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Since nobody ever tried to write a Mobius transform in triplex coordinate system, and this transform can open a new field of exploration (including the legendary "Mobius IFS" and the Quasi-fuchsians), I thought it was worth to open a new thread. Certainly, the effects that pop out are mind-blowing....
For now I don't know exactly how to obtain the Quasifuchsian fractals because they need many Mobius at once (probably conditional - but for now only normal transform is made), so these examples show only "freak"  effects ;D

First example (very basic)


Mandelbulb3Dv16{
M.....S....O/...w....2....kn5sZ9LHy5.bt.QmNK402EXJ.8VXsNl.AGn66hcrruzq5h0QdyM/zD
................................eWsjyKOSQz1........Y./..................y.2.....
................/ME//....6Ut/...n0....E2.....o2AkIM3sFsD/..........c./...w1....U
z.....kD..../..........wz.............................................sD...../..
.w1...sD1BgdG1bddufOIXSS0yZSzMrTYR9fDxrjFlavmMhaZunkaHUigyoTzgBSmSbUTdrDTt7S1K/S
2yn0Q/zAhRYAwWTi9OIf21fj......YA......................sD..kz0...................
.............................UJRR4.wppN.6OLb/.mRR4.irpN.EVLb/UCSR4..............
...........................U..6.P....M4...EB....W....61....F....8/...I1....UJl12
...U.iVFwxDE./ozPM2Tzz7lz16.mc..zXCc.El18XGQeGyDjvIRhrVAkz1............28.kFrA0.
FWb96aAIVzvh1se7Umvxz0........../6U0.wzzz1................................E.0c..
zzzz.................................2U.8.kzzzD.................................
/6U0.wzzz1...................................2CcN/UvNP6.eeWCNq0.yRii.EJJUk1f..XR
S1.mx3CcN/UvNP6.QsLsUa3.ibhV..bTV1OK.sSq40.ly3CcN/UvNP6.MwLsUa3.ibhV.kqTV1OK.sSq
40.kz3CcN/UvNP6...EsUa3.eeWCNq0.IJ36wk8.wyLsUa3.................................
E....6....E.....I....k....kLBxaMdJrQI/5S........................................
...................wz......................................................zd4jo
B74UzcjTel9RHWrjuvbOwGrYsx1........wz...........................................
.....................U...../....1....2IPVdLOiR460x4S.65.........................
.Qk0.................MaNaNaNatzD........Uz1........wz...........................
................................................................................
................................}

Mandelbulb3Dv16{
M.....S....O/...w....2....EudzCvp6MpzWrM918k912Egs1.4Z.xL.Q9wf6YctSmzmcK5tA/RvwD
................................9TJ6oo2jP.2........Y./..................y.2.....
................/ME//....6Ur2...s/....E2.....ocKwneo1IoD/..........c./...w1....U
z.....kD..../..........wz.............................................sD...../..
.w1...sDQRde7nMJetPkfd.sBClCzw5LkomhG.ojjEIr3FZ9atHJ5ac9r8/EzMQx2rRXHgnDyyECf8x.
3xHxxK6qqEgwvWa8wHe7r2bj......oL......................sD..kz0...................
.............................UJRR4.wppN.6OLb/.mRR4.irpN.EVLb/UCSR4..............
...........................U..6.P....M4...EB....W....61....F....8/...I1....UJl12
...U.iVFwxDE./ozPM2Tzz7lz16.mc..zXCc.El18XGQeGyDjvIRhrVAkz1............28.kFrA0.
FWb96aAIVzvh1se7Umvxz0........../6U0.wzzz1................................E.0c..
zzzz.................................2U.8.kzzzD.................................
/6U0.wzzz1...................................2CcN/UvNP6.eeWCNq0.yRii.EJJUk1f..XR
S1.mx3CcN/UvNP6.QsLsUa3.ibhV..bTV1OK.sSq40.ly3CcN/UvNP6.MwLsUa3.ibhV.kqTV1OK.sSq
40.kz3CcN/UvNP6...EsUa3.eeWCNq0.IJ36wk8.wyLsUa3.................................
E....6....E.....I....k....kLBxaMdJrQI/5S........................................
...................................................wz...........................
...wz...........................................................................
.....................E4....3....8....oINiRKNmB1.0x4S.65.........................
.....MU/4MU/4................U.E........kz1........wz.........zD................
................................................................................
................................}

