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Welcome to Fractal Forums > Fractal Software > 3D Fractal Generation > Mandelbulb 3d > Mobius triplex transformation
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Author Topic: Mobius triplex transformation  (Read 8557 times)
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DarkBeam
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Fragments of the fractal -like the tip of it
« on: March 04, 2011, 06:39:32 PM »
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 grin

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...........................
................................................................................
................................}

* mobiustriplex.jpg (169.05 KB, 724x1308 - viewed 567 times.)
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DarkBeam
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Fragments of the fractal -like the tip of it
« Reply #1 on: March 04, 2011, 06:46:47 PM »
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................
................................................................................
................................}

* mobiustriplex.jpg (84.58 KB, 724x653 - viewed 348 times.)
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DarkBeam
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Fragments of the fractal -like the tip of it
« Reply #2 on: March 04, 2011, 06:54:03 PM »
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................
................................................................................
................................}

* mobiustriplex.jpg (94.22 KB, 724x653 - viewed 383 times.)
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DarkBeam
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Fragments of the fractal -like the tip of it
« Reply #3 on: March 04, 2011, 06:59:54 PM »
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")...
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DarkBeam
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Fragments of the fractal -like the tip of it
« Reply #4 on: March 04, 2011, 07:26:13 PM »
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  grin

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
........................................................}
« Last Edit: March 04, 2011, 08:00:36 PM by DarkBeam » Logged
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Jesse
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« Reply #5 on: March 04, 2011, 09:38:58 PM »
Seems that there is still a problem with the formula, nothing to see here with the parameters.  undecided

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...
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DarkBeam
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Fragments of the fractal -like the tip of it
« Reply #6 on: March 04, 2011, 10:44:29 PM »
Quote from: Jesse on March 04, 2011, 09:38:58 PM
Seems that there is still a problem with the formula, nothing to see here with the parameters.  undecided

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! shocked
I will try to submit the file again...
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« Reply #7 on: March 05, 2011, 03:07:51 PM »
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.
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Jesse
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« Reply #8 on: March 05, 2011, 03:31:27 PM »
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?
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DarkBeam
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Fragments of the fractal -like the tip of it
« Reply #9 on: March 05, 2011, 03:35:12 PM »
Quote from: Jesse on March 05, 2011, 03:31:27 PM
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. smiley

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 cool --- //

    // --- so at first try to compute the divisor. if it's zero or near, we can go out!!! cool --- //
    // --- 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 cool
    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 {
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Jesse
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« Reply #10 on: March 05, 2011, 08:41:54 PM »
Quote from: DarkBeam on March 05, 2011, 03:35:12 PM

   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  Azn
« Last Edit: March 05, 2011, 10:34:46 PM by Jesse » Logged
DarkBeam
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Fragments of the fractal -like the tip of it
« Reply #11 on: March 05, 2011, 10:32:47 PM »
The assignment x=1E90 is okay? smiley
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Jesse
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« Reply #12 on: March 05, 2011, 10:58:40 PM »
Quote from: DarkBeam on March 05, 2011, 10:32:47 PM
The assignment x=1E90 is okay? smiley

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.
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Fragments of the fractal -like the tip of it
« Reply #13 on: March 06, 2011, 07:08:17 PM »
Check it accurately, so I can add it to the list. angel
* _MobiusTpx.m3f (3.47 KB - downloaded 196 times.)
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Fragments of the fractal -like the tip of it
« Reply #14 on: March 06, 2011, 07:40:43 PM »
Quote from: Jesse on March 05, 2011, 08:41:54 PM
you could also use this for the plenty initialisations to get a smaller code.

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... sad I'm writing an Ikenagabulb, but without the power code I have to write a "while" cycle too time consuming Azn
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No sweat, guardian of wisdom!
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