• September 19, 2021, 12:27:10 AM

Author Topic:  Mandelweird 3D burning ship  (Read 200 times)

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Offline Alef

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Mandelweird 3D burning ship
« on: June 23, 2021, 12:26:34 AM »
Very ugly;) But maybe it is a fractal curiosity.
Probably conditionals can create some equivalent of abs function, a mirror.

Some time agou I did this:
4D
- Calculate hypercomplex number based 3D tricorn fractal.
- Calculate power 2 quaternion mandelbrot set.
- Then chose largest value in each axis.
- Add + C.


Code: [Select]
[OPTIONS]
.DEScale = 0.5
.SIPow = 2
.Version = 9
.Double Height4D = 0
[SOURCE]
procedure MandelWeirdN(var x, y, z, w: Double; PIteration3D: TPIteration3D);
var
   x1, y1, z1, w1, x2, y2, z2, w2: double;

begin

//========================================
x1:=x;
y1:=y;
z1:=z;
w1:=w;

//===============================
//Now goes algebra. Calculates two formulas

// hyper tricorn - hypercomplex number tricorn.
x2:= x1*x1 - y1*y1 - z1*z1 + w1*w1;
y2:= 2* z1*w1 - 2*x1*y1;
z2:= 2*x1*z1 - 2* y1*w1;
w2:= 2*x1*w1 + 2* y1*z1;

//==================================================================

//quaternion pow2
x := x1*x1 - y1*y1 - z1*z1 - w1*w1;
y := 2*x1*y1;
z := 2*x1*z1;
w := 2*w1*x1;

//=============================================================
//then choses larger value of the two

If (x2>x) then
x:=x2;

If (y2>y) then
y:=y2;

If (z2>z) then
z:=z2;

If (w2>w) then
w:=w2;

//========================================
// + C
x := x +   PIteration3D^.J1;
y := y +   PIteration3D^.J2;
z := z +   PIteration3D^.J3;
w := w +   Height4D;
 
end;
[END]
4D
TEST

 * * *
By Edgar Malinovsky

As in this thread: https://fractalforums.org/share-a-fractal/22/burning-ship-sunken-by-a-little
I don't want to steal Mr Rebooted thread with my fractal.

In 2D result must be the same.
(as orbits travell throught all 4 dimensions only if z<>0 as z and w are "entangled").

- calculate mandelbrot
- calculate tricorn
- chose largest value in the axis Y.
- Add C.

x1=   x*x - y*y

y2= - 2*x*y
y  =   2*x*y

If (y2>y) then
y1=y2
else
y1=y

x=x1+Cx
y=y1+Cy

There must be burning ship. This hypothesis is not tested. PC is burning becouse of weather, so maybe later. Conditionals here works as abs function. Anyway there is mutch more easy way to calculate Burning Ship.
This means Burnig Ship fractal is a combination of Mandelbrot set and Tricorn fractal. Now it seems so obvious.

In attachment Mandelbulb3D formula I used to render this.

Linkback: https://fractalforums.org/index.php?topic=4290.0
« Last Edit: June 23, 2021, 05:12:57 PM by Alef »
a catalisator / z=z*sinh(z)-c2

Offline Alef

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abs - combinations of mandelbrot and tricorn?
« Reply #1 on: June 23, 2021, 06:54:21 PM »
One can generate all abs based fractals in this way.

Iteration backbone, Mandelbrot set:
Code: [Select]
x= real(z)
y= imag(z)

x1=   (x*x - y*y)
x2=   (x*x - y*y)

y2=    (2*x*y)
y1 =   (2*x*y)

IF (y2>y1)
y=y2
ELSE
y=y1
ENDIF

IF (x2>x1)
x=x2
ELSE
x=x1
ENDIF

z = x + flip(y)  + c

Celtic 1:
x1=   (x*x - y*y)
x2=   -(x*x - y*y)

y2=    (2*x*y)
y1 =   (2*x*y)

Burning ship:
x1=   (x*x - y*y)
x2=   (x*x - y*y)

y2=    -(2*x*y)
y1 =   (2*x*y)


