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Game of Life

Tool to simulate and customize Conway game of life. The game of life is a cellular automaton created by John Horton Conway. A cellular automaton is a set of cells represented in a grid which can evolve through time thanks to simple rules.

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Game of Life -

Tag(s) : Fun, Biology, Algorithm

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# Game of Life

## The Game of Life

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.

Tool to simulate and customize Conway game of life. The game of life is a cellular automaton created by John Horton Conway. A cellular automaton is a set of cells represented in a grid which can evolve through time thanks to simple rules.

### How does Game of Life work ?

The game of life is represented on a 2D grid (theoretically of infinite size) composed of square boxes called cells which have a binary state (1 for living and 0 for dead).

The game of life is based on the principle of evolution of the grid over time. At each step, called generation, the cells evolve according to their neighborhood (each cell has 8 neighboring cells).

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 may lead to an explosion of the cell population (e.g. by indicating favorable of conditions for birth) or a rapid decline (e.g. indicating several defavorable conditions for life).

### Why game of life was 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 simple 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 or living cells evolution in an organism.

### What are common patterns in the game of life?

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

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

The spaceship patterns are shifted horizontally or vertically.

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

Example: See the reference book Cellular automata here 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.