Self-explaining Game of Life?

A question sent to the everything-list.

I have listened to Sean Carroll’s Big Picture. His world view is actually similar to the Game of Life, well, the rules are a bit more complicated. Below is the link to the equation that he proposes.

Carroll claims that his equation describes human beings as well. He takes a compatibilist position in respect to free will: free will is compatible with the determinism. At the same time, he says that his equation is the very strong intellectual achievement of the mankind.

I thought that it could be possible to invent some sort of the Game of Life where during the system evolution one gets the rule of the game printed on the screen. In my view, this should be somewhat analogous to what Carroll says. Well, it is hard to say in what form the rules of the game should appear, but this after all gives some freedom to invent such a game.

I should mention that I mean nothing fancy. “Explaining” is meant in pure epiphenomenal fashion: an equation spontaneously appeared on a sheet of paper, nothing else.

What do you think? Could it be possible to invent a self-explaining Game of Life in that sense?

P.S. Carroll’s Game of Life: