gerrit images

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Offline gerrit

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« Reply #675 on: December 01, 2018, 05:21:14 AM »
Needle.

Offline gerrit

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« Reply #676 on: December 03, 2018, 10:30:44 PM »
Embedded Julia with Julia bands.

Offline gerrit

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« Reply #677 on: December 05, 2018, 05:05:22 AM »
Julia lines.

Offline gerrit

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« Reply #678 on: December 06, 2018, 05:02:36 AM »
Pretty mini.

Offline gerrit

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« Reply #679 on: December 07, 2018, 12:46:54 AM »
Julia bouquet.

Offline gerrit

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« Reply #680 on: December 07, 2018, 09:13:20 PM »
Embedded Julia corresponding to this https://fractalforums.org/index.php?action=gallery;sa=view;id=1876 Julia.

Offline gerrit

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« Reply #681 on: December 08, 2018, 05:38:21 AM »
Classical Newton-method fractal for the functions \( F_{11}(z) \) and \( F_{20}(z) \), where \( F_n(c) \) is the Mandelbrot function \( z^2 +c \) iterated \( n \) times and evaluated at \( z=0 \).

Offline gerrit

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« Reply #682 on: April 20, 2019, 06:13:00 AM »
If you imagine the balls are all really the same size it becomes 3D.

Offline pauldelbrot

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« Reply #683 on: April 20, 2019, 06:55:43 AM »
What is this one, Mandelbrot Foam? With an orbit trap coloring?

Offline gerrit

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« Reply #684 on: April 20, 2019, 09:13:21 AM »
What is this one, Mandelbrot Foam? With an orbit trap coloring?
Of course. Orbit trap is \( \min_k |z_{k+1}-z_k| \).

Offline gerrit

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« Reply #685 on: April 22, 2019, 12:19:52 AM »
At the mountains of madness.

Offline Dinkydau

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« Reply #686 on: April 23, 2019, 12:30:59 AM »
very nice

Offline gerrit

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« Reply #687 on: June 15, 2019, 04:57:16 AM »
Spiral in Mandelbrot foam.

Offline gerrit

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« Reply #688 on: September 25, 2019, 08:45:53 AM »
Julia-like set for Lorentz attractor.

Offline gerrit

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« Reply #689 on: October 01, 2019, 08:21:01 AM »
Newton fractal for \( z^3-2z+2 =0 \), which (i.e., Newton's method) has a 2-cycle [0 1].
It actually has areas where it does not converge to the root but to a cycle.
I think such polynomials are very rare, never found one by chance.
This one is from the link in https://fractalforums.org/kalles-fraktaler/15/kalles-fraktaler-2-14/1916/msg16992#msg16992
First image shows the plain Newton, second damped (relaxed) Newton with a damping 0.98 (coefficient of f/f').
The green areas are the interior regions with no convergence.
For smaller damping no 2d areas of non-convergence survive.


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