The Game of Life

The Game Board

Try some of these remarkable figures

or click a square of the grid to add or remove a cell.

A glidder or click a square of the grid to add or remove a cell.

A Π-Heptonomino An R-Pentonomino A spaceship A Methuselah 3 parallels A letter H A letter W

Generation

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Live cells

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A Short Introduction

John Conway, a professor of Finite Mathematics at Princeton University, invented Life by the end of the 60's.
Martin Gardner, who at that time held the mathematical games column in Scientific American, devoted his columns to it in October 1970.
The result is what became famous as "The Game of Life", or simply "Life".

Life is just one example of a cellular automaton : a system of rules applied to cells and their neighbours on a grid. Many other cellular automata have been invented, with more states, more dimensions, more rules, but Conway's "Life" is the best known and the most studied one.

Life is one of the simplest examples of what is called emergent complexity or self-organizing systems, the study of how elaborate patterns and/or behaviors can emerge from very simple rules, or, in other words, how simple rules can structure very complex phenomena. It helps us understand, for example, the diversity that can arise from a small group of living cells.

Life is not only a mathematical game, it is also a source of philosophical reflexion and of aesthetical pleasure. The saying even goes that graphical computer screens have imposed themselves because programmers were so eager to admire the evolution of their favorite Life-patterns.

Life is just one example of a cellular automaton : a system of rules applied to cells and their neighbours on a grid. Many other cellular automata have been invented, with more states, more dimensions, more rules, but Conway's "Life" is the best known and the most studied one.

Life is one of the simplest examples of what is called emergent complexity or self-organizing systems, the study of how elaborate patterns and/or behaviors can emerge from very simple rules, or, in other words, how simple rules can structure very complex phenomena. It helps us understand, for example, the diversity that can arise from a small group of living cells.

Life is not only a mathematical game, it is also a source of philosophical reflexion and of aesthetical pleasure. The saying even goes that graphical computer screens have imposed themselves because programmers were so eager to admire the evolution of their favorite Life-patterns.

The Rules

- A checkerboard represents the world (in principle an infinite world, here limited to a 40 by 40 grid, projected on a sphere, so that the borders touch all around).

- Each cell of this grid has 8 neighbours.

- A cell can be death () or alive ().

- The evolution of the cells is determined by three simple rules:

- Survivals : a cell that has 2 or 3 neighbours survives.

- Deaths : a cell dies
- from overpopulation when it has more than 3 neighbours or
- from isolation when it has less than 2 neighbours.

- Births : an empty square that has 3 "living" neighbours is a birth cell.

- Survivals : a cell that has 2 or 3 neighbours survives.
- Births and deaths occur simultaneously: births and deaths that might occur at the same time are not taken into account to determine the number of neighbours of a cell.

Links To More Information

- A copy of Martin Gardner's article, can be consulted on the net.

- For more information and links, consult Wikipedia the free encyclopedia.

- A good introduction can also be found at the math.com site.