Mandelbulb3Dv16{
M.....S....O/...w....2....EudzCvp6MpzWrM918k912Egs1.4Z.xL.Q9wf6YctSmzmcK5tA/RvwD
................................9TJ6oo2jP.2........Y./..................y.2.....
................/ME//....6kt....s/....E2.....ocKwneo1IoD/..........c./...w1....U
z.....kD..../..........wz.............................................sD...../..
.w1...sDQRde7nMJetPkfd.sBClCzw5LkomhG.ojjEIr3FZ9atHJ5ac9r8/EzMQx2rRXHgnDyyECf8x.
3xHxxK6qqEgwvWa8wHe7r2bj......22......................sD..kz0...................
.............................UJRR4.wppN.6OLb/.mRR4.irpN.EVLb/UCSR4..............
...........................U..6.P....M4...EB....W....61....F....8/...I1....UJl12
...U.iVFwxDE./ozPM2Tzz7lz16.mc..zXCc.El18XGQeGyDjvIRhrVAkz1............28.kFrA0.
FWb96aAIVzvh1se7Umvxz0........../6U0.wzzz1................................E.0c..
zzzz.................................2U.8.kzzzD.................................
/6U0.wzzz1...................................2CcN/UvNP6.eeWCNq0.yRii.EJJUk1f..XR
S1.mx3CcN/UvNP6.QsLsUa3.ibhV..bTV1OK.sSq40.ly3CcN/UvNP6.MwLsUa3.ibhV.kqTV1OK.sSq
40.kz3CcN/UvNP6...EsUa3.eeWCNq0.IJ36wk8.wyLsUa3.................................
E....6....E.....I....k....kLBxaMdJrQI/5S........................................
...................wz...........................................................
.....................................AnAnAnAnAyDOaNaNaNaNz1.....................
.....................E4....3....8....oINiRKNmB1.0x4S.65.........................
.....MU/4MU/4................U.E........kz1........wz.........zD................
................................................................................
................................}

Last raccomandation.

If used mindlessly the Mobius transform gives garbage. For example, every transform where a=c and b=d returns 1 at every pixel (nothing)

And also, never set both coeffs to zero at the same time (every transform where a=b=0 or c=d=0 are pure "nonsense")...

The quasifuchsian groups? Hard to understand how to get them. I tried with one transform and I see some circles, but it's not enough  ;D

Mandelbulb3Dv16{
M.....S....O/...w....2.....z6wqBmVLxzmDgsyUUgV1E.fyFbgl6JwXVOrE8PAG3zsYu/EeKBbyD
.................................LJUZ.jnxz1........A./..................y.2.....
................/ME//....6U2....9.....E2.....QH.y4HiBCqD/..........c./...w1/...U
z.....kD..../..........wz.............................................sD...../..
.w1...sDLUV4kYPXXx1........Yue7cFY2g2.djIadYq3dDuqv3Mc/AtqsMzwbdtS2g2.dj0cOi5/9/
EuX4Y4FGkG.Yy.k9qtGiBCqD......I6......................sD..kz0...................
.............................UJRR4.wppN.6OLb/.mRR4.irpN.EVLb/UCSR4..............
...........................U..6.P....M4...EB....W....61....F....8/...I1....UJl12
...U.iVFwxDE./ozPM2Tzz7lz16.mc..zXCc.El18XGQeGyDjvIRhrVAkz1............28.kFrA0.
FWb96aAIVzvh1se7Umvxz0........../6U0.wzzz1................................E.0c..
zzzz.................................2U.8.kzzzD.................................
/6U0.wzzz1...................................2CcN/UvNP6.eeWCNq0.yRii.EJJUk1f..XR
S1.mx3CcN/UvNP6.QsLsUa3.ibhV..bTV1OK.sSq40.ly3CcN/UvNP6.MwLsUa3.ibhV.kqTV1OK.sSq
40.kz3CcN/UvNP6...EsUa3.eeWCNq0.IJ36wk8.wyLsUa3.................................
E....E....E.....I....k....kLBxaMdJrQI/5S.IaQ....................................
...................wz...........................................................
...../.............................wz...........................................
...........................3....A....wJHj7KOpB5JkV5.b/..........................
..............................zD................................................
...............E..............................yD........Uz1.....................
.....................................wzzzzD.....................................
........................................U.2.....................................
................................................................................
..........................................E.....I....M....kL1xaPYZ2RXxKRiFbI....
.....................YE006U.0......................wz........E/E........kz1.....
...wz...........................................................................
........................................................}


