Conway's Game of Life or Life or GOF is a Cellular automaton game created by British mathematician John Conway in 1970 in which a cell in a grid is alive or dead. Each Cell's next generation state is determined by the current state of its 8 neighbours (up, left, down, right, upleft, downright, downleft, upright). The Game future states depends solely on its initial state.

if a Cell is Dead :

it will be alive in the next generation(step) if it has exactly 3 alive neighhours 

if a Cell is Alive :

it will die if it has 4 or more alive neighbours due to overpopulation.

it will die if it has 1 or less alive neighbours due to underpopulation.

it will continue to live to the next generation if it has 2 or 3 alive neighbours.

The Game of Life is Undecidable. A person cannot logically or mathematically predict exactly the future state of the game over a finite amount of time. It is very interseting and fun way to show and discuss undecidability in Mathematics.

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