I'd be careful assuming 2D problems having similarity with 3D problems.
An example Frank can tell you more about is the commutability of
rotations. This works fine in 2D but not in 3D.
In an area I'm more familiar with, polynomial time vs exponential time
algorithms, there is a huge break between 2 and 3 versions. Indeed,
much of the NP-Complete world has to do with the 2-3 split.
- Graph 2 coloring is in P, 3 coloring is not.
- 2 variable boolean clause satisfiability is in P, 3 is not.
and so it goes. Even more surprising, is that k-coloring can be
reduced to 3-coloring and similarly for satisfiability.
Thus there is a split in difficulty between 2 & 3, and larger
dimensions can be reduced to 3, but not 2.
Even worse, for your computer programming, most algorithms you are
using are likely reducible to these algorithm classes above. I'm only
partly through the study, CS500 sent to the group earlier, but boy am
I surprised by the oddities we're finding.
So I'd be very careful about the 2D-3D distinction, at least in the
geometric domain and the algorithmic domain.
-- Owen
On Mar 1, 2010, at 8:02 AM, Ted Carmichael wrote:
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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FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org
