Images of 27x27 table of tersums (like Nim-sums but base 3)

[Gerald McGarvey]

PARI has some graphics capabilities but not color graphics as far as I know,
but I'm not a PARI expert. It can be called from other languages that could
do the graphics, e.g. C++ or better yet Python (via PariPython).
http://www.fermigier.com/fermigier/PariPython/readme.html
Looking at the differences between A048720 and A051776 (Nim-products)
it looks like there is some sort of relationship between them. Differences
for n and m > 1:
  1  5  0  0  1  5  4  4 5
  5  3  0  0 -3 -5 20 20
  0  0 10 18 10 18 21
  0  0 18 10 22 14
  1 -3 10 22 15
  5 -5 18 14
  4 20 21
  4 20
  5
Cheers,
Gerald

At 04:48 PM 12/31/2006, Antti Karttunen wrote:
>Gerald McGarvey wrote:
>
>>tersums are like Nim-sums but base 3 is used instead of base 2,
>>see sequence A004489, 'write m and n in base 3 and add mod 3 with no carries'
>>http://www.research.att.com/~njas/sequences/A004489
>>
>><http://www.research.att.com/%7Enjas/sequences/A004489>Below are images 
>>based on a table of tersums for n and m from 0 to 26.
>
>Nice quilt-patterns, thanks! Are there routines in PARI for drawing images 
>as well?
>Lately I have used Python and its PIL-libary for drawing.
>
>>
>>I would think that ter-multiplication etc. is or could be defined 
>>similarly to
>>the way Nim-multiplication is defined. Is that correct? If so, is there some
>>practical significance?
>
>Another way to continue analogy is to consider the multiplication table 
>for GF(3)[X]
>polynomials (encoded in the ternary base), à la table 
>http://www.research.att.com/~njas/sequences/A048720
>for GF(2)[X] polynomials.
>If one considers polynomials with also negative exponents of x
>(called "dipolynomials", with coefficients taken from any commutative 
>ring, in an old Wolfram-paper:
>http://www.stephenwolfram.com/publications/articles/ca/84-properties/3/text.html 
>)
>then in case of the GF(3)[X]  one could use the variant of ternary system 
>(what was it called?
>"balanced ternary, something"? Invented/Discussed by Knuth, at least) that 
>was discussed
>here a few months ago. Adding/multiplying those might yield something 
>interesting.
>
>
>
>
>Cheers and Happy New Year,
>
>Antti Karttunen
>
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