More interesting


Mandelbulb3Dv16{
M.....S....O/...w....2....U556qGmTM3.vaRaiwqt23ENTF2TqZApw1FpUBcR7HBzYnotQoyTb.E
................................6UvWMeLiRz1........A./..................y.2.....
................/ME//....6U2....R5....E2.....w30F0kpPCsD/..........c./...w1/...U
z.....kD..../..........wz.............................................sD...../..
.w1...sDW.zuyPxa1yHV6cEBfrwwuqP/2S9EE.fjOgfUJDMIOrf6kjizKjtUzMK2fM9EE.fjWkk8q022
kunK5Esh.//gyIyp4pjpPCsD......I9......................sD..kz0...................
.............................UJRR4.wppN.6OLb/.mRR4.irpN.EVLb/UCSR4..............
...........................U..6.P....M4...EB....W....61....F....8/...I1....UJl12
...U.iVFwxDE./ozPM2Tzz7lz16.mc..zXCc.El18XGQeGyDjvIRhrVAkz1............28.kFrA0.
FWb96aAIVzvh1se7Umvxz0........../6U0.wzzz1................................E.0c..
zzzz.................................2U.8.kzzzD.................................
/6U0.wzzz1...................................2CcN/UvNP6.eeWCNq0.yRii.EJJUk1f..XR
S1.mx3CcN/UvNP6.QsLsUa3.ibhV..bTV1OK.sSq40.ly3CcN/UvNP6.MwLsUa3.ibhV.kqTV1OK.sSq
40.kz3CcN/UvNP6...EsUa3.eeWCNq0.IJ36wk8.wyLsUa3.................................
E....E....E.....I....M....kL1xaPYZ2RXxKRiFbI.........................YE006U.0...
...................0./.......x7E..........2...................zD........kz1.....
................................................................................
.....................2.....3....A....wJHj7KOpB5JkV5.............................
...............................................................E................
..............zD.....................oAnAnAnAnyjOaNaNaNaty1.....................
................................/....E/...U/....TBoPiFKGoBqPpt4RG/..............
..........E076U.06......................6.2.......ob./......../E........kz1.....
................................................................................
..........................................E.....I....k....kLBxaMdJrQI/5S........
................................................................................
...../.............................wz0....................EnAnAnAnAvzcNaNaNaNavj
........................................................}

Seems that there is still a problem with the formula, nothing to see here with the parameters.  :-\

On first check i saw that you still subtract from esp before pushing,
not sure if that causes the problem or if there are others...

Impossible! :o
I will try to submit the file again...

Wow, that is strange:
It works on the current version, but not on the new beta that i was using!
Good to know before releasing it, i must have done a bug once again.

I guess i found the issue, you are using an absolute address:

00459741 DD45E4               fld qword ptr [ebp-$1c]
00459744 DC1D04804000     fcomp qword ptr [$00408004]  // this must be changed!!!
0045974A DFE0                  fstsw ax
0045974C 9E                     sahf

Else it would not work in upcoming versions.  What should be compared in the code up there?

