Polyomino

A polyomino (or simply omino) is a finite collection of orthogonally connected cells. The mathematical study of polyominoes was initiated by Solomon Golomb in 1953. Conway's early investigations of Life and other cellular automata involved tracking the histories of small polyominoes, this being a reasonable way to ascertain the typical behaviour of different cellular automata when the patterns had to be evolved by hand rather than by computer. Polyominoes have no special significance in Life, but their extensive study during the early years lead to a number of important discoveries and has influenced the terminology of Life.

A cross.

It is possible for a polyomino to be an oscillator. In fact, there are infinitely many examples of such polyominoes, including the cross and its larger analogues. The only other known examples are the block (which has period 1), the blinker, the toad, the star and (in two different phases) the pentadecathlon.

A polyomino can also be a spaceship, though the only known examples are the lightweight spaceship, the middleweight spaceship, and the heavyweight spaceship.

Sizes of polyominoes

Polyominoes of with n cells for n = 2, 3, 4, ... are called dominoes, triominoes, tetrominoes, pentominoes, hexominoes, heptominoes, octominoes, and n-ominoes in general. The number of distinct polyominoes with n cells for n = 1, 2, 3, ... is given by the sequence 1, 1, 2, 5, 12, 35, 108, 369, 1285, ... (Sloane's A000105).

Dominoes

There is only one domino and by itself it dies after one generation. A number of objects, such as the heavyweight spaceship and the pentadecathlon, produce domino sparks.

Triominoes

There are exactly two distinct triominoes. The term is rarely used in Life, because the two objects in question are simply the blinker and the pre-block.

Tetrominoes

There are five distinct tetrominoes, each of which is shown below. The first is the block, the second is the T-tetromino, and the remaining three rapidly evolve into beehives.

The five distinct tetrominoes.
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Pentominoes

There are 12 distinct pentominoes. John Conway assigned them all letters in the range O to Z, loosely based on their shapes, and they are all shown below in order.

The O-pentomino is a traffic light predecessor, though not one of the more common ones.
The P-pentomino is a common spark that dies in generation 4.
The Q-pentomino is a traffic light predecessor.
The R-pentomino is a methuselah and by far the most well-known pentomino.
The S-pentomino dies in generation 5.
The T-pentomino is a common parent of the T-tetromino.
The U-pentomino dies in generation 4.
The V-pentomino evolves into a loaf in generation 3.
The W-pentomino is a common loaf predecessor.
The X-pentomino is a traffic light predecessor.
The Y-pentomino dies in generation 3.
The Z-pentomino dies in generation 3.