00 What is Conway’s Game of Life?

Conway’s Game of Life – Wikipedia

Conway’s Game of Life is a game designed by mathematician John Horton Conway in 1970, based on a two-dimensional cellular automaton. It is a simple and still popular implementation of Stanisław Marcin Ulam’s automata theory.

The game board is divided into rows and columns and is ideally infinite in size. Each grid square is a cellular automaton (cell) that can assume one of two states, which are often referred to as alive and dead.

First, an initial generation of living cells is placed on the grid. Each living or dead cell has exactly eight neighboring cells on this playing field, which are taken into account (Moore neighborhood). The next generation results from following simple rules.

The next generation is calculated for all cells simultaneously and replaces the current generation. The state of a cell (alive or dead) in the next generation depends only on the current state of the cell itself and the current states of its eight neighboring cells:

A dead cell with exactly three living neighbors will be reborn in the subsequent generation.
Living cells with less than two living neighbors die of loneliness in the subsequent generation.
A living cell with two or three living neighbors remains alive in the subsequent generation.
Living cells with more than three living neighbors die of overpopulation in the subsequent generation.
With these four simple rules, a variety of complex structures emerge from certain initial patterns as the game progresses. Some remain unchanged, others oscillate, and still others grow or decay. Some structures, called gliders, move around the board. Even logical functions like AND and OR can be simulated by certain initial patterns. Thus, even complex functions of circuit logic and digital computer technology can be simulated.

Further rule sets and worlds

In addition to the original, further worlds can be defined, which differ in the specifications regarding survival and death.

NameSurvives ifRebirth with
Copy World1, 3, 5, 7 Cells1, 3, 5, 7 Cells
3/3 World 3 Cells 3 Cells
13/3 World 1, 3 Cells 3 Cells
34/3 World 3, 4 Cells 3 Cells
35/3 World 3, 5 Cells 3 Cells
2/3 World 2 Cells 3 Cells
24/3 World 2, 4 Cells 3 Cells
245/3 World 2, 4, 5 Cells 3 Cells
125/36 World 1, 2, 5 Cells 3, 6 Cells
Anti-Conway World 0, 1, 2, 3, 4, 6, 7, 8 Cells 0, 1, 2, 3, 4, 7, 8 Cells
Anti Copy World 0, 2, 4, 6, 8 Cells 0, 2, 4, 6, 8 Cells