Here I paste the source code, it can be useful for future users too. :)

int main (void){
    // --- PIXEL DATA --- //
    /*
    double x=243847928;
    double y=4252352;
    double z=453452;
    */
    double x=243847928;
    double y=4252352;
    double z=453452;
    // double w=100;
    // --- USER INPUT A --- //
    double a1=1;
    double a2=0;
    double a3=0;
    // --- USER INPUT B --- //
    double b1=0;
    double b2=0;
    double b3=0;
    // --- USER INPUT C --- //
    double c1=0;
    double c2=0;
    double c3=0;
    // --- USER INPUT D --- //
    double d1=1;
    double d2=0;
    double d3=0;
    // --- TEMPORARY --- //
    double xt0=-9999999;
    double yt0=-9999999;
    double zt0=-9999999;
    double xt1=-9999999;
    double yt1=-9999999;
    double zt1=-9999999;
    double r=-9999999;
    double rho1=-9999999;
    double rho2=-9999999; // they are many ( 8 ) - I need all of them to calculate final division

    // --- objective; do (SxA+B)/(SxB+C) as faster as possible, without errors. --- //
    // --- we use triplex theory to do a Mobius 3D transform or something similar 8) --- //

    // --- so at first try to compute the divisor. if it's zero or near, we can go out!!! 8) --- //
    // --- DO S x C store in t1 --- //
    rho1=sqrt(x*x+y*y);
    rho2=sqrt(c1*c1+c2*c2);
    if (rho1*rho2==0){
    // I fear we can't divide by zero. We are on the origin - or in a point in z axis
    // very very approx, hopin it's ok!!! +- z*k/(0.xx*0.xx) >> 1 but +-0.xx*0.xx*z*k/(0.xx*0.xx) should again be +-z*k ?
    xt1 = -z*c3;
    yt1 = z*c3;
    } else {
    xt1 = (x*c1-y*c2)*(1-z*c3/(rho1*rho2));
    yt1 = (c1*y+x*c2)*(1-z*c3/(rho1*rho2)); 
    }
    zt1 = rho1*c3+rho2*z;   
    // --- now do S x C + D (easy!) --- //
    xt1 = xt1 + d1;
    yt1 = yt1 + d2;
    zt1 = zt1 + d3;
    // --- okay but the radius? --- //
    r = xt1*xt1+yt1*yt1+zt1*zt1;
    if (r<=1e-90){
    // ouch singular point, or singular transform, or point very very near to this trouble
    // Return something very big. It should be okay.
    x = 1e90;
    y = 1e90;
    z = 1e90;
    return (1); // go out of here
    } else {
    // --- DO S x A store in t0 --- //
    // rho1=x*x+y*y; already done
    rho2=sqrt(a1*a1+a2*a2); // new transform, new rho2
    if (rho1*rho2==0){
    // I fear we can't divide by zero.
    // very very approx, hoping it's ok!!!
    xt0 = -z*a3;
    yt0 = z*a3;
    } else {
    xt0 = (x*a1-y*a2)*(1-z*a3/(rho1*rho2));
    yt0 = (a1*y+x*a2)*(1-z*a3/(rho1*rho2)); 
    }
    zt0 = rho1*a3+rho2*z;   
    // --- now do S x A + B (easy!) --- //
    xt0 = xt0 + b1;
    yt0 = yt0 + b2;
    zt0 = zt0 + b3;
    // --- we are almost done, now only do t0 / t1 --- //
    // --- surely, it is NOT a singular point since r is not zero. --- //
    // --- We stay away from singularity because r > epsilon. We should be in a safe zone --- //
    r = 1/r; // to compute faster 8)
    rho1=sqrt(xt0*xt0+yt0*yt0);
    rho2=sqrt(xt1*xt1+yt1*yt1);
   
    if (rho1*rho2==0){
    // I fear we can't divide by zero.
    // very very approx, hoping it's ok!!!
    x = zt0*zt1;
    y = -zt0*zt1;
    } else {
    x = r*(xt0*xt1+yt0*yt1)*(1+zt0*zt1/(rho1*rho2));
    y = r*(xt1*yt0-xt0*yt1)*(1+zt0*zt1/(rho1*rho2));
    }
    z = r*(rho2*zt0-rho1*zt1);
    // done!
    }
   return (1);
}

