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After over 30 years of playing the Game of Life, it has been reduced to a game of patterns. No matter what initial random pattern you start the game with, you almost certainly will end with a small set of patterns extremely common in the world of Life. Our group could not find a random starting pattern that did not end with recognizable still lifes and oscillators. That is not to say that such never-ending patterns do not exist however. Computer programs have greatly contributed to the analysis of Life patterns, and with the aid of computers several types of infinitely growing patterns have been discovered. Conway himself first thought that all patterns stabilized so he offered a prize for any example of patterns that grow forever. Soon two starting patterns were discovered that grew forever. Thus, Conway's prize was collected and this started the many contests that have existed and still exist to find new and exciting patterns in the Game of Life.
So what is a still-life or
oscillator?
A still-life is just that: a set of cells in equilibrium with each other
and do not change unless they interact with other cells. In a still life
every live cell most have 2 or 3 live neighbors, and every dead cell may
have any number of neighbors except 3. The most common still life is the
block. In it every live cell has exactly three neighbors, and every dead
cell has two or fewer live neighbors. The four other most common still
lifes are the beehive, the boat, the ship, and the loaf. Computer search
has been used to find all still lifes with up to 20 live cells. An online
catalog of these can be found here.
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| Block | Beehive | Boat | Ship | Loaf |
An oscillator is a pattern that flips back and forth between a set number of periods but will never grow or die. Most patterns end up forming these along with still lifes. The simplest oscillators are period-2 oscillators, which only have two varying states. The period has the same meaning as the period of a sinusoidal wave. Oscillators with as many as 100 periods are known to Life enthusiasts. Parts of an oscillator can be described using motor terminology: the rotor, the stator, the bushing and the casing. The Rotor consists of the cells that change from generation to generation. The Stator consists of the cells that never change (including the important dead cells). The bushing is the part of the stator that borders on the rotor, and affects its function. The Casings are those cells that do not play a part in the Rotor's oscillation, but are needed to provide stability. Click here for more information.
The most common oscillator is the blinker that appears in numerous Life games. A complete list of period-2 oscillators is available on the internet.
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