Welcome back everybody! We hope you had a good break, today we will be exploring a fascinating topic called Conway’s Game of Life, a mathematical game invented by mathematician John Conway in 1970 that shows how simple rules can create surprisingly complex patterns. The game is played on a large grid where every square represents a cell, that can be dead or alive. The game evolves in “turns", which we call generations, or just time, and the rules are as follows:
Birth: if a cell is dead at time \(t\), it will become alive at time \(t+1\) exactly when \(3\) of its \(8\) neighbours are alive (we count diagonal neighbours too, hence \(8\)).
Death: a live cell can die from two ways:
Overcrowding: if an alive cell has \(4\) or more alive neighbours, it will die of overcrowding.
Loneliness: if an alive cell has \(1\) or \(0\) alive neighbours, it will die of loneliness.
Survival: a cell that is alive will remain alive exactly when it has \(2\) or \(3\) alive neighbours.
This game is far too complex to understand all of it in only one session, but if you want to learn more, you should read the Wikipedia article or the freely available online book Conway’s Game of Life, Mathematics and Construction by Johnston and Greene. Many simulators are available online to play the game too.