May it be;

    if (r<=1e-90){
    // ouch singular point, or singular transform, or point very very near to this trouble
    // Return something very big. It should be okay.
    x = 1e90;
    y = 1e90;
    z = 1e90;
    return (1); // go out of here
    } else {

Just add between the [OPTIONS] and {CODE]* sections in the m3f file this:

[CONSTANTS]
Double = 1e-90

And then you can compare with   qword [edi]   ,if edi is the Pvar pointer to the user vars&constants.

Next Double constant would be in [edi + 8] and so on, you could also use this for the plenty initialisations to get a smaller code.


*had to change this because of scripting language issue  ^-^

The assignment x=1E90 is okay? :)

Yep, but because there are not many different values, you could also use constants instead of direct assignments:

0045974F C78544FFFFFFC759 mov [ebp-$000000bc],$092959c7
00459759 C78548FFFFFF0F6B mov [ebp-$000000b8],$529f6b0f
00459763 C7854CFFFFFFC759 mov [ebp-$000000b4],$092959c7
0045976D C78550FFFFFF0F6B mov [ebp-$000000b0],$529f6b0f
00459777 C78554FFFFFFC759 mov [ebp-$000000ac],$092959c7
00459781 C78558FFFFFF0F6B mov [ebp-$000000a8],$529f6b0f

what is:
    x = 1e90;
    y = 1e90;
    z = 1e90;
(these x,y,z are not the ones of the Iteration3D struct)

would become with additional constant:
[OPTIONS]
Double = 1e-90
Double = 1e90

fld  qword[edi + 8]
fst  qword [ebp-$000000b8]
fst  qword [ebp-$000000b0]
fstp qword [ebp-$000000a8]

Hint: offsets between -$80 and $7F uses only 1 byte for the offset, if possible you can use a second pointer with offset -$80 or -$100.

Check it accurately, so I can add it to the list. :angel1:

I know... But they take almost zero time but as it is I can reuse the entire block for future stack-using formulas

Please can you tell me the integer power formula optimized? (without any sin() cos() but with radiuses instead) I can't find them... :sad1: I'm writing an Ikenagabulb, but without the power code I have to write a "while" cycle too time consuming ^-^

If you change the 2nd OPTIONS to CONSTANTS (with brackets), it will render... but a little different to what it should be.
Attached is the image of the parameters from http://www.fractalforums.com/index.php?topic=6114.msg29165#msg29165 (http://www.fractalforums.com/index.php?topic=6114.msg29165#msg29165)

I could not find a link to them either, are they removed?

So i hope that is allowed to me to send the integer powers of the sine bulb, that were made by Daniel White!


Ok, this is probably not what you was searching for, you can make the formulas also with two complex rotations.

I have this one not here, so this is only from my mind, maybe the function becomes obvious so you can make it work:

newR = x*x + y*y + z*z

m = 1/Sqrt(x*x + y*y)  //normalize vec(x,y)
x = x*m
y = y*m
z = z*m
ComplexPower2(x,y)     //rotate vec(x,y), radius=1 is unchanged

m = 1/Sqrt(x*x + y*y + z*z)  //normalize vec(x,y,z)
x = x*m
y = y*m
z = z*m
m = Sqrt(x*x + y*y)    //length of vec(x,y)
mt = m
ComplexPower2(z,m)     //rotate vec(z,|vec(x,y)|)

m = m/mt*newR
x = x * m + Cx
y = y * m + Cy
z = z * newR + Cz

I don'r understand what you mean ... it's wrong or no? :)

If the result differs from what it should be, i am afraid that it is wrong  :dink:

But cannot say exactly why, you should have a closer look at the code again.

