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Okay! After a long search, and the help of Aexion with his new ideas and Jesse with some technical support (and his fantastic software ) I have found a "new" type of fractal.

It is the same as the Amazing box, as the base, but the folding part is much more complicated. I use four foldings instead of 3, and they are "skewed" like the tetrahedron's faces.

Let's define Rotated Folding this formula

- Rotate by the given angles
- Do; x = abs(x+Fold) - abs(x-Fold) - x (double folding) , or x'=1-abs(x-1) (single folding) - Maybe I am using y or z for folding. Can't be 100% sure 'cause assembly code is not clear! (due to fp stack swaps and other hell )
- RotateBack by the given angles

Given a rotation matrix, RotateBack multiplies the axis by the transposed matrix.

Okay, now let's see what angles are needed;

 RotatedFolding(+45,+45,+45,Fold) // base
 // other planes. this can be tweaked
 RotatedFolding(-45,-45,+45,Fold)
 RotatedFolding(-45,+45,-45,Fold)
 RotatedFolding(+45,-45,-45,Fold)

I calculate only the 1st rotation matrix. The remaining ones can be obtained changing signs from the previous, following a fixed "geometric rule"


Very nice variations have been done changing those rules. Fantasy is the only limit!
The ABox formula is;

just out of interest.  While I've been trying to wrap my head around this..

the mandelbox formula can be applies to any shape right?

e.g.

2D   -    3D

Square   - Cube

Triangle  - Pyramid



So therefore there must be a generic formula  as such:

Pass Number of Points in shape  ( x )
    Do Mandlebox folds.


So  Pass Number of Points in shape ( 4)

    Creates a square mandel  box.  and cube mandel box in 3d.


So  Pass Number of Points in shape ( 3)

    Creates a triangle mandex box, and pyramid mandbox in 3D.


So in terms of generic polyhedra  what is the mandelbox formula ?

e.g. for  convex polyhedron

{3} is an equilateral triangle
{4} is a square

cube has 3 squares around each vertex and is represented by {4,3}.

Tetrahedron {3, 3}   Cube {4, 3}   Octahedron {3, 4}   Dodecahedron {5, 3}   Icosahedron {3, 5}

So there fore  what is the code  to create a mandel box  given  the function header:


Create Mandelbox by Schläfli  {p, q}


  code to create n sided polyheda mandel box?


where Create Mandelbox by Schläfli  {4, 3}

    would create a standard mandel box ?

Might be also of interrest
http://www.fractalforums.com/new-theories-and-research/generalized-box-fold
Buddhi implemented that in mandelbulber