• October 20, 2021, 03:42:53 AM

 


Skeinstrange trilobiteJolly spirals
strange trilobite
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Description: JuxV3.301{
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{Title: Jux  trilobietje 3 by Klazien}
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Keywords: jux trilobite 
Posted by: Caleidoscope October 13, 2021, 07:36:19 PM

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Comments (6)

xenodreambuie
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October 14, 2021, 09:57:11 AM
Oops, in my last comment, a and |a| should be k and |k|.
xenodreambuie
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October 14, 2021, 09:25:47 AM
I can tell you the formula. It is near enough to (z3 -1.5z)/(kz2 +1) + c, with k complex. Here, a has magnitude 1.01, angle 12 degrees (this is much more convenient for adjustment when the magnitude is very sensitive) and c is about -0.25, 0. With |a|>1 the Julia sets spiral out to fill space, while <1 makes curly bugs. I've never seen any sign of Herman rings with it, or with variations of the numerator z coefficient or adding some z in the denominator.
Caleidoscope
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October 13, 2021, 10:12:21 PM
Is this helpful?
https://sta.sh/034w81dktay
If I check under Julia/mandelbrot it says to have 4 critical points. I don't know if that is what you mean?
twice
(0,147.2,18) : (-0,147,-2,18)
(0,558, -0,0208):(0,558, -0,0208)

All else I can do is put the whole stuff in 'share a fractal' with the zipfile if you like?
Last modified by: Caleidoscope October 13, 2021, 10:24:00 PM
pauldelbrot
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October 13, 2021, 09:56:15 PM
A subset of cubic rationals have the capability. (Needs minimum of 3 critical points and 2 free critical points, I think.) Can you be more specific as to which cubic rational?
Caleidoscope
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October 13, 2021, 08:25:31 PM
It's a cubic rational.  Is that what you mean?
pauldelbrot
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October 13, 2021, 08:01:57 PM
What fractal formula is this? It looks like it might be one capable of producing Herman rings.

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