On Jan 6, 2005, at 21:20, Brian van den Broek wrote:
Oh, the Life rules allow a world where every cell will change in the next generation, iff your world is a torus (i.e. the lower row "touches" the upper row as if it were immediately above it, and the right column "touches" the left column as if it were immediately left of it). It is quite trivial: set all cells to LIVE. Next generation they're all DEAD.
Topologist! (That's cheating!) ;-)
If we are going that way, you 'iff' seems a bit hasty. Take the 1x1 matrix 'full' of live cells.
Well, if the only cell of a 1x1 torus matrix is LIVE, that means it is surrounded by 4 LIVE cells, doesn't it? :D
Also, other 'funny' (in the sense that a torus is funny) planes could be defined (say a torus-like structure with more than 1 whole -- cannot recall the general terminology from ill-remembered topology), etc. I meant the claim for a standard non-trivial (i.e. M > 1 and N > 1) MxN euclidean plane matrix, but your correction is both amusing and welcome.
Thanks :)
However, the main reason why I talked about a torus is that it's one of the two obvious choices when you're implementing Life using a 2D matrix (the other being a finite rectangular plane).
-- Max
maxnoel_fr at yahoo dot fr -- ICQ #85274019
"Look at you hacker... A pathetic creature of meat and bone, panting and sweating as you run through my corridors... How can you challenge a perfect, immortal machine?"
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