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Example of CA : Game of Life
Let us illustrate this with a very simple but famous CA model: the 
Game
of Life. It is a cellular automaton invented by Cambridge mathematician John
Conway in the late 1960s. The neighbourhood is consisting of the nearest 8 cells
to a cell on a two-dimensional grid of cells.
The space of the Game of Life is an infinite two-dimensional orthogonal grid of square cells, each of which is in one of two possible states, live or dead. Every cell interacts with its eight neighbours, which are the cells that are directly horizontally, vertically, or diagonally adjacent. At each step in time, the following transition rules take place:
- Any live cell with fewer than two live neighbours dies, as if by loneliness.
- Any live cell with more than three live neighbours dies, as if by overcrowding.
- Any live cell with two or three live neighbours lives, unchanged, to the next generation.
Many types of different patterns occur in the Game of Life, some of them
are static patterns (“still lives”), repeating patterns (“oscillators”), and
patterns which translate them self across the board (“spaceships”).
We can break the patterns in three categories:
- the block and boat are still lives
- the blinker and toad are 2-phased oscillators , while pulsar is the most common period 3 oscillator
- glider and lightweight spaceship (LWSS) are spaceships that move across the grid as time goes on
EXERCISE:
This is a PC based Game of Life program. Just click on the link below and you will be redirected to the program, you can choose from many patterns from the list in the lower left of the window and run the game and notice how these patterns move and take shapes, some of them keep on going either moving over the grid or moving in the same space over time. Some freeze after some time and some just disappear. You can create your own shapes and see how many generations they can last or change or even die, use the transition rules for the Game of Life to create new patterns so that you can understand first hand the behaviour of evolving shapes from time to time. As you will notice, some shapes live forever and some short or long life cycles. The Game of Life |
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