Implementing MixPinski

[mclarekin]

Here is a zoom at distance 4e-06, showing an area with fine detail.  Step fudge 0.8.

[Crist-JRoger]

I have learnt  new things working with you guys

Me too 

example - symmetrical pattern (not tested)

magForward
* scale
+ offset1
rotForward
fasb(z+offset2)
rotBack
- offset1
* -scale
magBackwards

or a simple magForward ,  MBox ,  magBack

or    +offset  ,      ( scale,  fabs,  rotate, menger)  , -offset

this sort of thing is often "good maths"

will try handle this  Thank you very much!

Back to the MixPinski
...
figure out the difference. so we can make the true mixPinski4.

In frag "default" shape with scaleC=(1,1,1,0.5). I fixed Default preset

[mclarekin]

The spherical fold seems to work well with the mixPinski.  I am using 3 formula slots in MandelbulberV2. MixPinski in slots 1& 3 ,  and randomly  trialling formulas and transforms in slot 2 and have been barely scratching at the surface of the mixPinski possibilities.

[mclarekin]

@ crist. The default is cool.

[Sabine]

mclarekin wrote

I have learnt  new things working with you guys

  You don't want to know how much I am learning from all of you and it's such fun! I am quite in awe of the knowledge present here. I know I can only add very little and simple stuff, but to know how little you know seems to be the first step ;}

@Crist-JRoger: It was the bailout I forgot to delete! Agree now with you on simple DE And great that you found the standard shape with the zScale=1. In mb3d it gives the standard shape with zScale=0,5 I do not know why and if that is important.

@Dark-Beam Thank you, Luca!  It's not yet right I think, I need to adjust all the things I know to find in mb3d: raystep multiplyer, stepwidth limiter, stepcount binary search, smooth normals, and I have no idea how/where to set them in frag! It would be so nice if everything had the same name But really, the _reciprocals in mb3d need really fine settings to render nicely, so I cannot at this moment tell you if my efforts lead to any good result The good thing it that I have not blown up Fragmentarium yet while hobbying  Thank you for challenging me;)

If anyone has any idea which settings in Fragmentarium correspond more or less with raystep multiplyer, stepwidth limiter, stepcount binary search, smooth normals, at least, if they exist at all in Fragmentarium? Would be a great help in figuring out if I am on to something or not.

[Crist-JRoger]

Some fun for MixPinski  z.w manipulations and sphere for cut. At one's own sweet will (_{thankls to googleTranslate})
When tested has recalled Dr.Strange movie

[mclarekin]

This transform i will insert into my openCL version, probably after the menger4D,
this transform uses Dd so cannot use pow(scale,-i)

uniform int foldSphStart; slider[0,250,250]  ??start default 250 = transform disabled
uniform int foldSphStop; slider[0,250,250]
uniform float offsetS; slider[-5., 0.0, 5.]
//uniform float scaleS; slider[-5., 1.0, 5.] // neg scale so abs(Dd) needed
   
uniform float minR2; slider[-5., 0.25, 5.]
uniform float maxR2; slider[-5., 1.0, 5.]
float mMR2 = maxR2 / minR2;

   


if( i >= foldSphStart && i < foldSphStop)
{ // this transform uses Dd so cannot use pow(scale,-i)
   float r2 = dot(z,z);
   z += offsetS;

   //z *= scaleS; // if using pow(scale, -i) then comment out this and the next line
   //Dd = Dd * abs(scaleS) + 1.0; // beta, is the +1.0 needed in this function?


   if (r2 < minR2)
   {
      z *= mMR2;
      Dd *= mMR2;
   
   }
   else if (r2 < maxR2)
   {
      z *= maxR2 / r2;
      Dd *= maxR2 / r2;
   
   }
   z -= offsetS;

}

[Sabine]

Already had fun with your great Sity, Crist-JRoger!   Really great image too!


A bit of preview what maybe is or one day might be reciprocalX3b:

[Crist-JRoger]

This transform i will insert into my openCL version...

Thank you  Very interesting randomize of fractal. In standard settings i got upper half of apple with leaf 
So it works even after z scaling, but before z+=offsetM looks better I think

A bit of preview what maybe is or one day might be reciprocalX3b:

Code not optimized? Fractal goes to infinity

[Sabine]

Code not optimized? Fractal goes to infinity

I have no idea how to optimize this code for fragm

As I have written I haven't even got a clue if its basic is ok, I have asked Dark-beam, will wait what he says. This transform goes into some sort of almost-infinity in mb3d with Sierpnski4ex too, and it does always have DE issues if you use small limiters Maybe you can have a look at its behaviour in mb3d with mixpinsky4ex, it looks like it is only seemingly going infinite there (big change in scale so must zoom out very much!)...

But all in all it does make nice images   so might be a 'nice' error if it is one :}

Update Heard from DarkBeam: All is ok with it, this is normal behaviour for non-linears... But I have made it conditional, so you can just uncheck it;)

[M Benesi]

  So I made it 3d and mixed it with the "slice" formula (going to remove the accordion function I think, but for now it's still embedded in the slice part).  

  Makes for some interesting infinitely zoomable patterns...


  Files here.  The rotation technique seems applicable to both 2d and 3d fractals, and adds lots of details.  More on it later...  probably a name for it that educated people know.  

https://drive.google.com/open?id=0B0EcJQ49B_yOUG1lRk5GdUk1MEk

[Sabine]

@Matt Very cool toy! 
I cannot get the AccCycleSplit to do anything, is there a condition that it needs to work that I am not aware of? But great fun anyhow!

[M Benesi]

lol.   AccCycleSplit actually sets the cycle length for repetition along the x component.  Doesn't do that much if you use it beyond the first iteration, and even then it's probably a superfluous part of the code. 

  Was going to remove the whole accordion part of the code anyway... right now.   

[DarkBeam]

Hi Matt
For Crist: the fractal goes to infinity because the reciprocal transform map big numbers to zero and epsilons to infinity. This causes strong stretching but goes well with kifs
See the graphic of y=1/x for comparison.

[M Benesi]

Luca.    


  This is the 3d "Kaleidoscopic rotation" thing (rotates at multiple points to preserve continuity while adding movement/rotation).  I uploaded the newer code with the rotations added, and accordion taken out to the link I posted above.   

<a href="https://www.youtube.com/v/P94WJoCtnSU&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/P94WJoCtnSU&rel=1&fs=1&hd=1</a>



  How do we do giphy gifs on the forums?

https://giphy.com/gifs/kaleidoscopic-rotation-W5KN3GmUmVT4k

  Math guys- what is the technical term for those types of rotations?  They do not introduce discontinuity as long as there are even numbers of rotations.