Benesi "pinetree" (fold+bulb)

[M Benesi]

Cool.  That might work, but for some reason I don't think it will be quite as smooth (I'm often wrong... the only way to check is to test it out).  As a matter of fact, I think the major difference in the 2 images above is... one uses 4 iterations of Pine1 before the transform, the other uses 3.  See... I told you I make lots of mistakes.  


  The math/geometry of T2 and T3 is:  Rotate, Transform (T2 or T3), Rotate back.  My idea is to blend the transforms inside the rotation, instead of outside.  The 2 transforms are quite similar...  Luca's descriptions are in the code block below.  Just made another transform because I was thinking about it.  I'll make up an original name for this one.  Maybe... transform 4?    

T4:

T4 with XYZ pixel too, like the next 2 images...


  These next 3 images have an additional transform (2?? or 3???) later on.  The 2 images above this do not.  You can see that it changes the details a bit.  Question: do the transforms have a different effect if you select odd or even numbers of prior iterations?  For some reason, I think that it does. 

T4, xyz, extra transform 2 later on:



T2:


T3... This one also has full xyz pixel component added in at one point, which makes it wavier in areas... and maybe other stuff...:

[KRAFTWERK]

...And Johan - where is the pretty image

Too little time... Here is a one default setting render...

[thargor6]

One more play with the JIT-version of this formula:

[DarkBeam]

Great work Johan and Andreas...

[M Benesi]

Very nice.  Thank you for using the formula!

[KRAFTWERK]

Very nice.  Thank you for using the formula!

It's an honor!  And thank you Luca!

[M Benesi]

I don't know if anyone noticed that the 0,0,0 Julia of this fractal is arranged like a stellated octahedron.  That's the next project..  aligning a stellated octahedron (maybe a pseudo-Sierpinski type) and hybridizing it with this fractal.

  I had something I thought was one... but now I'm not too sure (actually.. I don't think it is):
<a href="https://www.youtube.com/v/GC8IKrIB1pA&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/GC8IKrIB1pA&rel=1&fs=1&hd=1</a>

  Luca showed me the shape's formula in M3D, but it's DIFS...

[DarkBeam]

Difs are calculated in one shot, so hybrids are not possible.
In other words given x, y, z they just return the distance estimation. I hope it is clear?  

on the other hand. Using difs you can create more general fractals replicating even de combinates and fractals with more than three variables like phoenix ... etc
Of course you must handle the bailout the cycle everything.
I wanted to import the script by Bulatov but it is hyper complicated...

[M Benesi]

  So Luca.. I can maybe extract what I want from the binary... and make a plain formula.  I'll have to look.  Doing other things now. 

[M Benesi]

Pine tree frag with lolsquares.    Will add more lolsquares functionality to it later.
  Fixed DE for T3...    Thanks Mclarekin...

[mclarekin]

Looking even better


BTW   .frag  is missing    dr*=T3Scale;

[M Benesi]

  Fixed DE yesterday, thanks!

So I need to work on getting these formulas ported to M3D.  I'm thinking the separate cube to sphere, and sphere to cube formulas, and a combo formula with Pine Tree 1, so we don't have to use a whole bunch of formula tabs to use it...

from the frag:

Code:

sr32=sqrt(3/2); //both use square root of 3/2 ...
// spheric  code
 rCyz= (z.y*z.y)/(z.z*z.z);
 rCxyz= (z.y*z.y+z.z*z.z)/(z.x*z.x);
if (rCyz<1.) {rCyz=sqrt(rCyz+1.);} else {rCyz=sqrt(1./rCyz+1.);}
if (rCxyz<1.) {rCxyz=sqrt(rCxyz+1.);} else {rCxyz=sqrt(1./rCxyz+1.);}

z.yz*=rCyz;  
z*=rCxyz/sr32;  


// unSpheric 
	
 rCyz= (z.y*z.y)/(z.z*z.z);
if (rCyz<1.) {rCyz=1./sqrt(rCyz+1.);} else {rCyz=1./sqrt(1./rCyz+1.);}
z.yz*=rCyz;

 rCxyz= (z.y*z.y+z.z*z.z)/(z.x*z.x);
if (rCxyz<1.) {rCxyz=1./sqrt(rCxyz+1.);} else {rCxyz=1./sqrt(1./rCxyz+1.);}
z*=rCxyz*sr32;
 

  That might be tomorrows work.

[DarkBeam]

This is what I experienced;
People tend to ignore transforms.
Also they ignore slow formulas.
Even worse transforms that must be used in conjunction!
They tend to use easy to handle formulas and to combine them in a random way.
That is why I did your formulas that way
More importantly there is already a tospherical/invsph transform for MB3D

[M Benesi]

hahahha... Awesome.  Less work... whoops.  IT does work..  Maybe not exactly how I expected it.

  Ehh... So...  I looked at them some more.  While they can transform an amazing box to a sphere, and back, they don't have the same effects.  They introduce distortions and stuff... and they don't work like the sphere transforms I wrote. 

  I'll try them on some other stuff.. but they don't seem to be working the same way.  Instead of making a "squary" pine tree, they make a brain:

[DarkBeam]

Ah!!! That's because you are not using really the standard spherical coordinates! Because the transforms itself do their work
That's right. You are maybe doing a "spherization"?
Luca