Around 1970,  John Horton Conway created a fascinating game called “Life” [1].  The reason for the name is going to be quite obvious as I quote the rules of the game. Before that just imagine a large white checkboard (the world where ‘Life’ happens) and a plentiful supply of counters (the creatures that plays ‘Life’). Counters could be simple ‘poker chips’. See Figure 1. to be clear.

Figura 1. The set of the game “Life”. A checkboard with counters (the black dot) represents live individuals, the rests are dead ones.

So, how to play? In fact you (or the computer) just have to follow three rules. “Conways genetic laws are delightfully simple. First note that each cell of the checkerboard (assumed to be an infinite plane) has eight neighboring cells, four adjacent orthogonally, four adjacent diagonally. The rules are:

  1. Survivals. Every counter with two or three neighboring counters survives for the next generation.
  2. Deaths. Each counter with four or more neighbors dies (is removed) from overpopulation. Every counter with one neighbor or none dies from isolation.
  3. Births. Each empty cell adjacent to exactly three neighbors–no more, no fewer–is a birth cell. A counter is placed on it at the next move.” [1]
So the game is fairly simple and seems boring. But take a look at Table 1. Those are 10 different examples of possible words. As you can see, several group behaviours are produced with the same three Conway’s rules. The only thing that has change in each world is the initial configuration of the game. Thing of each column as small society. The first column would be examples of societies that never change (‘classic’). The second column would be cyclic societies (I would say mesoamerica is a good example or the oscillation between republicans and democrats). The third column, well, that is for sure a nomadic group.

Table 1. The table presents three kinds of examples. First column is about still lives, the world is not going to change and it doesn’t matter how many times you apply the rules. The second column is about oscillators, this worlds produces cycles of  2 or 3 periods following the same rule. The third one is about spaceships, the individuals “move”  through the grid indefinitely. (Source: Wikipedia [2])

Still lifes
BlockGame of life block with border.svg
BeehiveGame of life beehive.svg
LoafGame of life loaf.svg
BoatGame of life boat.svg
Oscillators
Blinker (period 2)Game of life blinker.gif
Toad (period 2)Game of life toad.gif
Beacon (period 2)Game of life beacon.gif
Pulsar (period 3)Game of life pulsar.gif
Spaceships
GliderGame of life animated glider.gif
Lightweight spaceship (LWSS)Game of life animated LWSS.gif
Remember, this doesn’t have a top down construction. This is build from each individual rules. It doesn’t matter that it seems a very coordinated and dictatorial group behaviour. Each cell has its own behaviour and there is no centred government. Don’t trust me? try it in a piece of paper, it is going to be just as little less boring than a Sudoku.
There is more, but this blog is already large and I feel like keeping the best part for the next post. But before going, enjoy the little example in the Figure 2. What could it be? Two little societies in a battle?
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Figure 2. Glidders. This is a slightly more complex example. Also from [2].

[1] Gardner, Martin (1970-10). Mathematical Games – The fantastic combinations of John Conway’ new solitaire game “life”223. pp. 120–123. ISBN 0-89454-001-7. Archived fromthe original on 2009-06-03. Retrieved 2011-06-26.

[2] http://en.wikipedia.org/wiki/Conway’s_Game_of_Life

One thought on “Yet another blog about the “Conway’s Game of Life”

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