measuring distance in grids

[Paul E Johnson]

I have a project where agents are in a grid and it is important to 
measure distance.  The authors of the original article I'm replicating 
do not define a distance metric, but I originally assumed the distance 
was Euclidean. That is, I guessed the distance between x=(x1,x2) and 
y=(y1,y2) would be measured

dist = sqrt[ (x1-y1)*(x1-y1)+(x2-y2)*(x2-y2) ]

but I get some funny results using that, and I'm starting to wonder what 
other metrics people might think are standard on a rectangular grid.

One I'm considering is "radial square" distance, where distance is the 
radius of the square centered on a point that touches another point. 
That means the distance from a cell to all immediate Moore neighbors is 
1, and for the next larger neighborhood, the distance would be 2. See 
what I mean?  Here, the distance from the center point 0 to a neighbor is:
           3333333
           3222223
           3211123
           3210123
           3211123
           3222223
           3333333

Does anybody have an opinion?
--
Paul E. Johnson                       email: address@hidden
Dept. of Political Science            http://lark.cc.ukans.edu/~pauljohn
University of Kansas                  Office: (785) 864-9086
Lawrence, Kansas 66045                FAX: (785) 864-5700



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