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Game of Life

Tool to simulate and customize Conway game of life, a cellular automaton: a set of cells on a grid which can evolve through time thanks to basic rules.

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Game of Life -

Tag(s) : Fun/Miscellaneous, Biology, Algorithm

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Game of Life

The Game of Life Simulator


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By default, the game of life according to Conway has the following rules: - A dead cell with exactly three living neighbors becomes alive. - A live cell with two or three living neighbors stays alive; otherwise it dies.

Answers to Questions (FAQ)

What is the Game of Life? (Definition)

The game of life (gol or game of life) is a cellular automaton evolving on a grid (of theoretically infinite size) made up of boxes squares called cells which have a binary state (1 for alive and 0 for dead). The cells evolve over time according to their neighborhood (each cell has 8 neighboring cells), which modifies the grid at each evolution step (called generation).

How does Game of Life work? (Rules)

By default, if a living cell is too isolated (0 or 1 neighbor) then it dies the next evolution (death by under-population). If it is reasonably surrounded (2 or 3 neighbors) then it remains alive, but what if it is surrounded by too many cells (4 or more neighbors) it dies to the next generation (death by over-population).

A cell can also become a live cell if a dead cell is surrounded by three living cells then it becomes alive (she was born) in the next evolution (birth by reproduction).

All configurations are possible but different rules/variations may lead to an explosion of the cell population (e.g. by indicating favorable conditions for birth) or a rapid decline (e.g. indicating several unfavorable conditions for life).

Why was game of life invented?

The game of life is an invention of John Horton Conway in 1970. Conway, professor of mathematics, in response to a problem of John von Neumann who was looking for a machine capable of self-replication, built a mathematical model based on an algorithm with basic rules that became the game of life.

Today, cellular automata as the game of life are used in computer simulations such as evolution of population in a given place or evolution of living cells in an organism. The dCode simulator above allows you to test different rules.

What are common patterns in the game of life?

There are stable patterns (which do not evolve), periodic patterns (called oscillators or blinkers) that repeat in a loop every X generations.

The most famous pattern is the glider, this is a pattern that shifts itself in a diagonal in 4 generations.

The spaceship patterns are shifted horizontally or vertically.

There are also patterns called guns or puffer or generator that generate gliders or spaceships.

Example: See the reference book Cellular automata here (link) of Edgar F. Codd.

What is a Garden of Eden?

In the game of life, a Garden of Eden is a configuration such that there is no previous configuration possible. No pattern can generate in its next generation a Garden of Eden.

How to go back in time with the game of life?

It is not possible to go back, in fact, an infinite number of combinations lead to the same given next position.

What is the relationship between the game of life and mathematics?

The game of life is a cellular automaton, a field of study in computer science and mathematics.

Cellular automata can be described as mathematical algorithms with several parameters.

Mathematical models make it possible to model discrete dynamic systems from simple rules that can generate complex shapes.

Who invented the Game of Life?

The game of life has been created by John Horton Conway.

Source code

dCode retains ownership of the "Game of Life" source code. Except explicit open source licence (indicated Creative Commons / free), the "Game of Life" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "Game of Life" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Game of Life" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
Reminder : dCode is free to use.

Cite dCode

The copy-paste of the page "Game of Life" or any of its results, is allowed as long as you cite dCode!
Cite as source (bibliography):
Game of Life on dCode.fr [online website], retrieved on 2022-12-09, https://www.dcode.fr/game-of-life

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