Lesson 2.1 - Introduction to Conway's Game of Life
Throughout this lesson, we will investigate how 2D cellular automata works and unique patterns in Conway's game of life.
Learning Objectives
By the end of Lesson 2.1, you should be able to...
- Identify the period of a pattern
- Learn terminology for classes of patterns
Conway's Game
The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. This CA is famous for its variety of patterns and interesting properties. Conway's game of life is turing complete so can simulate any turing machine. Conway's game is traditionally played on an infnite grid. For ease of use, we will play on a torus. In short, you can imagine cells on the left/right and top/bottom sides to be touching.
Conway's Rules
Conway's game of life operates in a similar way to the 1D automata from the previous lesson. Cells change based on the state of nearby neighbors. In Conway's game, the 8 surrounding neighbors are counted. The cell's inital state depends on which rules are checked.
1. Any live cell with fewer than two live neighbours dies, by underpopulation.
2. Any live cell with two or three live neighbours lives on to the next generation.
3. Any live cell with more than three live neighbours dies, by overpopulation.
4. Any dead cell with exactly three live neighbours becomes a live cell, by reproduction.
Part 2. Patterns
Step through each pattern using the Step button and note how many steps it takes for a pattern to repeat. To reset the simulation, use the ⟳ button in the top left.
Oscillators
Repeating patterns are known as oscillators
The steps to repeat is an oscillator's period
The pattern on the left is an ocillator called the Pulsar Pattern
What is the period of the Pulsar Pattern?
Spaceships
Moving repeating patterns are known as spaceships
Spaceships come in many shapes and sizes
What is the period of this spaceship?
Glider Guns
This gun creates gliders that will travel down and right.
The first glider gun won a $50 prize ($400 today)
What is the period of the gliders being shot from the gun?