Tessellations of plane / space

[DarkBeam]

Question;

Is anybody able to do a non-squarry/cubic tessellation of the plane / space with following requirements?

(Final result should look much like http://en.wikipedia.org/wiki/Hexagonal_tiling ).

1. Transforms a Cartesian plane (x,y can vary to -infy to + infy) to a Cartesian plane where length(x,y) < 1 (or a constant value).

2. Inside every hexagon, x and y should vary from negative to positive values; this to not get an "overly symmetric" tiling.

3. The tiling function should be continue (again - it is easy to do a discontinue tessellation but it causes trouble near the cutplanes).

This because I already figured out how to make a hex-tile but it should look like http://en.wikipedia.org/wiki/Trihexagonal_tiling or http://en.wikipedia.org/wiki/Triakis_triangular_tiling or even http://en.wikipedia.org/wiki/Triangular_tiling ... So don't ever post those tessellations because I already know how to obtain those

Trihexagonal should be simple. Something like;

Code:

a. repeat three times:
 a1. y=Infinitefold(y,distance)
 a2. (x,y) = Rotate(x,y,30°)
b. x = -x

  InfiniteFold is;

Code:

x = round(x/2)*2 // it is discontinue, let's make it continue.
if x>1 {x = 2-x}
if x<-1 {x = -2-x}
// done! It is a continue folding function - but it folds infinite times in one shot

[DarkBeam]

If it helps, it's a visual scheme of how it should works...

Red lines -> x and y should be "exchanged"?
Black lines -> x is constantly = 0

As you see, it can not be done with a simple unconditional "fold" I think!