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Topic: Tiling the plane with checkerboard patterns
Replies: 21   Last Post: Jul 14, 2010 10:33 PM

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 Rouben Rostamian Posts: 193 Registered: 12/6/04
Re: Tiling the plane with checkerboard patterns
Posted: Jul 9, 2010 4:08 AM

On Fri, Jul 09, 2010 at 04:23:22AM +0000, mark wrote:
>
> I don't know if this is helping or not, but I think your definition of
> the problem has a flaw. The reason #2,#3,#5, & #9 create the same
> wallpaper is that "the plane" does not have any corners. On the same
> note I think "the plane" does not have any rotational orientation.
> If that is true, #4,#13,#6, & #11 also generate the same wallpaper.
> This would change all your numbers. a(2) now =6. think a formula is
> possible for either definition. I'm working on it. Thanks for the
> interesting puzzle.

Hello Mark, I can't tell if bringing in rotations makes
the problem simpler or more difficult. If it does make
it simpler, then by all means, that should be the primary
case to be studied.

I would be interested in hearing about any insights into this.

Rouben

Date Subject Author
7/6/10 Rouben Rostamian
7/7/10 Avni Pllana
7/8/10 mark
7/9/10 Rouben Rostamian
7/9/10 Avni Pllana
7/9/10 Rouben Rostamian
7/10/10 Avni Pllana
7/10/10 mark
7/11/10 Rouben Rostamian
7/11/10 mark
7/11/10 Rouben Rostamian
7/11/10 mark
7/12/10 Rouben Rostamian
7/13/10 mark
7/14/10 Rouben Rostamian
7/14/10 mark
7/11/10 Rouben Rostamian
7/14/10 Avni Pllana
7/14/10 Rouben Rostamian
7/13/10 Mary Krimmel
7/14/10 Rouben Rostamian
7/14/10 mark