# 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 (being the banana spark, V spark and a fuse of length 3 respectively).

### Tetraplets

Of the 22 distinct tetraplets:

- 5 vanish
- 2 into P-pentominos after 1 generation
- 1 into a V spark
- 2 into duoplets

- 9 into blocks
- 1 is the block itself
- 4 become a block in 1 generation
- 4 become a pre-block in 1 generation

- 4 into beehives
- 1 into a pond
- 1 is the tub
- 2 into alternate phases of the traffic light
- 1 is the T-tetromino
- 1 is a parent of the T-tetromino

### 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).

### Hexaplets

Lifeline Volume 4 analysed all six-cell patterns. Of the 524 that are polyplets, here are the results:

- 171 into nothing
- 38 into traffic lights
- 34 into loaves
- 33 into beehives (including the beehive itself)
- 30 into blocks
- 23 into honey farms
- 21 follow the pi-heptomino sequence
- 20 into blinkers
- 19 into boats
- 19 follow the lumps of muck sequence
- 17 into ponds
- 17 follow the R-pentomino sequence
- 10 follow the block and glider sequence
- 9 follow the century sequence
- 7 into ships (including the ship itself)
- 6 into barges (including the barge itself)
- 6 into toads (including the toad itself)
- 6 into beacons
- 5 follow the teardrop sequence
- 5 into gliders
- 5 follow the B-heptomino sequence
- 4 follow the I-heptomino sequence
- 3 into two asymmetric loaves
- 3 follow the two-glider octomino sequence
- 2 into the long boat, both shown on the long boat page
- 2 into the moth sequence
^{[1]} - 1 (a hexomino) into aircraft carrier
- 1 (a hexomino) into two far blinkers
- 1 is the snake
- 1 is the clock
- 1 follows the butterfly sequence
- 1 follows the dove sequence
- 1 is a Herschel without the B's block
- 1 is the Iwona active region
- 1 is Thompson's methuselah (3o$3bo$3b2o!)

Tubs are absent from this list.

## References

- ↑ David Raucci (April 4, 2022). Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums

## External links

- Polyplet at the Life Lexicon