Buffalo:
x1=   (x*x - y*y)
x2=   -(x*x - y*y)

y2=    -(2*x*y)
y1 =   (2*x*y)

Celtic Tricorn:
x1=   (x*x - y*y)
x2=   -(x*x - y*y)

y2=    -(2*x*y)
y1 =   -(2*x*y)

Tricorn (obviously):
x1=   (x*x - y*y)
x2=   (x*x - y*y)

y2=    -(2*x*y)
y1 =   -(2*x*y)


JPG slightly smeared my pictures, but I think everyone here knows these fractals. Not shure where this can be used and what this adds to theory. Of corse abs with certain signs are same as conjugation function.

I tried combination of different powers and it don't works well, that made distorted fractals. However different coeffitients or sine, cosine or log functions can make something meaningfull, jet simmilar to existing fractals.

Offline youhn

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Re: Mandelweird 3D burning ship
« Reply #2 on: June 23, 2021, 07:31:07 PM »
It's dualisms^2  8)

Seems like mandelbrot set variations are like magic numbers (Pi etc), they turn up in seemingly different ways. Same for some math concepts, which can be derived using different methods and/or notations and still give the same result. Does it hint at something universal underlying this all, or does the universe naturally allow separate paths to the same goal?

Also wave and particle dualism comes to mind, as well the common practice in quantum mechanics to summarize all paths together to get a probability distribution. Sorry, drifting off a bit. I wish we could meaningfully visualize the calculation steps in 3D (projected 4D) fractals. Not like a buddhabrot, but more animated.

Offline Alef

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Re: Mandelweird 3D burning ship
« Reply #3 on: June 23, 2021, 10:54:30 PM »
I think something universal underlying that all, like science beyond standart model (so far realy none had figured it out, as no theories had been proven by experiments), or many proofs of Ferma theorem.

Here I think seperate methods in some obscure way create same function. But maybe it alsou says something about fundamental properties beyond these sets.

In picture Y1 sine modification.

Ultra Fractal formula ( a bitt slow maybe):
Code: [Select]
Fractal1 {
::vKdCrin2lJVwuxJMQ07Ix/gFfA7azuQotyHSVVOUpev5EyxMGmEjNyYyG+7rNG20qebm3bev
  ZsnR5ESvQ/18MCxjeNwLeKBxKI3wO/Av+KlMAY/gnfthS0iVwNzZRFSH0h+ZexjaQ9t6zlXO
  XSLZF5ZbVt5qUM5RrhX8dh8tendx0VQsTCJ6X5MKNPbUMNhm+U1gxDOO9MlMK6Nx2osuxFtY
  jeU8BG5D6ITgTOAy34WlioQNYEjhx/HLCdw62fJMdg+GguuTLqxio8g5u17lUQmafRga7iPa
  Y0y2xbt/mxZ7RlHRPzSP4USEW1qWMyYxYXw275l/b+z78RxHQHlM1ODe/6EwTz6LO7G4N0LH
  Oo+5iGFpW/aMkTPd5M9U9hbT2Z/d/Qz7gzDdcjNPDNzB80m1JMzqw/mxag8swD+/p0oBEu8s
  enoDD2txOPathTgVYmghR8DOlItarj38AruspZHNuOS4saWJrpqanoMufJ7cXrr+Cbn4ynKq
  qDTU6e4v7pxevlHXLlVV5Z/BpBu32C==
}

Duality_Mandelweird.ufm:Duality {
; 1.Calculates 2 complex powers for each axis
; aka mandelbrot or tricorn.
; 2. chose largest value in the axis X and Y.
; add C
; https://fractalforums.org/fractal-mathematics-and-new-theories/28/mandelweird-3d-burning-ship/4290/msg29214#msg29214

