gerrit images

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• 3e
• Posts: 1042

Re: gerrit images

« Reply #435 on: June 13, 2018, 10:03:02 PM »
Mandelbrot Foam
This is a parameter-space image of a system of two complex variables:
w -> cw/z
z -> z2 + w2 + d
The image is in the d-plane with fixed values for c, initial z, and initial w.
I set $$c=0.4, z_0=1, w_0 = i$$ for this image. The map has no critical point (zero Jacobian) but its determinant is zero when $$z_0^2+w_0^2=0$$.

• 3e
• Posts: 1042

Re: gerrit images

« Reply #436 on: June 14, 2018, 03:12:30 AM »
Mandelbrot foam c=0.3

• 3e
• Posts: 1042

Re: gerrit images

« Reply #437 on: June 14, 2018, 03:47:52 AM »
Scary looking M-foam mini. (c=0.3)

• 3e
• Posts: 1042

Re: gerrit images

« Reply #438 on: June 15, 2018, 04:22:42 AM »
$$z \leftarrow z^3/(z+0.3) + c.$$

• 3e
• Posts: 1042

Re: gerrit images

« Reply #439 on: June 15, 2018, 05:52:58 AM »
$$z \leftarrow z(z-0.02)(z-0.01)/(z+0.01) +c.$$

Dinkydau

• Fractal Friar
• Posts: 149

Re: gerrit images

« Reply #440 on: June 15, 2018, 02:58:27 PM »
$$z \leftarrow z^3/(z+0.3) + c.$$
Very nice

• 3e
• Posts: 1042

Re: gerrit images

« Reply #441 on: June 16, 2018, 05:07:09 AM »
Rocket propelled minis in $$z \leftarrow cos(\sqrt z)^2 + c$$.

pauldelbrot

• Fractal Frogurt
• Posts: 404

Re: gerrit images

« Reply #442 on: June 16, 2018, 05:17:18 AM »
Degree-infinity transcendental minis, at that, I suspect.

• 3e
• Posts: 1042

Re: gerrit images

« Reply #443 on: June 17, 2018, 09:41:28 AM »
$$z \leftarrow z(z-0.6)(z-0.3)/(z+0.3) +c$$

• 3e
• Posts: 1042

Re: gerrit images

« Reply #444 on: June 17, 2018, 09:43:26 AM »
Lace.

• 3e
• Posts: 1042

Re: gerrit images

« Reply #445 on: June 19, 2018, 02:10:53 AM »
Kickoff.

• 3e
• Posts: 1042

Re: gerrit images

« Reply #446 on: June 20, 2018, 05:46:22 AM »
Modified Mandelbrot foam:
$$w \leftarrow qw/z +c$$
$$z \leftarrow z^2 +qw^2 +c$$
$$z_0=w_0= c$$
c parametrizes the plane, q=0.001.

• 3e
• Posts: 1042

Re: gerrit images

« Reply #447 on: June 20, 2018, 06:03:20 AM »
Same formula as above.

• 3e
• Posts: 1042

Re: gerrit images

« Reply #448 on: June 20, 2018, 08:21:21 AM »
Mandelfoam sunrise.

Fraktalist

• Strange Attractor
• Posts: 846

Re: gerrit images

« Reply #449 on: June 20, 2018, 11:23:32 AM »
those last three are great, very unique!

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