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

[Antti Karttunen]

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