Ahhhhh now I got it! I mistaken "CONSTANTS" ... :)

But you, bad boy, suggested me wrong the offsets of x,y,z... :evil1: they was BC, B4, AC and not what you told me...  :dink:

Fixed also a wrong relative jump. :embarrass:

Now looks okay ;D

I'm updating the database too ;D

Now it works, well done!
 :beer: :beer: :beer:

 :thumbsup1:

Yay ;D

Remember to test also the Ikenagabulb. I eliminated all constants I hope ^-^

I was trying to implement Tan4D, Atan4D and the hyp's in a single formula; too bad it became a monster  :o and it's plenty of constants that I am not able to eliminate without being literally overwhelmed. :-\

Moreover, I have a sci calculator that supports complex numbers but he says;

atan (3,4) = 1.4483 + i 0.159

My formulas for atan are

        Te0 = y*y+z*z+w*w;
        if ((fabs(x)+fabs(Te0-1) > cutoff) && ((fabs(Te0) > cutoff)) ){
         Te2=.25*(log(x*x+(Te0*Te0+1)*(Te0*Te0+1))-log(x*x+(1-Te0*Te0)*(1-Te0*Te0)));
          y=Te2/Te0*y;
          z=Te2/Te0*z;
          w=Te2/Te0*w;
         } else {
         y=1/cutoff;
         z=y;
         w=y;
        }
        Te1=.5*(atan2(1-Te0,phase+x)-atan2(1+Te0,phase-x));
        x=Te1;

It seems that atan(3,4,0,0) is different from it, but maybe I am mistaken due to the extreme tricky-ness of atan and logs of all kinds... :-\

Probably, it's better if I abandon this jungle, return to simple functions again :dink:

Looks good to me, though i don't know how the original looks like, just compare the default settings:

Okay, at least the slice at z=0 is okay. Can't know about other, but I copied faithfully the cube formula. ^-^

Now, I have released a Menger - Koch variation. But I am not that satisfied with it...

I wanted to draw a Menger sponge with some "towers" over each hole. The best result I can get is this.

(http://img40.imagefra.me/i539/kriptokapi/y6du_91b_u6bci.jpg)

I do this;


FLD QWORD PTR DS:[ESI-78]
FSUB ST,ST(2)
FABS                        <------ folds st(1)
FXCH ST(2)
FSTP ST
FSUB QWORD PTR DS:[ESI-80]
FABS                        <------ folds st
FNOP

If I multiply with something, nothing happens or shapes become weird.
dunno who is ST(2) or ST, due to the many swaps it's confusing... :hmh:

This is done here (formula from http://www.fractalforums.com/3d-fractal-generation/kaleidoscopic-(escape-time-ifs)/ )

Menger3(x,y,z){
   r=x*x+y*y+z*z;
   for(i=0;i<MI && r<bailout;i++){
      rotate1(x,y,z);

      x=abs(x);y=abs(y);z=abs(z);
      if(x-y<0){x1=y;y=x;x=x1;}
      if(x-z<0){x1=z;z=x;x=x1;}
      if(y-z<0){y1=z;z=y;y=y1;}

*** FOLDING ***

      rotate2(x,y,z);
    
      x=scale*x-CX*(scale-1);
      y=scale*y-CY*(scale-1);
      z=scale*z;
      if(z>0.5*CZ*(scale-1)) z-=CZ*(scale-1);
      
      r=x*x+y*y+z*z;
   }
   return (sqrt(x*x+y*y+z*z)-2)*scale^(-i);
}

Dunno if this can be improved. :)

