# Tetracaidecahedron cellular automaton

For 2D cellular automata (CA) there are 4-neighborhood and 9-neighborhood on
a square grid. But it is much more natural to use a hexagonal grid (see Hexagonal
Engineering for more information). I think for 3D CAs the "natural"
structure is the the tetracaidecahedron. It is a 14-faced, space filling polyhedron.
The following picture demonstrates the space filling attribute with some tetracaidecahedra:

(the source, with which I generated this
picture with Povray)

## Binary totalistic tetracaidecahedron cellular automaton

I've played a bit with a binary totalistic tetracaidecahedron cellular automaton
and with rule B014S1237 (new cells are born on 0, 1 and 4 active neighbours
and active cells survive on 1, 2, 3 and 7 active neighbours), the initial space
filled with random active cells with a density of 30 %, a structure like the
coral in my 2D Totalistic Explorer emerges
after some time. A picture rendered from Povray with a DF3 file (128x128x128
voxels, produced from a Java program) for the interior of a box:

18. May 2003, Frank Buß