Spacefilling

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Offline pauldelbrot

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« Reply #30 on: May 08, 2018, 07:21:15 PM »
Thanks!

Offline pauldelbrot

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« Reply #31 on: May 20, 2018, 07:32:00 AM »
Polkadot Lunacy

Offline pauldelbrot

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« Reply #32 on: June 12, 2018, 06:49:40 PM »
Approaching Event Horizon

Offline pauldelbrot

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« Reply #33 on: June 22, 2018, 05:58:21 PM »
Stirred Brew

Offline pauldelbrot

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« Reply #34 on: July 03, 2018, 06:47:25 AM »
Severe Thunderstorm Warning

Offline pauldelbrot

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« Reply #35 on: July 16, 2018, 06:42:53 AM »
NGC-74656

Offline pauldelbrot

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« Reply #36 on: July 28, 2018, 06:43:13 AM »
Cloud Tops of Phi Ophiuchus VII

Offline pauldelbrot

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« Reply #37 on: August 07, 2018, 11:11:59 AM »
X-Ray Emissions

Offline Fraktalist

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« Reply #38 on: August 07, 2018, 11:56:27 AM »
my favourit of your imagethreads. very unique look! :thumbs:

Offline pauldelbrot

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« Reply #39 on: August 07, 2018, 12:22:43 PM »
my favourit of your imagethreads. very unique look! :thumbs:

Thanks!

One thing I find interesting -- for the Julia sets in this thread, the geometry is technically the same for all of them: the whole Riemann sphere. And yet they all look different, because something in the dynamics is different. I think maybe the arrangement of the shorter-period periodic points has something to do with it. But it goes to show there's structure beyond just set-membership here, once one considers the orbits as wholes. Some clearly cling to spirals for a while before ending up as spread-out fuzz.

Offline pauldelbrot

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« Reply #40 on: August 18, 2018, 09:06:16 AM »
Journeying Through Space

Offline gerrit

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« Reply #41 on: August 18, 2018, 11:07:50 AM »
Nice, what is that?

Offline pauldelbrot

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« Reply #42 on: August 18, 2018, 11:54:27 AM »
Nice, what is that?

Thanks. It's a Triple Matchmaker Mandelbrot slice, d-plane, with elliptic harlequin coloring. I've attached a parameter file that should be able to duplicate this beastie in UF. You could see what makes it tick there and/or pan, zoom, and parameter-tweak it to explore.

Offline gerrit

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« Reply #43 on: August 19, 2018, 02:02:58 AM »
Thanks!

Offline gerrit

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« Reply #44 on: August 19, 2018, 05:15:50 AM »
Is it called Triple Matchmaker because the  \( r=\sqrt{3} \) factor puts the nonzero critical points at \( \pm a \)?

Another interesting choice  is \( r=\pm i \) or \( r=\pm 3i \) which puts them both at \( i a \).
Those choices give different fractals but for both there is a full "M-set" (made visible with an atom domain like coloring) including all the embedded Julia sets and minis that you can zoom into just like the M-set. (Using 0 as starting point.)

I'll probably post some pictures later.