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Life's Rules
Conway took several years to select his rules with great care to avoid two extremes: patterns that grow too quickly without limit and patterns where many would fade away. By striking a delicate balance he constructed a model of surprising unpredictability and one that produced an incredible variety of activity. Conway chose his transition rules to meet these general desiderata:
1) There should be no initial pattern for which there is a simple proof that the population can grow without limit.
2) There should be initial patterns that apparently do grow without limit.
3) There should be simple initial patterns that grow and change for a considerable period of time before coming to an end in three possible ways: fading away completely (from overcrowding or from becoming too sparse), settling into a stable configuration that remains unchanged thereafter, or entering an oscillating phase which repeats an endless cycle of two or more periods.
In brief, the rules should be such as to make the behavior of the population unpredictable. Conway's genetic laws are delightfully simple. Recall that each cell has exactly eight neighboring cells; four adjacent orthogonally and four adjacent diagonally.
The rules are:
BIRTHS: each empty cell with exactly 3 neighbors whose cells are full (contain a bit) is a birth cell. A bit is placed in it for the next move.
DEATHS: each full cell (containing a bit) with 4 or more neighbors dies from overpopulation. Every full cell with 1 or no neighbors dies from isolation. The bit is removed from it for the next move. In other words, every bit with 2 or 3 neighbors survives (remains) for the next move.
When Conway first stated his rules, he presented a third law for survivals but here we have included it with the death rule since survivals are implied. It is very important to understand that all births and deaths occur simultaneously. Together they constitute a single move, or as we shall call it, a "generation," in the complete Life history of an initial configuration.
Note that we are free to chose any pattern desired for this beginning or zero generation. After this, the pattern is governed by Conway's rules. We will find the population constantly undergoing unusual, sometimes beautiful and always unexpected change. In a few cases the 'society' eventually dies out (all bits vanishing), although this may not happen until after many generations. Most starting patterns do not die out but become either stable figures (Conway calls them "still lifes" - patterns that cannot change) or patterns that oscillate forever. Patterns with no initial symmetry tend to become symmetrical. Once this happens the symmetry can never be lost, although it may increase in richness.
More on how to play the game to be added to this page!