Suppose you were standing in a finite world that was just big enough to fit, say, ten people comfortably, or twenty people. How would you all arrange yourselves so that everyone was comfortable, with nobody scrunched up against anyone else?
It’s easy to think about something like this if the finite world is a sphere. That’s pretty much the situation represented by my applet Little creatures in a little world.
But it’s not so obvious what happens if the world is toroidal — like the world of an Asteroids game. Since the finite world itself is featureless and without boundaries, any interesting pattern that emerges is going to depend mainly on the number of people all trying to maintain their personal space.
More tomorrow.
For some reason, this scenario reminds me of a brilliant animated film called “Balance”
http://www.youtube.com/watch?v=kkxOHD7-3E8
I love that animation! It won a well deserved Academy Award for best short animation the year it came out.