If I do a conditional folding, the shapes are cutted off with a weird effect. I must do everything without conditions (it seems)

param


Mandelbulb3Dv16{
M....Es....V1...w....2.............6.1.......s3E................................
................................8QxckpX05z1........Y./..................y.2.....
................/ME//....6Uy....e/....E2.....2e8GShyvfsD/..........c./...w1....U
z.....kD..../..........wz.............................................sD...../..
.w1...sD..cjZvMS3tn6C1JzzzzvzOEUhUisqclD2Rw3Oc.cazXCrqeAEZc2zSWyooeAVOyj.Zh4j8Hc
aznAWreAEZc2zconlUV0UOyD......oE......................sD..kz0...................
.............................UJRR4.wppN.6OLb/.mRR4.irpN.EVLb/UCSR4..............
...........................U..6.P....M4...EB....W....61....F....8/...I1....UJl12
...U.iVFwxDE./ozPM2Tzz7lz16.mc..zXCc.El18XGQeGyDjvIRhrVAkz1............28.kFrA0.
FWb96aAIVzvh1se7Umvxz0........../6U0.wzzz1................................E.0c..
zzzz.................................2U.8.kzzzD.................................
/6U0.wzzz1...................................2CcN/UvNP6.eeWCNq0.yRii.EJJUk1f..XR
S1.mx3CcN/UvNP6.QsLsUa3.ibhV..bTV1OK.sSq40.ly3CcN/UvNP6.MwLsUa3.ibhV.kqTV1OK.sSq
40.kz3CcN/UvNP6...EsUa3.eeWCNq0.IJ36wk8.wyLsUa3.................................
E....2....E.....I....k....EHZtqNZ7rGjB4O.IaQ..............................U/4MU/
4M.................0./.......UzD........sz1........wz...........................
.............................................6/E........kz9.....................
........................}

hi there, may i ask how you compile your formulas ?
can you do some kind of tutorial on how to set up a formula compiler ?!?
e.g. with a very simple funciton, e.g. "add"

I use a mixed system
For simple ones I write directly in assembly with Ollydbg who helps with debugging :D
Lately I compile my c sources then I convert to Mb function removing beginning, end and all constants from the assembly code. then replacing with actual addresses of each needed,variable and costant.
A manual and difficult work too bad...

Released the final version of my Menger-Koch, I'm finally happy with it :D

Your not just happy, your happy and obsessed , thanks for your hard work DarkBeam!  :beer: :beer:

MagVsXYZ released + many variants

http://www.fractalforums.com/theory/an-old-formula-revised/msg29695/#msg29695

Here you find some images and examples :D

(http://img37.imagefra.me/i53h/kriptokapi/w1vp_bd1_u6bci.jpg) (http://i.imagefra.me/2cci3oj2)

Hey, relax, it is not the holy grail. Looks like, but no... :angel1:

Yes, not the holy grail, but it looks like ... sometimes.



Mandelbulb3Dv17{
V.....K0...M7...M7...2A...k6k5X0G/dxyujzm0W73cmDkrI5StN3PzHaytO0g8lmzggyBPZchWgD
................................yBqR/5Ba422........A./..................y.2.....
................/w.1/....6Ue/...p6....E2.....Q7UZvDYWGXD/w......0/US1xckpn1/OaN4
.3....cD12../2E4ZRlAqAYrzyaw22Y5QOyj.......................u1....y1...sD...../..
.wXaNadDyK3narqCdsvbb7N7A83Ay8dMH7oL6rRDkpZfj7kYWsny2Dnv63g4yGxEijjXf2XDcx7bue7r
esvhWHbY9cK7y.5646i0TPWD......2oi/..Ig2.......kD.2....sD/2E.....................
.............ckpXm1...sD....z.MRb9.6qRi..Prt0.qRb9..sRi.UWrt0.ISb9EnAnwDK0...k1.
..................kz.wzzz1k2..6.A/...61...kA....m....c3....F....8/...I1...U4Yp4g
TU5U.8YL8yzlcisz0tZWzTAe90..2c..zzzz.g5MarH7iXyDWra4dabdnz1..........2k.8.kXWF1.
QvM93P58iz9GMmnWK2zwz0..........VAFKw16...kqS6q383Szz2D8YqFpt/.E..........E.0c..
zzzz.................................Il.F3kzzzD.FShDJnpv/.gKRfRUeyk..jSRN9Nj8G/k
32E4zzzzz1kW36PrFOuvzKzXyRh2eVxDVNfUU2SWYz9...8cU0.E./2.zz/cU08../2E.szDU08c..2E
./EzT/8cU0.E./2.Qs5cU08../2E..bTU08c..2E./.ly/8cU0.E./2.Mw5cU08../2E.kqTU08c..2E
./.kz/8cU0.E./2....cU08.zz/cU08.yz1cU08.xz3cU08.................................
E....6....E.....I....k....kLBxaMdJrQI/5S.IaQ....................................
.....................................................g53iSIsuFsD..........UNaNaN
aNavz0........yD...................sz...........................................
.....................2..........0....YYPoJqNZ756ExqRZ75.........................
8.............................0E........kz1........wz.........zD..........2.....
................................................................................
................................}

