The Game of Life

I was speaking with a participant at the Melbourne OAS yesterday and she is designing a project for students around games, particularly optimization strategies. She is going to start with the Prisoner’s Dilemma. From Wikipedia (source of all true knowledge), “The prisoner's dilemma is a standard example of a game analyzed in game theory that shows why two completely rational individuals might not cooperate, even if it appears that it is in their best interests to do so. It was originally framed by Merrill Flood and Melvin Dresher while working at RAND in 1950.” I have done this with students before where two students will play the game while the rest observe and we talk about optimizing strategy.

Our conversation also reminded me of this wonderful simulation called Conway’s Game of Life. It is a simulation that is played out on a grid, where each square, or cell, represents a living organism. It is modeled after the idea that a certain size population is required to maintain an equilibrium; too few is not enough to sustain, too many and it chokes itself out. The exact rules are as follow:

For a space that is 'populated': Each cell with one or no neighbors dies, as if by solitude. Each cell with four or more neighbors dies, as if by overpopulation. Each cell with two or three neighbors survives. For a space that is 'empty' or 'unpopulated’: Each cell with three neighbors becomes populated.

Here is a website that runs the simulation, and you can create your own starting parameters and see what happens; will life stabilize, thrive, or die out? There are also some cool Youtube videos of patterns people have had to create. https://bitstorm.org/gameoflife/

Enjoy!

Michael Waski