Ted -
There are probably a lot deeper and more well supported answers, but I
have two observations that might help.
In 2D vs 3D force-directed (energy minimization) graph layout, there is
a big difference in nodes being trapped in "local minima" in the 2D
case. It is *much* less likely for a node to get trapped in a local
minima in 3D. Depending on your agent model, similar effects are likely
to be experienced (for better or worse).
3 is the smallest number of dimensions where an arbitrary set of nodes
can by connected by an arbitrary set of edges w/o the edges crossing.
This is sort of a degenerate argument and is a corrolary to the former
point made.
I *am* interested myself in the question of how the dimensionality of
the embedding space effects the dynamics of an agent model.
Around 1984 I think it was Doyne Farmer who demonstrated the equivalence
between higher dimensional and lower dimensional Cellular Automata.
The lower dimensional CA had to have a larger state space (and/or
neighborhood) but he demonstrated (and proved) that any CA in a high D
could be implemented in a lower D (all the way down to 1D of course).
I think this probably could be shown to be a corrolary to the
Computational Universality of the Turing Machine.
I look forward to deeper and broader discussion here...
- Steve
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