Visual Basic 2010 (Windows) Guide
Conway's Game Of Life:Introduction
The 'Game Of Life' was conceived by British mathematician John Conway in the 1970's. It isn't really a game but an example of a 'zero-player game'. In such 'games', the user sets up the starting conditions and the game evolves without any further interaction from the user.
The Game Of Life is a cellular automaton. The cells are shown on a grid square. Each cell can be alive (black) or dead (white). After a pre-determined time interval, the next generation of cells is calculated based on this initial setup and a set of rules. For Conway's Life, there are only 4 rules used to calculate the next generation.
- If a live cell has fewer than 2 neighbours, it becomes a dead cell
- If a live cell has 2 or 3 neighbours, it survives as a live cell in the next generation
- If a live cell has more than 3 neighbours, it becomes a dead cell
- A dead cell with exactly 3 neighbours will spring into life in the next generation
The Meaning Of Life
A lot of exploration of the game has taken place since its conception. The origins of the idea were to explore concepts surrounding computation and mathematics. Life turned out to be much more interesting than that.
The Game Of Life allows us to see how complex, repeating patterns can emerge from simple input and a very small set of rules. This links well with theories of evolution as well as the origin of the universe itself.
Many repeating patterns have been found in the years that people have spent exploring the universe that can be generated by the game. Some of these patterns are shown and explained below,
Still lifes are patterns that do not change from generation to generation. Two of these patterns are shown below,
The still life patterns are interesting since the application of the rules does not result in any change. They show how permanence can emerge and evolve from simple input. These two patterns are tiny but larger patterns can be found.
An oscillating pattern consists of 2 or more patterns that alternate from generation to generation. The simplest of the oscillating patterns can be made with a vertical or horizontal line of 3 cells.
Spaceships are patterns that move across the grid. The simplest of these patterns is the glider,
The spaceships tend to change shape as they move but generally preserve the number of live cells on they have on their journey.
Named after the character in the Hebrew bible with the oldest recorded age, Methuselahs are patterns that last a large number of generations before all of the cells die or the pattern stops changing.
The following pattern is called the R pentamino - it consists of 5 live cells. If used as input in Life, it lasts for over a thousand generations before it stabilises. During this time, it spits out a glider.