[Gimp-print-devel] Magic squares

[Robert L K. <rl...@al...>]

Is anyone here familiar with the generation of magic squares
(particularly "most perfect" magic squares, where each 2x2 block sums
to the identical value)?  I have some ideas about using magic squares
to improve dither quality, but I need to generate some to use a
matrices for that purpose.  They need to be linear (i. e. using a
sequence of numbes between 0 and 255, not using primes or anything
else).

Actually, what I want is something a bit more than that, even: I want
four magic squares that when stacked are "magic" in the third
dimension, too.  Better yet (if it's possible) would be for three of
the four to have the same 3D sum, as well as all four.

Even better would be 16x16 squares, where each 2x2, 4x4, and 8x8
sub-block sum to the same value (obviously each 4x4 block will sum to
twice what each 2x2 block will).

They don't actually have to be absolutely perfect, but the closer the
better.

The specific idea right now is to use this to implement variable
density (the current implementation of density is broken, even though
it generally behaves fairly reasonably).  So what I want to do is drop
some number of dots depending upon what the chosen density is.

The reason I'm thinking of this kind of super-perfect magic square is
so that any given region of the paper will receive on average the same
amount of ink.

-- 
Robert Krawitz <rl...@al...>      http://www.tiac.net/users/rlk/

Tall Clubs International  --  http://www.tall.org/ or 1-888-IM-TALL-2
Member of the League for Programming Freedom -- mail lp...@uu...
Project lead for The Gimp Print --  http://gimp-print.sourceforge.net

"Linux doesn't dictate how I work, I dictate how Linux works."
--Eric Crampton