Search found 4 matches

by Sam Alexander
August 11th, 2010, 11:31 pm
Forum: General Discussion
Topic: Replicator idea.
Replies: 7
Views: 8190

Re: Replicator idea.

I'm kind of a newbie so I might not be understanding you right. But it seems to me like if such metacells could be found where the "dead" metacell has population zero, and these metacells satisfied life-like rules where a spaceship can achieve diagonal speed c/3, then the corresponding metacell spac...
by Sam Alexander
August 3rd, 2010, 2:30 pm
Forum: General Discussion
Topic: Two Forbidden Directions
Replies: 5
Views: 3206

Re: Two Forbidden Directions

The Two Forbidden Directions theorem can be proved more directly: As you say, for n = 1, the proposition is clearly true. A cell being alive (x,y,t) implies that the sum of the nine neighbours in the previous generation is at least 3. The converse is not true, but this is irrelevant. Due to the Dir...
by Sam Alexander
August 2nd, 2010, 11:13 pm
Forum: General Discussion
Topic: Two Forbidden Directions
Replies: 5
Views: 3206

Re: Two Forbidden Directions

Here's a direct proof of the Two Forbidden Directions result, without using any of my more general graph theory. The drawback for the directness & elementariness is that it must seem "pulled out of my hat". I never would have stumbled on it without the more general stuff... Also I think the proof us...
by Sam Alexander
August 2nd, 2010, 2:34 pm
Forum: General Discussion
Topic: Two Forbidden Directions
Replies: 5
Views: 3206

Two Forbidden Directions

Hello everybody, first time posting here :) I'm Sam Alexander, a logic phd student from Ohio State University. Used to think Life was just a silly diversion, until I realized it was a fertile ground for applying some graph theory I've been doing, and then when I started studying it I finally saw how...