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I'm trying to describe a grid and I want to say that the adjacent grid square is chosen if it's horizontally or vertically adjacent, but not diagonally adjacent, to the current grid square.

I was thinking maybe, laterally adjacent?

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Contiguous, if the two diagonal squares are not touching. – KCH Apr 18 '14 at 15:07
Fails the "one word" criterion, but considering the question I think of the word perpendicular, as well as the phrase "cardinally adjacent" (that is, adjacent in a cardinal direction). – asfallows Apr 18 '14 at 15:15
@KCH contiguous does not seem to match: contiguous being in actual contact : touching along a boundary or at a point (from m-w.com) – Jack Ryan Apr 18 '14 at 15:55
Not that I know of. Orthogonally adjacent is used. – Edwin Ashworth Apr 18 '14 at 16:06

10 Answers 10

I've seen both "Orthogonally Adjacent" (Adjacent at right angles) and "Edge Adjacent" (Adjacent across edges rather than corners) used. They do mean slightly different things, but it's only relevant when dealing with something other than a regular rectangular grid.

Since measuring distance in this kind of topology is called "Manhattan distance" you might also try "Manhattan adjacent" although I've never seen that usage myself and it would probably require some explanation before using it.

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You must be a programmer too :) Thanks for this, I think I'll use edge adjacent. – BenjaminFranklin Apr 18 '14 at 21:19
Do you have any references or sources for "Edge Adjacent"? I'm looking, but cannot find any. – Christopher Apr 18 '14 at 22:44
I found several when searching on Google for "edge adjacent" "corner adjacent" This PDF about Quadtree colouring makes the distinction in those terms arxiv.org/pdf/cs/9907030.pdf – smithkm Apr 19 '14 at 19:44

Consider Orthogonal

Orthogonal - intersecting or lying at right angles

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But the two diagonals are also orthogonal to each other. – Wandering Logic Apr 18 '14 at 18:18
@WanderingLogic I still think it makes sense, because the diagonals are not orthogonal to the grid, but you make a good point. – JakeP Apr 18 '14 at 18:22
This would answer the original title of the question, which only specified synonyms for "horizontal" and "vertical" -- they're all directions. There can be many cells that are orthogonal, but not necessarily neighboring/touching. – Martin F Apr 18 '14 at 19:25

Abut: an area that is next to and has a common boundary with.

His land abuts mine

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But the answer should be an adjective :-) ... abutting – Martin F Apr 18 '14 at 17:52

Please consider:

bor·der noun : a line separating one country or state from another; a boundary between places

(or bordering)

from m-w.com

Geospatially (not necessesarily mathematically) anything that was diagonal would share a point, which is commonly considered not a line. E.g. Utah borders Colorado and Arizona but not New Mexico.

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I sort of agree that bordering might be a good word to replace "adjacent" but you have to be careful with your last sentence. In geometry, the three undefined terms are point, line, and plane. Most math folks are comfortable with the common definitions but it's still considered taboo to say they have been defined and to compare those definitions. – jboneca Apr 18 '14 at 15:04
@jboneca Point taken; I've edited as appropriate. – Jack Ryan Apr 18 '14 at 15:52
Your example is technically incorrect in so far as there is a point of Utah that touches a point of New Mexico, thus placing them at each other’s border. I suggest you choose a correct example. – tchrist Apr 18 '14 at 19:44
@tchrist -- the example perfectly mirrors the OP's question. You may disagree that bordering is an appropriate word choice, but the example is not badly chosen. – WinnieNicklaus Apr 18 '14 at 20:23

If you want to say that the adjacent grid square is chosen if it's horizontally or vertically adjacent, but not diagonally adjacent to the current grid square, why not say that it's "nondiagonally adjacent?"

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That's pretty good, thanks for the suggestion! – BenjaminFranklin Apr 18 '14 at 21:19

I think that the best term is rectilinearly adjacent. Compared to orthogonal, rectilinear has a stronger connotation of being axially aligned.

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I'd say "squarely adjacent" rather than any of rectilinearly, orthogonally, or nondiagonally adjacent – jwpat7 May 9 '14 at 19:26

Also consider

coterminous or conterminous: having the same or coincident boundaries

essentially, synonymous with bordering.

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I don't think this is the correct usage of "coterminous". Regions that border have part of a boundary in common, but I think "coterminous" means that the entire border is the same; that is, the two entities comprise the same region. Queens (the borough of New York City) is coterminous with Queens County (a county in New York); they're arguably not the same thing, but they have the same borders and they comprise the same region. – Tanner Swett Apr 18 '14 at 23:27
@TannerSwett -- That is another meaning (one i only discovered today) of coterminous. The other meaning is to share part of a boundary. See onelook.com/?w=coterminous&ls=a – Martin F Apr 18 '14 at 23:51

It's not one word, and I'm not sure how many people would follow it, but from cellular automata, you could refer to "squares that are in the von Neumann neighborhood of the current square".

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You should probably read the Wikipedia article about pixel connectivity.

The case you describe is called 4-connectivity, so the adjective you seek is 4-connected.

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In this case, I like the term axial to describe a direction that is along the horizontal or vertical axis relative to the current position.

Axial - situated around, in the direction of, on, or along an axis.

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