ConwayLife.com

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 ...

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 ...

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 ...

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 ...