Just because it fits, doesn't mean it's true: 
my $possibilities = 2 ** $N; # $N is number of dimensions

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Nope! yes, it's true for $N=1. But look at your example. When $N=2, neighbors = 8. But, your equation says 3 dimensions has 8 neighbors - and Zero dimensions would have 1! 
my $possibilities = (3 ** $N) - 1;

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Think of the 3D example - 3 x 3 x 3 (- one in the middle)

.02

cLive ;-)

Or I could just be completely wrong coz I'm too tired to read through the other replies :)

In reply to (cLive ;-) Re: getting my neighbours in an N-dimensional space by cLive ;-)
in thread getting my neighbours in an N-dimensional space by dash2

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