Anonymous 07/11/2017 (Tue) 23:51:33 No. 10357 del
You're thinking of Conway's game of life. It's the most well-known cellular automaton.
It's Turing-complete, so given enough time and space you can use it to make any calculation you can perform in any other programming language. A much simpler cellular automaton that's also Turing-complete is Rule 110.
Cellular automata are fun, and rarely even useful - Rule 184 creates a workable simulation of single-lane traffic flow.
Try implementing one. Then generalize it to a program for executing any Wolfram rule. Then if you're feeling extra adventurous, generalize it to cells with more than two states and neighborhoods of more than three cells.