The Game of Life
Life is short. Life is boring. Life sucks. So let's get away from everyday life and explore a different kind of life - the mathematical life.
What is the Game of Life?
The Game of Life is basically a simulation of 'life forms', where via certain rules, a certain pattern of 'cells' is either killed off or created. It was created by a mathematician by the name of John Horton Conway. The rules of life are probably more simple than you imagine.
Life is played on a square grid of infinite size. Certain squares in this grid are occupied by 'cells', the others are left vacant. these cells form the 'life form(s)'. An example is shown below in Fig 1:
_ _ _ _ _ _ _ _ _ _ _
|_|_|_|_|_|_|_|_|_|_|_|
|_|_|0|_|_|_|_|_|_|_|_|
|_|_|0|_|0|0|_|0|_|_|_|
|_|_|0|_|_|0|0|_|_|_|_|
|_|_|_|0|_|_|0|_|_|_|_|
|_|_|_|_|_|_|_|_|_|_|_|
|_|_|_|_|_|_|_|_|_|_|_|
Fig. 1 An example of 'life'.
Here, the lines represent the grid and the '0's represent the cells. Note that the grid is actually infinte in size and so has no boundaries, and that the life form need to be connected, it can be composed of cells separated from each other. From now on, life forms will be drawn without the grid to save space. Now for the rules of life:
1) Every occupied cell with 1 or fewer (vertically, horizontally or diagonally adjacent) neighbouring cells dies(of isolation) and is removed from the grid.
2) Every occupied cell with 4 or more neighbours dies(of overcrowding) and is removed.
3) Every vacant square that has exactly 3 neighbours is a birth cell, and so a cell is added there.
These 3 processes are done simultaneously, therefore the birth cells cannot be considered after the dea cells are removed, nor vice versa. Instead, the birth(or death) cells should be marked, then the death(or birth cell) are marked differently ignoring any previously marked cells. Then the dead cells are removed and the birth cells added, and a turn, or 'tick' is completed. Fig. 2 shows how this is done:
I 0
000 -> X0X -> 0
I 0
Fig. 2 A life transformation.
The '0's represent the cells, the 'X's represent the dead cells and the 'I's represent the cells to be born. The 1st pattern is at tick 1, the second being an intermittent stage and so is not considered a tick and the last stage the result of the transformations on tick 1, and so is tick 2. Should it be continued to tick 3, one discovers that the cells have the same arrangement as those in tick 1. Thus a cycle continues, with the pattern repeating itself every 2 ticks. This figure, commonly known as the 'blinker' is one of the more common 'life forms'.
Life Forms
Click on the links below to explore each type of life form in depth:
Still Life
Gliders
Guns, Factories and Puffer Trains
Oscillators
Methuselahs
Fuses
Exploring Life
Pencil and paper is one way of exploring the wonders of Conway's Life, but it is tedious and tiring, and probably will make you more bored than excited. To fully appreciate life unfolding before your eyes, download a computer simulation of life. These are just a few:
Get a Life
Laboratory of Life
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