17 Dec
2013
17 Dec
'13
9:22 a.m.
Marc LeBrun wrote: Alternatively we might start with the simpler 4 cell neighborhood, thus only 2^10 cases.
--the checkerboard neighborhood graph is bipartite, so this probably not a good idea.
A cell is connected to itself, so I fail to see what the problem is. Anyway, I seem to recall that Edgar F. Codd already looked at all of these 1024 rules and found that none were interesting.
Using the equilateral triangle lattice, 6 neighbors, might be better, though.
Yes, the hexagonal lattice A_2 is awesome. The next time that a single lattice simultaneously wins the packing, covering and quantising problems is the Leech lattice in 24 dimensions (rather unfairly, A_8* beats E_8 in terms of covering). Sincerely, Adam P. Goucher