Thanks for sharing, trafassel! Seems like a good place to start exploring some more  :beer:

Cool spot. :beer:

Thanks for sharing... I'm new and these help a lot to understand just the tip of this Fractal Iceberg... What lies underneath is a mystery!!

Not far form a "good" mobius fractal but it's not yet what I want

http://klein.math.okstate.edu/IndrasPearls/limitsets/puncture.html


go here for all answer and all understand
  ericr

is the fractal name "bon" code below, which seems to interest to people
under it a vision inside the same  fractal  name "bon" (inside render)

Mandelbulb3Dv18{
b.....S....O/...61.........FGIOjEFPazK/J/XOtjdtD2Bbi0Y1c3zPDbPPXUuiwzqAC6CKbmRnD
................................JTclu1BKz.2........A./..................I.2...wD
...Uz.....U/.....Mk./.....U0....y....6E3.....E7VLJu/M8mD...........m/dkpXm1/...E
./....sD12../..............................................u1....y1...sD...../..
.z1...EEYsAIxzzzjz1..........WAbUdisqcljTcFzUvMS3t97C1JzzzzvzUNehUisqcljMaO9c9iB
Ow1mQ0auWPX4zU2bVezzzzyD......I...............sD.6....sD.IE.....................
.............oAnAt1...sD....z.2915.sgAQ..qmk/.W915.kiAQ.Uxmk/..A15......7....k1.
.....AQxcz1.......kz.wzzz1.U..6.P....c1...EB....D/...c3....F....8/...Y1.....fN52
...U.uVW5yjjA4ozpcguzzDnN06.3c..zzSi............4wyBIC4OWz1...........238..9VE/.
.Ub96aAIVz9.1se7Umvxz0........../6U0.wzzz1...........s/...................E.0c..
zzzz.............0...................2U.8.kzzzD............8....................
/6U0.wzzz1...................................6W6W.kJLRpJzDUrS1D.G6V9i6XB2lIQ.oG9
hoW2u6W6W.E9hoG9gwXvi1D.G6V9igCMdF2G.sW2Js04ttivk1E9hk4Pfxb6W60.LRpJLpvTW6W6.QpJ
LRp2.8W6W.kJLRpJ..UrS1DsMR1FA3bHEvXvi1jvc9KO2V2I................................
E.U..M....E.....I....k....kLBxaMdJrQI/5S.IaQ....................................
...................0.1......................................../k................
..............zj...................wz...........................................
.....................2.....3....A....wJHj7KOpB5JkV5.Z75.........................
..............................zD...............................E................
..............................................zD................................
................................/....E/....1....TpoPWZKRnF3Qs/ENm/..............
........................................kz1.....................................
..........................2.............................kz1.....................
................................................I....k....kLBxaMdJrQI/5S.IaQ....
...................................................wz...........................
...................................................................wz...........
...........................................................3....0....wJRkFKMoJqE
...............................................................E................
................................................................................
................................................................/.........U.....
7t4RZRKNm/0IjRLNm/........................U0............................U.2.....
...0.1..........................................................................
............................................................................}

An other test with 2 mobius transformation ,the last after I try to  in 3d  :fiery:

41 persons for the fractal "bon" but I just do more
but not alone I ask for your help with this
May we can  do it but not ALONE  imagine this 3D
this image comes not from Mandelbulb but from the net

please help me the site above gives the solution but I'm lost
thank you
ericr