Block

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Block
Block image
Pattern type Strict still life
Number of cells 4
Bounding box 2×2
Discovered by John Conway
Year of discovery 1970

Block is an extremely well-known and common still life that was found by John Conway in 1970. In terms of its 4 cells it is tied with tub as the smallest still life, and in terms of its 2×2 bounding box it is the outright smallest. It is also the only known still life that is a polyomino.

Due to its small size, its ability to act as an eater, and its simple glider syntheses, it is extremely useful in the construction of large patterns. It can be used as an induction coil as in block and dock, block on table and griddle and block. It can also work as a reflector for two gliders via the interchange synthesis, as can be seen in 106P135.

The block was one of the patterns described in the original 1970 article by Martin Gardner that introduced the Game of Life to the world.

Commonness

The block is the most common still life (and indeed object) that occurs as a result of random starting patterns. In Achim Flammenkamp's census it occurred almost twice as often as beehive, the next most common still life.[1]; it is also the most common object on Adam P. Goucher's Catagolue.[2]

Eater

There are multiple ways in which the block may act as an eater. These fall into roughly two camps, according to how the block will be regenerated (since the block's cells already have three neighbors, it cannot act as a rock). Oscillators such as blocker, p56 B-heptomino shuttle, queen bee shuttle, twin bees shuttle and unix showcase mechanisms which leave a pre-block, while the mechanisms seen in Coe's p8, eater 5 and octagon 4 leave a grin. A different mechanism yet, where only a single cell of the original block survives the whole ordeal, appears in 37P7.1. It has been seen eating mangos, boats, loaves, and beehives.

Some more complex eaters can be based on the block as well. Eater 2 is a construction allowing a block to eat gliders: while the collision would normally destroy both, the addition of further still life(s) or inductees allows the remaining three-cell spark to regenerate into a block.

Since the block is the most common object to emerge from soups, it is also the most common object to show transparent debris effect. Several larger oscillators including p54 shuttle, 78P70, 47P72 and Achim's p144 are examples. A particular reaction with a B-heptomino is commonly used in the construction of Herschel tracks.

See also

References

  1. Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.
  2. Adam P. Goucher. "Statistics". Catagolue. Retrieved on June 24, 2016.

External links

  • Block at Eric Weisstein's Treasure Trove of Life
  • Block at the Life Lexicon