;Edgar Malinovsky
::VROpihn21aVbvttNQ4PbD4/DH8+isrjXkGw+w2YRepJApYpYYpYwCYAFMSUxcVWUTkKWyo/4
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  x9is6ikPUq0mgEU8b+5HuhI/lF4dv5ubnMenzVIxPydebdukfKPZ3X1TcGeHD6I4ME6A/BhI
  xrnrs7grMZcuSVaD+NMoSwztcbZgcD/J73TG/jXx1yEYfksUtVUpRFCZA0MvBODan3injGeG
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  7tcVYQTIGicANgTUQTklT7R6EHG060p9IdijCad6svAqN61osUYisvL6jfH2LsSi1E96GSsG
  WTnY439FbHWm2AvCyyllBtzA8zrJ6Pyl5qa6Vxn29J4ngL8EIepiMedOxzIN5CEhpvpmnLNt
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  WzrE+8PY/Z0offy4gNdviAVFYqkJqqiZjGNqnQImrVaEPzaBkzreSoNwz88ahXKSw9ieZaqG
  ue0ILEIlVhLWFtIOcRc0BihLs/CSNc4ZMQ0Oj+jo/enrs0hLPXrqBLbSP0jE5Gsw2rCR5q6q
  CM4APsWWCeg8Myy45qOan1T/9WBjgii0u47pD13qq2gRW4qcVyH/MNcdvK5V8NQXKvn2X5oB
  /GF4m2VLgsCPH/Zy4NyCXietswmLf/aMOYBUYEVAqgsAzCrVbBtCBlXg5sHlGr50AB+21Sss
  SiijPPLeyfvsYcsPafyOwDXFO0tO4JXzLUF4T+cXaXDhU1yZh/d4HNE/oXY8jH6/xv0+f8Q/
  P+/u/jNlAffuOoZTvFpYNS/MATmKKMBzcWpnQZI0h4LQB+m2SArbWB8Gp2ZNC/jMW0JNW0/L
  GL+k3s4/t3s4vuxO5NLO6F0YnqTgdY/XoPgr6xvYQPv7BhBIS9ctzJdr3MYXGP4HV44Bdr0k
  s+YoJHyxBMqjrQJ8JBOpFeWqlPaHDhNI1ihmEOs1g14+1Rom9d3JXc4BhgGYRc2fzCOf53tA
  Of53PzR/glO5OTA03ynKifftxtwxnFv7XOQ7I1Lk/L0KVwGeZJNYIzn5/HUbgakLFpQadFpp
  vfqtGRak4Abt94S4ditYYSVhOjdiLOF3uHHFS9gFcK+zWC2u7J1VPjkLwpfJLgHxO40M2yce
  hYBg2D7njp1sKeiBbugKkWx3WsA7/jczbB7FA2cGGTJu4V1WXbzVUNoeJ8riEcg4WV1H1AHt
  osKhGRQLoqFLHWr7y07XetXCY6tS9a4m2hDuu9S7iRug3l2YmG2LJuMBvQjezGXozo8hGfLy
  AfeZ2xNJd1y0OSUVy+FkQhc3qDrK7nyy6m2u3xZHuB7L2O6pzgjsOydFRselTZux+M//9StK
  k11I33kl11s13Ik11Q03si110yO9l5nBbHVy8DMtz1Y+pb2hQM/oo/SswURG
}

Alsou UF formula is in attachment file.  Maybe someone can figure out some more canonical fractals out of this.

Offline Alef

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Re: Mandelweird 3D burning ship
« Reply #4 on: June 24, 2021, 12:45:33 AM »
Finaly I found this image shared by Deseptor. Kind of fits here.
https://fractalforums.org/index.php?action=gallery;sa=view;id=5823
Quote
Description: I discovered recently that the Burning Ship fractal is just 2 Mandelbrots and 2 Mandelbars connected. I whipped up a formula in Ultra Fractal that helps illustrate this. Compare it to a Burning Ship. See the resemblance?

There are some simmilarities in owerall shape. But maybe alsou in more fundamental aspect that abs function is conj function in disguise, or maybe not.

Log function here for Y works like halfway to burning ship. Zooms on x=-1.6 on antenna where ships should be it shows a lot of distorted tricorns and mandelbrots and further zoom on distorted tricorn.
« Last Edit: June 24, 2021, 01:17:03 AM by Alef »


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