String Theory

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String Theory

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

https://fractalforums.org/index.php?action=gallery;sa=view;id=1364

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.

• 3f
• Posts: 1581

Re: String Theory

« 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
$$w_{old} = w\\ w = c_w w/z\\ z = z^2 + w_{old}^2 + c_z$$

• Posts: 171

Re: String Theory

« 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.

• 3f
• Posts: 1581

Re: String Theory

« 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 $$z_0 = \sqrt{-cw/2},\ \ w_0=i z_0$$.

• Posts: 171

Re: String Theory

« 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.

• 3f
• Posts: 1581

Re: String Theory

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

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