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Author Topic:  Mandelbrot 3D: Mandelnest  (Read 765 times)

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Offline 3DickUlus

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Re: Mandelbrot 3D: Mandelnest
« Reply #30 on: February 17, 2021, 03:17:28 AM »
I'm sure you will find this amusing...

...and here's the code for the iteration loop...

Code: [Select]
vec2 shift = Shift*PI;

while(r <Bailout && (i<Iterations)) {
if( Switch && (int(float(i)*.5)*2 == i) ) {
z = sin(shift.x+Power*asin(z/r));
} else {
z = cos(shift.y+Power*acos(z/r));
}
// z /= sqrt(dot(z,z)+(.5*abs(z)));
z *= pow(r,Power);
z+=(Julia ? JuliaC : pos);
r = length(z);
d = d * Power*r;
if (i<ColorIterations) orbitTrap = min(orbitTrap, abs(vec4(z.x,z.y,z.z,d*r)));
i++;
}

...in this case Shift is a vec2 slider, uncommenting the Norm line will make the spikes smaller

...just tested... the bulb png image does contain the settings after downloading from here :D  :thumbs:
« Last Edit: February 17, 2021, 04:07:24 AM by 3DickUlus »

Offline Sabine62

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Re: Mandelbrot 3D: Mandelnest
« Reply #31 on: February 17, 2021, 12:55:08 PM »
@Jeannot Thank you, so kind of you! Will have a good look, hopefully tonight!

@3Dickulus  :thumbs: Have you changed anything? Because, honestly, to my best knowledge I have more often than not to get the parameters from a FragM-.png posted on here...
PS Hedgehoggie will have to wait till later too... Thank you for sharing, looks cool!
To thine own self be true

Offline claude

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Re: Mandelbrot 3D: Mandelnest
« Reply #32 on: February 17, 2021, 01:12:39 PM »
Code: [Select]
// z /= sqrt(dot(z,z)+(.5*abs(z)));
should be
Code: [Select]
...abs(z.x * z.y * z.z)... afaict

Offline Jeannot

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Re: Mandelbrot 3D: Mandelnest
« Reply #33 on: February 17, 2021, 04:05:04 PM »
I tried another exotic norm for fun: norm(Z)= sqrt(abs(X)+abs(Y)+abs(Z))
(the vectors normalized by this pseudo-norm correspond to the surface of an octahedron and no longer the unit sphere or ordinary norm).
Julia power12 (asin-sin, Z0: -0.81, 0,0) gives a surprising result that I have never met with Mandelbrot 3D: it is hollow. Certainly a matter of filtering, the interior is not smooth. Above my modest steampunk style rendering  :embarrass:
The exact code I use untill now with my exotic norms: caution with the use of M or Me
   do
   {
             Me=sqrt( abs(Z[0])+abs(Z[1])+abs(Z[2]));//exotic Module Me 
             for(i=0;i<3;i++) Z/=Me; // exotic normalisation of new Z       -1<=x<=1
             a0=asin(Z[0]); // angles calculated with exotic Me
             a1=asin(Z[1]);
             a2=asin(Z[2]);
             a0=P*a0;
             a1=P*a1;
             a2=P*a2;
             M=pow(M,P);//Caution: here M is ordinary norm and not Me (possible to do with Me too)
             Z[0]=sin(a0);
             Z[1]=sin(a1);
             Z[2]=sin(a2);
             Z=normalize(Z,3); //Caution: ordinary normalization (possible to do with exotic Me too)
             for(i=0; i<3;i++) Z*=M;//Caution: ordinary norm here (possible with exotic Me too)
             Z=Z+C;
             M=norm(Z,3);//Caution: here ordinary norm for test and further pow (possible Me too)
             N++;
     }
          while((M<Mc) & (N<Maxit));         

Offline Jeannot

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Re: Mandelbrot 3D: Mandelnest
« Reply #34 on: February 18, 2021, 12:37:32 AM »
Here is a sketch of Mandelnest P11 acos-cos pseudonorm octahedron (sqrt(abs(X)+abs(Y)+abs(Z)). The general shape and bulbs seem specific and the patterns very rich. :joy:

Offline 3DickUlus

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Re: Mandelbrot 3D: Mandelnest
« Reply #35 on: February 18, 2021, 02:33:29 AM »
@claude  abs(xyz) is abs(x*y*z) yes, but my interpretation (typo? due to lazy) is part of the exploration process ;)

@Sabine62 if an image filename ends with .png then the server should not be altering it except when presenting a thumbnail so it should have parameters, as does Mr. Hedgehog image.

@Jeannot I find the evolution of something like this incredibly fascinating  :joy: takes on a life of it's own. The "standard" power for Mbulb is 8, I like to see the lower power versions to examine what lives there, Mbulb P2 displays the outline of the Mset etc.. the Mnest is a different animal still being explored, not sure if one can set a "standard" power... we'll see as it progresses ;)

Offline Jeannot

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Re: Mandelbrot 3D: Mandelnest
« Reply #36 on: February 18, 2021, 05:09:20 PM »
@3DickUlus:  I find the evolution of something like this incredibly fascinating
Very exciting adventure indeed, happy to share it with you. There is so much to explore.
« Last Edit: February 19, 2021, 04:59:07 PM by Jeannot »

Offline Jeannot

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Re: Mandelbrot 3D: Mandelnest
« Reply #37 on: February 21, 2021, 09:03:19 PM »
The non-Euclidean pseudo-norms associated with Mandelnest’s algorithm is a general method to provide many interesting variants.
The only constraint is to use a norm where components of the normed vector satisfy -1<=x<+1 (below an other exemple: draft of a cube-shaped fractal Modulus M= maxi (|x|, |y|, |z|)= Pnorm infinite. https://en.wikipedia.org/wiki/Lp_space#The_p-norm_in_finite_dimensions).
The P-norm is used at all levels of the code (calculation of angles, change to M^P and after the adition).
This cube is a borderline case difficult to edit: may be a good test for Fragmentarium...  ^-^
« Last Edit: February 21, 2021, 09:16:28 PM by Jeannot »

Offline Jeannot

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Re: Mandelbrot 3D: Mandelnest
« Reply #38 on: February 22, 2021, 09:14:47 AM »
Here a sleek version of Sabine62 Julia (high filtration) :joy:: Mandelnest/Julia P3 asin sin , Z0=(-0.999, 0 ,0), pseudonorm sqrt(X^2+y^2+z^2+ 0.5 abs(xyz));
The pseudonorm is used for all normalizations of the code.
@Sabine 62: as I thought, the pseudonorm rounds off the bulbs a little, in comparison with your version.  :toast:
« Last Edit: February 22, 2021, 09:56:04 AM by Jeannot »


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