mark
Posts:
206
Registered:
12/6/04


Re: Tiling the plane with checkerboard patterns
Posted:
Jul 13, 2010 1:53 PM


> I see your reasoning and there may be some > significance to the > patterns that you have observed. If we knew the true > value of > a(6), it would have helped to settle the issue. If > we extend > your table of N and X to N=6 according to Avni's > formula, we get: > > N X > 6 6020 > > Since 6020 = 2^2 . 5 . 7. 43, the X value deviates > from your > pattern of multiples of (n1)*(n+1). Having the true > value > of a(6) would tell us if your formula, or Avni's, or > neither, > is correct. Unfortunately, the direct computation of > a(6) > is impossible with my computer algorithm which > searches all > possible patterns, because the number of patterns is > too large. > > Rouben >
My guess is that they are both wrong and both close. Since they approach the problem from different directions yet yield nearly identical results. We should be able to get clues from each. I wonder if it would be useful to force them to be equal (without the REM function)and add a variable like I did earlier. The action of that variable might be interresting. It's a shame we don't have a super computer handy. That a(6) number would definately help. About the other option: rotational symmetry. Could you modify your program to produce a 1 thru 5 list for that? We may find it has an easier solution.
Mark

