• June 20, 2021, 11:50:18 PM

Author Topic:  Mandelbrot 3D: Mandelnest  (Read 5152 times)

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3DickUlus

• Posts: 2278
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
« Last Edit: February 17, 2021, 04:07:24 AM by 3DickUlus »

Sabine62

• 3f
• Posts: 1225
• It's just a jump to the left...
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  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

claude

• 3f
• Posts: 1916
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

Jeannot

• Fractal Fruit Salad
• Posts: 67
• Mathematical philosophy
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
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));

Jeannot

• Fractal Fruit Salad
• Posts: 67
• Mathematical philosophy
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.

3DickUlus

• Posts: 2278
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  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

Jeannot

• Fractal Fruit Salad
• Posts: 67
• Mathematical philosophy
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 »

Jeannot

• Fractal Fruit Salad
• Posts: 67
• Mathematical philosophy
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 »

Jeannot

• Fractal Fruit Salad
• Posts: 67
• Mathematical philosophy
Re: Mandelbrot 3D: Mandelnest
« Reply #38 on: February 22, 2021, 09:14:47 AM »
Here a sleek version of Sabine62 Julia (high filtration) : 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.
« Last Edit: February 22, 2021, 09:56:04 AM by Jeannot »

Sabine62

• 3f
• Posts: 1225
• It's just a jump to the left...
Re: Mandelbrot 3D: Mandelnest
« Reply #39 on: March 02, 2021, 02:49:01 PM »
Love your experiments, Jeannot, though I am swamped with non-fractal stuff at the moment, so cannot really test them.
Keep them coming;)

Jeannot

• Fractal Fruit Salad
• Posts: 67
• Mathematical philosophy
Re: Mandelbrot 3D: Mandelnest
« Reply #40 on: March 12, 2021, 06:18:05 PM »
Hello,
Mandelnest’s standard algorithm can include 4 different pseudonorms and I’m testing some combinations to obtain variants:

do //
{
M0=norm0(Z); // Modulus 0 for angles calculation asin/acos
M1=norm1(Z); // Modulus 1 for power calculation pow(M1,P)
a0=asin(Z[0]/M0) ;  a1=asin(Z[1]/M0); a2=asin(Z[2]/M0);
a0=P*a0; a1=P*a1; a2=P*a2;
M1=pow(M1,P);
Z[0]=sin(a0); Z[1]=sin(a1); Z[2]=sin(a2);
M2=norm2(Z) ; // Modulus 2 for second normalization
for(i=0; i<3;i++) Z*=M1/M2;
Z=Z+C;
M3=norm3(Z);// Modulus 3 for test after adition
N++;
}
while((M3<Mc) & (N<Maxit));  */

I tested also a new pseudonorm: cardioid 3D (we had to try , but it doesn’t give anything very structured)
Zp=Z; Zp[0]=Z[0]-0.5; M=1.5*norm(Zp)/(1.-Zp[0]/norm(Zp));

Below are some other examples of Mandelnest-Julia hollow, with the slice on the center image.
« Last Edit: March 12, 2021, 07:43:15 PM by Jeannot »

mclarekin

• 3c
• Posts: 870
Re: Mandelbrot 3D: Mandelnest
« Reply #41 on: March 14, 2021, 11:12:07 AM »
I missed this post, glad i have found it.

I have to do the even odd iteration thing like this when i code it in Mandelbulber, to work with hybrid slots

float posneg = 1.0;
while(r <Bailout && (i<Iterations)) {
if( Switch && posneg  < 0.0)  {
z = sin(shift.x+Power*asin(z/r));
} else {
z = cos(shift.y+Power*acos(z/r));
}
posneg *= -1.0;

Jeannot

• Fractal Fruit Salad
• Posts: 67
• Mathematical philosophy
Re: Mandelbrot 3D: Mandelnest
« Reply #42 on: March 14, 2021, 12:15:56 PM »
@mclarekin I missed this post, glad i have found it
Hello
Other solution, personally for switches, I use modulo 2:
byte switch=0;
if(switch==0) {} else {}
switch=(swich+1)%2;

mclarekin

• 3c
• Posts: 870
Re: Mandelbrot 3D: Mandelnest
« Reply #43 on: March 14, 2021, 01:26:41 PM »
it is just the way mandelbulber is set up, if i am making a simple alternating hybrid with mandelnest and another formua/transform (using 2 slots) then all the mandelnest iters will be even, so i cannot easily use iter numbers for switching.

anyway interesting formulas,  here is a quick attempt power 11, with fudged DE calc.  3200 x 3200 14 seconds on a GTX 960M, nice and fast

3DickUlus

• Posts: 2278
Re: Mandelbrot 3D: Mandelnest
« Reply #44 on: March 14, 2021, 01:42:33 PM »
I am not very familiar with mandelbulber but it seems you could just divide i by 2 so 2,4,6,8 becomes 1,2,3,4 ? or put the formulas in each slot, z = sin(shift.x+Power*asin(z/r)); in one slot and z = cos(shift.y+Power*acos(z/r)); in the other ?

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