Hi Ted,
I think I have read somewhere (in Wolfram's NKS book or Ilachinski's
Cellular Automata book) that Cellular Automata in 3D do not behave
significantly different than those in 2D. For many abstract agent-based
models, say W. Brian Arthur's El Farol Bar Model, Axelrod's Dissemination
Model or Schelling's segregation model, it probably doesn't matter if the
environment is 2D or 3D.
A three dimensional environment certainly is important if you consider
models with direct physical interaction of the agents where the dimension is
part of the model, for example models about boids, swarms or flocks.
-J.
----- Original Message -----
From: Ted Carmichael
To: The Friday Morning Applied Complexity Coffee Group
Sent: Monday, March 01, 2010 4:02 PM
Subject: [FRIAM] Question for Friamers! ... 2D vs. 3D
So ... I've been programming a lot in NetLogo and so forth, and I've thought
about the inherent differences between 2D models and 3D models (or even
higher dimensions). But I haven't thought about it very deeply, and I
haven't formally investigated how the properties of, say, clusters of
self-organizing agents behave in a 2D environment vs. a 3D environment.
So the other day someone asked me: what are the issues, what are the
differences? Fundamental or superficial?
Offhand, I sort of assumed the relationship between different simulation
spaces would be pretty much the same in both 2D and 3D. Sure, I assumed
there would be a scaling issue, but not much else. (e.g., a 2D pred-prey
model would show different numbers than a 3D pred-prey model, but the
dynamics would be essentially the same.)
Is this true? Anyone ever investigate this question? Know of some good
papers out there? Other resources? I'm not assuming an infinite space, if
that makes a difference ... in a 2D environment I assume a torus, and
imagine if I programed a 3D simulation I would use similar assumptions.
Any guidance would be greatly appreciated! I have a presentation on Friday,
and I would like to be able to cover this issue.
Thanks!
-Ted
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