The most famous Conway’s invention is invented in 1969 the game of Life.
Strictly speaking, the idea of self-replicating systems was considered in 1940-ies John von Neumann and Stanislav Ulam. In particular, von Neumann, creating a self-replicating machine came to the idea of cellular automata — a discrete environment, where the cells change according to certain rules. Based on this environment, he was able to create a “universal constructor” — a machine that can endlessly reproduce itself. But cellular automata von Neumann was extremely difficult — they have had a few dozen of possible States that is encoded in different colors.
Conway has radically simplified the laws by which it works is a cellular automaton, and from that moment began the heyday of this area of mathematics and computer science.
They invented the game of “Life” is arranged as follows: on an infinite graph paper of the cells to be “alive” (or filled, they are usually painted), and the remaining “dead” (or empty). After that, the configuration starts all at the same time to evolve extremely simple rules:
1. If a live cell has two or three live “neighbor”, then on the next turn she survives. In all other cases it dies: or from “solitude” (neighbors < 2) or “overcrowding” (neighbors > 3).
2. If a dead cell with exactly three alive neighbors then the next turn it becomes alive.