(Question) Is there a name for this fractal?

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Offline 3DickUlus

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« on: April 14, 2019, 08:30:47 AM »
I've been mucking about with some old code (Amiga) and managed to get one of the plotter functions working in Fragmentarium...

iterate...
Code: [Select]
r=z.x;
i=z.y;
{
    a = (r * r - i * i) + r;
    b = (r * i + r * i) + i;
    m = (a * r - b * i);
    n = (r * b + i * a);
    r -= m;
    i -= n;
    if( (r*r+i*i) > EscapeRadius ) break;
}
..just wondering if anyone has seen this before or knows if it has a name ???
Resistance is fertile... you will be illuminated!

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Offline pauldelbrot

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« Reply #1 on: April 14, 2019, 04:35:58 PM »
Image looks like a cubic polynomial Julia set. A quick scan of the code and it does seem to be computing something cubic. Oddly I don't see a Julia seed anywhere, as if it's hard-coded to produce just this one.

Offline marcm200

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« Reply #2 on: April 14, 2019, 05:35:22 PM »
After some sheets of calculations it looks like zn+1=-zn3+zn2+zn + 0 (at least my software produces the following image that looks identical to me, although originally it was mirrored left to right).


Offline 3DickUlus

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« Reply #3 on: April 14, 2019, 08:22:15 PM »
Thaks for the input guys  :thumbs:

@pauldelbrort there is more code involved but I simplified it to show the base shape when all user inputs are at 0

@marcm200 looks like the exact same image to me

is "cubic julia" an accurate name for this formula ? zn+1=-zn3+zn2+zn1+0 looks like a declining series ???

looking to name this fragment indicatively
« Last Edit: April 14, 2019, 08:42:27 PM by 3DickUlus »

Offline 3DickUlus

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« Reply #4 on: April 14, 2019, 08:47:06 PM »
...the julia variant at 0, using C.xy in place of +r and +i in the first 2 lines looks like this...

Offline 3DickUlus

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« Reply #5 on: April 14, 2019, 10:47:57 PM »
...at first I thought "of course someone here has explored this before" but the closest thing I found is http://www.fractalforums.com/new-theories-and-research/metabrot/msg77460/#msg77460 post about the "Metabrot" but the above formula, zn+1=-zn3+zn2+zn1+0 , is different.

CubicMeta variant ?

Offline marcm200

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« Reply #6 on: April 15, 2019, 08:34:44 AM »
Maybe "Burt's bisector" is a suitable name for the formula?

If one sees the coefficients of the formula as a 4D point where the axis are the singleton polynomials zk (k=0..3) then, just as the point (1,1) is on the angle bisector in the upper right quadrant of the complex plane, (-1,1,1,1) is on the bisector of some 4D "quadrant". And taking the initial letters and naming the 3rd dimension quadrants obviously bottom/top and the 4th before/after leads (after shuffling) to BURT.

Offline 3DickUlus

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« Reply #7 on: April 20, 2019, 07:00:24 AM »
getting some interesting results, wondering if can be "bulbified" ?

Offline marcm200

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« Reply #8 on: April 20, 2019, 07:22:35 AM »
"AveragePlusandthenSum.jpg" - very nice image! Would've made a great picture for the image of the month contest - gold from me!


Offline 3DickUlus

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« Reply #9 on: April 20, 2019, 07:31:32 AM »
tnx  :D "Burt's bisector" sounds good, better than anything I thought of  :-\  yeah I got nothin' but "Cubic Meta variant"

will keep messing around with it and maybe come up with something for the contest  :thumbs:

Offline Sabine62

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« Reply #10 on: April 23, 2019, 09:03:54 PM »
@3Dickulus Beautiful results!  :thumbs:
If your entry is anything like "AveragePlusandthenSum.jpg", I agree with marcm200 and it's gold from me too! ;)
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Offline 3DickUlus

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« Reply #11 on: April 24, 2019, 02:39:31 AM »
tytyty  :D will put that one in next month?

Offline Sabine62

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« Reply #12 on: April 24, 2019, 09:06:28 AM »
 :yes: It's one of the most beautiful fractals I have seen in a while...


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