# Polyplet

A **polyplet** (or simply a **plet**) is a finite collection of orthogonally or diagonally connected cells. The form of connectivity allowed by polyplets is sometimes called *king-wise connectivity* because of the way a king moves on a chess board. King-wise connectivity is a more natural concept in Life-like cellular automata than the orthogonal connectivity of polyominoes.

## Sizes of polyplets

Polyplets with n cells for n = 3, 4, 5, ... are called triplets, tetraplets, pentaplets, hexaplets, heptaplets, and n-plets in general. The number of distinct polyplets with n cells for n = 1, 2, 3, ... is given by the sequence 1, 2, 5, 22, 94, 524, 3031, 18770, 118133, ... (Sloane's A030222).

### Triplets

There are exactly five distinct **triplets**, shown below. The first two are the two triominoes (pre-block and blinker), and the other three vanish after two generations.

### Tetraplets

Of the 22 distinct tetraplets, five vanish, nine evolve into blocks (including the block itself), four into beehives, one into a pond, one is the tub, and the remaining two into alternate phases of the traffic light.

### Pentaplets

The 94 distinct pentaplets evolve as follows:

- 39 into nothing
- 11 into loaves
- 10 into traffic lights
- 6 in the phase with "+" on even generations
- 4 in the phase with "o" on even generations

- 9 into beehives
- 7 into boats (including the boat itself)
- 4 into blocks
- 4 into gliders (including the two that are themselves phases of the glider)
- 3 into ponds
- 2 into tubs
- 1 into the pi heptomino (after two generations; the first generation evolution is the "<" hexomino)

The remaining four are or become the R-pentomino:

- one is the R-pentomino itself
- one becomes the R-pentomino after one generation
- two become the aforementioned pentaplet after one generation (and thus become the R-pentomino after two).

## External links

- Polyplet at the Life Lexicon