plane issue that happens if using zero imaginary for the set-up value.

Offline gerrit

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« Reply #5 on: September 19, 2018, 05:39:39 PM »
Superstrings!  :thumbs:


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