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Author Topic: Mobius triplex transformation  (Read 8284 times)
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Jesse
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« Reply #15 on: March 06, 2011, 08:09:40 PM »

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

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



* moebiustriplex.jpg (50.93 KB, 480x360 - viewed 941 times.)
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Jesse
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« Reply #16 on: March 06, 2011, 08:27:03 PM »

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

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



* WhiteZ Formulas.gif (15.58 KB, 946x527 - viewed 358 times.)
« Last Edit: March 06, 2011, 09:13:28 PM by Jesse » Logged
DarkBeam
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« Reply #17 on: March 06, 2011, 09:00:31 PM »

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

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


I don'r understand what you mean ... it's wrong or no? smiley
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Jesse
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« Reply #18 on: March 06, 2011, 09:09:05 PM »

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

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

But cannot say exactly why, you should have a closer look at the code again.
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DarkBeam
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« Reply #19 on: March 07, 2011, 09:40:08 AM »

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

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

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

Ahhhhh now I got it! I mistaken "CONSTANTS" ... smiley

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

Fixed also a wrong relative jump. embarrass

Now looks okay grin

I'm updating the database too grin

* _MobiusTpx.m3f (3.47 KB - downloaded 135 times.)
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Jesse
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« Reply #20 on: March 08, 2011, 08:05:36 PM »

Now it works, well done!
 A Beer Cup A Beer Cup A Beer Cup

 Repeating Zooming Self-Silimilar Thumb Up, by Craig
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DarkBeam
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« Reply #21 on: March 08, 2011, 08:51:30 PM »

Now it works, well done!

Yay grin

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

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

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... undecided

Probably, it's better if I abandon this jungle, return to simple functions again wink
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Jesse
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« Reply #22 on: March 09, 2011, 08:10:42 PM »

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

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


* ikenagabulb.jpg (48.83 KB, 480x360 - viewed 857 times.)
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DarkBeam
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« Reply #23 on: March 09, 2011, 08:34:58 PM »

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

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.



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... huh?

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. smiley

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.....................
........................}
« Last Edit: March 09, 2011, 08:36:46 PM by DarkBeam » Logged

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cKleinhuis
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« Reply #24 on: March 09, 2011, 11:17:34 PM »

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"
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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #25 on: March 09, 2011, 11:43:22 PM »

I use a mixed system
For simple ones I write directly in assembly with Ollydbg who helps with debugging cheesy
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...
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DarkBeam
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« Reply #26 on: March 10, 2011, 07:29:29 PM »

Released the final version of my Menger-Koch, I'm finally happy with it cheesy
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tomot
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« Reply #27 on: March 10, 2011, 09:11:14 PM »

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

Your not just happy, your happy and obsessed , thanks for your hard work DarkBeam!  A Beer Cup A Beer Cup
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DarkBeam
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« Reply #28 on: March 16, 2011, 10:45:23 AM »

MagVsXYZ released + many variants

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

Here you find some images and examples cheesy
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DarkBeam
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« Reply #29 on: March 17, 2011, 06:25:22 PM »



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