On Wed, Jul 14, 2010 at 12:14:48PM +0000, Mary Krimmel wrote: > From: Mary Krimmel <email@example.com> > Date: Wed, 14 Jul 2010 12:14:48 +0000 (UTC) > To: firstname.lastname@example.org > To: email@example.com > Subject: Re: Tiling the plane with checkerboard patterns > > Thank you all for an easy-to-understand puzzle. Mark's point that a > plane tiling has no orientation seems to me to make his identifying > rotations of the wallpaper a reasonable simplification of the original > problem, as does Avni's separating even n from odd.
Hello Mary, I think it's Mark's formula that talks about even and odd n. Avni's does not distinguish.
I am curious myself about rotational symmetries. I intend to look into them when I find some free time.
> What about starting directly with the number of possible patterns? > Maybe that's what you're doing, but not what I understood.
Well, yes, I computed a(1) through a(5) by examining all possible patterns. This does not work for a(6) because the number of patterns becomes too large for a computer to handle.
> What if we started with an m by n rectangle where m and n > are not necessarily equal?
My computer program is written to handle m by n rectangles but I would rather resolve the n by n case before getting into the general case.