# Difference between revisions of "Polyplet"

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*9 into [[block]]s | *9 into [[block]]s | ||

**1 is the block itself | **1 is the block itself | ||

− | *4 become a block in 1 generation | + | **4 become a block in 1 generation |

− | *4 become a pre-block in 1 generation | + | **4 become a pre-block in 1 generation |

*4 into [[beehive]]s | *4 into [[beehive]]s | ||

*1 into a [[pond]] | *1 into a [[pond]] |

## Latest revision as of 08:39, 18 February 2019

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).

## External links

- Polyplet at the Life Lexicon