ronk wrote:tso wrote:I don't know what you are referring to ...

The terms

orthogonal and

non-orthogonal refer to the presence or absence of a right angle (90 degree) relationship between lines (or curves). A sudoku cell is not a line. A line between two cells doesn't have an angular relationship to another line.

This usage of "orthogonal" in this sense is not uncommon in discussions of abstract games or puzzles, nor unclear, regardless of it current lay dictionary definitions. Diagonal lines run at a 45 degree angle to the edges of the grid. Orthogonal lines run parallell to and at a 90 angle to the edges. "Orthogonally adjacent" means adjacent along an orthogonal line, just as "diagonally adjacent" means adjacent along a diagonal line. We all agree on what "diagonally adjacent" means though some

dictionary definitions of "diagonal" don't really support that usage.

For examples, see the usage of "orthogonal"

here; in the discription of LOA, "The connections within the group may be either orthogonal or diagonal."

... or

here or

here.

... or especially

here, where the term is used repeatedly in a page made in collaboration with abstract strategy game inventor/expert and

senior lecturer at the University of Canterbury.

In the field of cellular automata, no less than John Conway, inventor of LIFE, uses the word orthogonal in this sense. An "orthogonal spaceship" is one that moves up, down, right or left -- not diagonally. The "orthogonal neighborhood" of a cell consists of the four cells that share a side with it.

And the adjective mutually in "mutually non-adjacent" is redundant.

Yes it is. I'm famous for my redundancies. (see above)

Therefore, I suggest the terms non-adjacent, laterally-adjacent, and diagonally-adjacent.

Sounds good to me.