Cross Menger!? Can anyone do this?

[mclarekin]

@ Crist

quote]Tried another code from your latest posts, what is fabs? Did you used Fragmentarium?[/quote

In openCL and C++ I have a fabs() which is abs() in most frags I have seen. Not sure if it a maths library thingy. And I have still haven’t learnt how to use fragmentarium:)

z = vec3({z.z, z.x, z.y); // reorientate

Yep, I dont know how that got there. I should really transpose the axis in the formula so that the reorientation wouldn’t be necessary.

Missing a z.y = abs(z.y);  before the    z.z = abs(z.z);      

also can add in a z.x = abs(z.x);  option checkbox.


BTW This is where I am up to this coding:

a) I  have written a fourth version of the PrismShape, it does all of what my first three attempts can do plus more. I will post this with an explanation of converting Mandelbulber code into .frag.
b) The CrossMenger Trick  i posted here on the 29th is my final version of that one.
c) I have yet to do a final CrossMengerKIFS version

PS you can replace
if(z.z > z.x){temp =z.z; z.z = z.x; z.x = temp;} type code
with
if(z.z > z.x){z.xz = z.zx;} in Fragnmentarium (and in openCL)

PPS  looking at the zipped file. As well as the prismShape code , you can add a dotScale to the dot in both the CrossMengerTrick and CrossMengerKIFS.

 

[mclarekin]

I have finished coding Darkbeams reciprocal3 x, y, and z. ( I have still got to get a SIGN() function code to work for optimising this code.)
 Here is Darkbeams code

Description:

Computes the reciprocal of x with a different (continuous) function:

x' = sign(x)(1/Lim - 1/(abs(x)+ Lim ))


The DE is almost untouched, it should work fine also with a Raystep 0.5 !
Just don't go too low with the limiter to avoid noise.

In Mandelbulber I have it set up this way at present. I have the default parameters at 1.0 but 0.5 might be better in most cases. Hmmm

Here is the z.x part. Start/stop iteration controls are also necessary. The transform can be run on all three axis  until termination but  using  1 or 2 axis  for  only a few iterations is generally best, starting at iteration 0 or iteration1.  (It works well with the menger types but I suspect surf/box types is where this transform maybe at it's best).  

Covert from Mandelbulber to .frag:

if (fractal->transformCommon.functionEnabledx) type code is a checkBox
fractal->transformCommon.offset111.x) type code is a vec3 default(1,1,1) axis .x
fabs is abs

Code:

		if (fractal->transformCommon.functionEnabledx)
		{
			if (fractal->transformCommon.functionEnabledAx)
				tempZ.x = (1.0 / fractal->transformCommon.offset111.x) - 1.0 / (fabs(z.x) + fractal->transformCommon.offset111.x);

			if (fractal->transformCommon.functionEnabledAxFalse)
				tempZ.x = (fractal->transformCommon.offsetA111.x) - 1.0 / (fabs(z.x) + fractal->transformCommon.offset111.x);

			tempZ.x += fabs(z.x) * fractal->transformCommon.offset000.x; // function slope

			if (z.x > 0.0)
			{
				z.x = tempZ.x;
			}
			else
			{
				z.x = -tempZ.x;
			}
		}

[mclarekin]

@Darkbeam. I checked out  chebyshev rotation on the net. 

I have just starting on MixPinski       In a day or two I will probably seek some clarification

[DarkBeam]

hehe by the way I got an identical effect using a shorter formula (not three just one I think?). I called it ngon (and ngon2) but I don't remember how it works! lol
Maybe with a combo of "normal" atan2 and stuff...
But now I am curious about MPinski
Sign(x) is normally a one line macro.
Or sgn(x)=x/abs(x) horrible!
Or you make some AND with sign mask then if it is 0 it is a positive number else a negative. Duh hackish stuff sorry
There are premade cakes in Stackoverflow too; http://stackoverflow.com/questions/1903954/is-there-a-standard-sign-function-signum-sgn-in-c-c
Btw I think you added too much stuff ... the mb3d counterpart is really a 1 line...

[claude]

my favourite version is: sign(x) = (x > 0) - (x < 0)

[Sabine]

@Luca Is this THE _reciprocalX,...Y,... - ...Z3 you're all talking about??? And if yes... We can haz for Frag? 

[DarkBeam]

Lol Sabi! Yes it is but what do you mean? You can code it as a one line transform then add it after a menger iter ... easy for a basic programmer like you!
 

[Sabine]

I never touched anything even remotely 'fractalesque' with basic in the last 30 years, I think, and what I did then was only very basic fractal stuff.
Basic I used in my work and later VScript and JScript (now Those are really hi-tec, I know!  ) for simple eventlog readouts, replication-logs and other info for rapporting, WMI stuff, that kind thing, mostly r/w & string-modification-hell. And sometimes still write something small and handy or fun for at home. Ohh forgot: some LISP for Autocad in the jolly 90's, whahaha now that will come in handy :}
So really, Luca, trust me now and forever, I'm a total nitwit when it comes to fractals AND programming, honestly!!!  

But will try nonetheless

[mclarekin]

@sabine02

Reciprocal3  x' = sign(x)((1/Lim - 1/(abs(x)+ Lim)  works best,
 including the linear slope    + (abs(x) * slope)       works well
adding a two limit mode works OK in some cases,  but can cause poor DE


@darkbeam & claude

template <typename T>
inline int sign(T val)
{
   return (T(0) < val) - (val < T(0));
}

is what Buddhi has added for me,although I currently cannot get it to work

With MixPinski "A strange but intriguing fractal",  progress stopped at 4D rotation,  , is there any examples of how this is done??

Meanwhile, when looking at 4D rotation I came across the tesseract

https://en.wikipedia.org/wiki/Rotations_in_4-dimensional_Euclidean_space#/media/File:Tesseract.gif

and I start wondering if this structure translation has been used in making a fractal?

[mclarekin]

CrossMengerTrick alternating with  rotateForward_fold_rotateBack (rotatedAbs, rotatedFolding & "rotatedMBoxFolding")

[Sabine]

@mclarekin Thanks a lot

[DarkBeam]

Dear mclarekin you may look at this shader for a reference

https://www.shadertoy.com/view/llSSzc

It has xw yw and zw routines. I am sure MBulber already has a 3d rotation support
You just modify routines accordingly. (A copypaste should do the job ).
The mixpinski itself is just a modded copypaste of Knighty Sierpinski fused with Menger but with one more dimension!

[mclarekin]

PrismShape for 1 iteration to deform crossmenger trick.

 This crude deformation is by replacing line in prismShape
         dot1 = (z.x * -SQRT_3_4 + z.y * 0.5) * fractal->transformCommon.scale;
by
         dot1 = (z.y * -SQRT_3 + z.z)     * fractal->transformCommon.scale;

@darkbeam. Answering two questions with one link, well done.

I recognise that 4D rotation from somewhere back then, it looks much simpler  now.

That tesseract is  hypnotizing/fascinating to watch.

Thanks again

[mclarekin]

This is the UI setup for darkbeams rotateForward_Fold_rotateBack,  that I have used to deform the CrossMengerTrick.  The UI only covers some of the possibilities. 

 Seems to work well with mandelbulbs too!

[mclarekin]

Here I have deformed the CrossMengerKIFS with Darkbeams tetra3D.