Patterns: examples

Patterns: examples

Let us see what happens to a variety of simple patterns. A single organism or any pair of counters, wherever placed, will obviously vanish on the first move. A beginning pattern of three counters also dies immediately unless at least one counter has two neighbors.


The cell (red) and its eight neighbors (blue)

This screenshot shows 2 generations for different patterns.

The first three [a, b, c] vanish on the second move. In connection with c it is worth noting that a single diagonal chain of counters, however long, loses its end counters on each move until the chain finally disappears. The speed a chess king moves in any direction is called by Conway (for reasons to be made clear later) the "speed of light." We say, therefore, that a diagonal chain decays at each end with the speed of light.

Pattern d becomes a stable "block" (two-by-two square) on the second move. Pattern e is the simplest of what are called "flip-flops" (oscillating figures of period 2). It alternates between horizontal and vertical rows of three. Conway calls it a "blinker".

The next picture shows you five triplets that do not fade on the first move. (Their orientation is of course irrelevant.)


The cell (red) and its eight neighbors (blue)

The illustration above shows the life histories of the five tetrominoes (four rookwise-connected counters). The square [a] is, as we have seen, a still-life figure. Tetrominoes b and c reach a stable figure, called a "beehive," on the second move. Beehives are frequently produced patterns. Tetromino d becomes a beehive on the third move. Tetromino e is the most interesting of the lot. After nine moves it becomes four isolated blinkers, a flip-flop called "traffic lights." The two illustrations above show the 12 commonest forms of still life.

As easy exercises, the reader is invited to discover the fate of the beacon, the clock and the letter H.


Beacon, clock and H

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