Life

This is the Game of Life, which follows two familiar and simple rules for deciding which cells will live and die from generation to generation.

1. If a cell is dead at time t, it comes alive at time t + 1 if and only if the number of living cells in the squares immediately surrounding the cell is greater than the lowest fertility threshold (fl) and less than the highest fertility cutoff(fh).
2. If a cell is alive at time t, it dies at time t + 1 if and only if the number of living cells in the squares immediately surrounding the cell is greater than the highest environmental support (eh, i.e., "overcrowding") or less than the lowest environmental support (el, i.e., "undernourishment").

Surprisingly complicated patterns of behavior by these cells can emerge based on just these two simple rules.

In addition, by varying the four variables: el, eh, fl, fh, we can obtain different versions of Life, each with its unique behavior and properties. We characterize the particular version by using four octal numbers for the four variables and stringing them together. The particular version of Life popularized by John Horton Conway is also the default one shown here: Rule 2333. This means that a cell will die if it is surrounded by less than 2 or more than 3 living cells, and a cell will only be born if its space is surrounded by exactly 3 living cells.

2333 Life has received much attention from mathematicians and computer scientists. Many interesting patterns, such as the Glider, the Glider Gun, the Spaceship, have been discovered.

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