gerrit images

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Offline gerrit

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« 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 \( z_0^2+w_0^2=0 \).

Offline gerrit

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

Offline gerrit

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

Offline gerrit

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

Offline gerrit

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

Offline Dinkydau

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

Offline gerrit

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

Offline pauldelbrot

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

Offline gerrit

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

Offline gerrit

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

Offline gerrit

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

Offline gerrit

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« 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.

Offline gerrit

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

Offline gerrit

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

Offline Fraktalist

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


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