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TadpoleTalisbulb abs juliaTalisbulb abs julia (2)
Talisbulb abs julia
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Description: Talisbulb abs julia
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Filesize: 1.28MB
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Keywords: Fragmentarium GLSL Fractal 
Posted by: 3DickUlus April 05, 2022, 02:00:49 AM

Rating: ***** by 5 members.
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Comments (8)

mclarekin
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April 12, 2022, 08:31:48 AM
8)
Alef
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a catalisator / z=z*sinh(z)-c^2


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April 08, 2022, 10:39:39 PM
This part of code is made just to set initial values for a iterations. Mandelbulb3D initialise iterations only with (0,0,0). But since formula is c*z -> 0*n=0 other iteration values is needed for mandelbrot set. (for julia set, not.) This is a tricky piece, this part of code often ruined my render.  

Code: [Select]
///=============================================
// setting initial value of (x,y,z)

// do once
  if w = 0.0 then
  begin

//========================================
///For Mset only, this will ruin julia sets
if Is_Julia_Set_0_or_1 = 0 then
begin
x := Initial_X;
y := Initial_Y;
z := Initial_Z;
  w := 0.1;
  end;
  w := 0.1;
  end;
Alef
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a catalisator / z=z*sinh(z)-c^2


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April 08, 2022, 11:07:55 AM
Code: [Select]
//=======================================================
/// trigonometric values of Z vector

hyp_xy_sq:= x*x+y*y;
radius := Power(hyp_xy_sq + z*z, 0.5);
hyp_xy:= Power(hyp_xy_sq, 0.5);

   if y > 0 then
   begin
   Theta := arccos(x/hyp_xy);
   end
   else
   begin
   Theta := -arccos(x/hyp_xy);
   end;
   Phi   := Arcsin(z/radius);


Not like of mandelbulb. Alsou mandelbulb have z=-z.
Here it is:
Code: [Select]
//==========================================
// calculate trigonometric values of for C*Z^(p+q)
intPower_R:= intPower_P + intPower_Q;

radius_result2 := intPower( radius , intPower_R)* radiusC ;
theta_result2  := intPower_R * theta + thetaC ;
phi_result2    := intPower_R * phi  + phiC ;

tempx:= radius_result2* cos(theta_result2)* cos(phi_result2) ;
tempy:= radius_result2* sin(theta_result2)* cos(phi_result2) ;
tempz:= radius_result2* sin(phi_result2) ;

Mandelbulb would have tempz:= - ....

Also initial x <>0.  By default I set Zvec=(0.8,0,0) but that depends on power.
Here is calculator, but maybe that is not needed as result is ok without and it could be set on eye.
https://sagecell.sagemath.org/?z=eJxNi8EKwjAQRO-B_MMcd7WWFHoSelrwM7y0CQZiUzZFJF9vrBfnMgzvjQgmSH5uyb9v0aeFBufYGmsCzV3lRudTvY-4HE3jeTiolkZKTi9PP7FfYgj0PUxwHWqzQlYo4gotV2vQsmlcd1L-XyKkvT4KMfMHXvclPA==&amp;lang=sage&amp;interacts=eJyLjgUAARUAuQ==
Alef
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a catalisator / z=z*sinh(z)-c^2


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April 08, 2022, 07:49:58 AM
Scaling with it is recomended. Or it often gets out of screen;)
Alef
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a catalisator / z=z*sinh(z)-c^2


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April 08, 2022, 07:48:15 AM
Formula look OK but the angles and other math for * and power are different from a bugmans, alsou this formula needs initial conditions other than 0. Maybe A*B*C<>(A*B)*C but probably no. More probably wrong math could generate something malformed than cuts.

In Mandelbulb3D there is some Talis with math from bugmans site, but it looks unrealistic and is not working, kind of mess.
3DickUlus
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April 08, 2022, 02:21:15 AM
FragM triplex derived from http://bugman123.com/Hypercomplex/ ???

My attempt at using the Talis formula as a bulby thing...
Talis: z -> z^p / (1 + z^(p - 1)) + c


the algebra from '3D fractals: Extending complex number to spaces with high dimensions'? yes I've tried the formula as...

z = triMul(c,triPow(Power,z)) - triMul(c,triMul(triPow(Power,z),triPow(Qower,z)));

...but my assumptions about the algebra could be completely wrong, my FragM version is full of "cuts" but I'm trying to follow along from your examples ;)
gerson
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April 08, 2022, 01:15:39 AM
interesting one.
Alef
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a catalisator / z=z*sinh(z)-c^2


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April 05, 2022, 09:20:48 AM
Looks like hedgehog GMO hybridised with a carterpillar;)
Is this the algebra from '3D fractals: Extending complex number to spaces with high dimensions'?

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