Posts Tagged ‘worlds’
Crowds in finite worlds
Suppose you have been standing in a finite world that was just huge sufficient to fit, say, ten individuals comfortably, or twenty people. How would you all arrange yourselves so that absolutely everyone was comfortable, with nobody scrunched up against anyone else?
It’s easy to think about one thing like this if the finite world is a sphere. That’s quite considerably the scenario represented by my applet Little creatures in a small globe.
But it’s not so obvious what takes place if the globe is toroidal — like the globe of an Asteroids game. Considering that the finite globe itself is featureless and with out boundaries, any exciting pattern that emerges is going to depend mainly on the number of individuals all trying to preserve their personal area.
Much more tomorrow.
Crowds in finite worlds, continued
I implemented a small simulation in which I positioned tiny circles, representing people in a crowd, into a finite square globe, and programmed each and every particular person to attempt to keep their distance from all the other individuals.
I made ten worlds in complete. In the 1st world I positioned a single particular person, in the second world two folks, and so on up to ten folks.
Each and every tiny square planet is a torus (just like the Asteroids game), so when a individual goes off to the appropriate, they come back on the left. Similarly, when a particular person goes up off the best, they come back on the bottom.
To make it less complicated to see patterns, I’m displaying a 4ࡪ arrangement of every single planet. So in each of the ten pictures beneath, there are truly 16 small worlds, in a fourࡪ tiling. I didn’t draw any edges in between tiles. Simply because every tile is really a small toroidal patch, it doesn’t matter where you draw the edges between neighboring tiles — individuals can wander continuously among tiles, and each particular person lives simultaneously on all 16 tiles.
As you can see from the pictures under, the globe containing nine individuals is the most visually fascinating. Whilst most of the other folks look very geometric and typical, the crowd of nine folks has a really all-natural high quality, like an actual milling crowd.
I find that extremely intriguing.
