/sci/ - Science & Math

[OP !!YtZEmFEhyRP No.6627281]

Okay, let me see if I got this right. I'm trying to determine a set that includes all possible patterns of any life-like cellular automata:
Where Z^2 is the 2-dimensional lattice, and S is the set of states (i.e. S = {0,1}).
<span class="math">
\mathbb{P}(\mathbb{Z}^2\cdot S)
[/spoiler]

If I am correct, this set contain all possible patterns in any life-like cellular automata.

[OP !!YtZEmFEhyRP No.6627288]

>>6627281
Also:
Let t = the evolution of some pattern in any life-like cellular automaton
<span class="math">
t\in \mathbb{P}(\mathbb{Z}^2\cdot S)
[/spoiler]

[OP !!YtZEmFEhyRP No.6627301]

>>6627281
Wait, I could also describe a set that includes all possible patterns in ANY cellular automaton:
<span class="math">
\mathbb{P}(\mathbb{Z}^{n+1})
<span class="math">[/spoiler][/spoiler]

[Anonymous No.6627310]

>>6627301

This is too general. My guess is that the particular rules of a given game will place an upper bound on possible states that has cardinality less than or equal to cardinality of the power set described here.

You're discussing an object (n-dimensional integer space?) that seems to relate to games only in an oblique way.

[OP !!YtZEmFEhyRP No.6627320]

>>6627310
i'm just bored none of this has any real use
also, there are cellular automaton that have infinite states, but even then, this has nothing to do with rules - it has to do with the patterns themselves

[Anonymous No.6627324]

>>6627320

>i'm just bored

Bored men make games. Bored God makes men.

[OP !!YtZEmFEhyRP No.6627327]

>>6627324
do bored men make board games

[Anonymous No.6628092]

>>6627327
Bored men make board games about bored God making bored men