Game of Life and Universal Computation
Game of Life
Life, along with this “Game of Life”, is simply a mathematical model of a self-replicatable machine. It was named “Game of Life” since the rules of the game are similar to life of an organism although over-simplified.
“Game of Life” is played on a theoretically infinite, 2 dimensional square grid where each cell of the grid can take one of two states: “Alive” or “Dead”. The game requires the player to put in an initial pattern of living and dead cells and a program, following some rules, computes the next generation of the pattern. The standard rules of Life are:
- Any live cell with less than 2 live cells in the surrounding 8 cells will die (loneliness)
- Any live cell with more than 3 live cells in the surrounding 8 cells will also die (overcrowding)
- Any live cell with 2 or 3 live cells in the surrounding 8 cells will continue to live to the next generation
- Any dead cell with exactly three live cells in the surrounding 8 cells will come alive (reproduction)
A very good program for exploring cellular automata including “Game of Life” is “Golly”. Operating it is as simple as MS Paint, and it make things much easier to procure the numerous generations.
There are some basic patterns occurring frequently:
The patterns which remain still for all subsequent generations are called 'Still Lives'. Examples include the “Block” and the “Beehive”.
Some patterns moving across the field at different speeds and directions are called spaceships. The smallest spaceship is known as the “Glider”. The “LWSS” is short for “Light Weight Space Ship”.
Other patterns repeat after certain generations while maintaining their positions. These are called oscillators. The “Blinker” and the “Beacon” are the most common oscillator.
Golly Ticker
The more complex patterns must be constructed from a set of basic patterns. The “Golly Ticker” is also no exception. Let’s see what it does first.
When you start generating it, you should see the word “Golly” (with a stylized “o”) move across the screen and then disappear at the left. This process continues infinitely, just looks like a stock ticker.
