Polyplet

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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 OEISicon light 11px.pngA030222).

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.

The five distinct triplets.
Download RLE: click here

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.

The twenty-two distinct tetraplets.
Download RLE: click here

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 Eric Weisstein's Treasure Trove of Life