Block

Block is an extremely well-known and common still life that was found by John Conway in 1970.[1] 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, and the only still life where all cells have three neighbors.

Block
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Pattern type Strict still life
Number of cells 4
Bounding box 2×2
Frequency class 0.0
Discovered by John Conway
Year of discovery 1970

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 on dock, block on table and block on griddle. 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.[2]; it is also the most common object on Adam P. Goucher's Catagolue.[3] It is also the most common object produced by 2-glider collisions (six different ways).

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, except in special cases.). Oscillators such as blocker, p56 B-heptomino shuttle, queen bee shuttle, twin bees shuttle and unix showcase mechanisms which leave a pre-block or a hook, 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, two blockers hassling R-pentomino and Achim's p144 are examples. A particular reaction with a B-heptomino is commonly used in the construction of Herschel tracks.

Blockic constellation

A blockic constellation is a constellation consisting entirely of blocks. It's possible to arrange blocks in a way that can be triggered by a single glider to produce any glider constructible pattern.[citation needed]

Block arrays

Pseudo still lifes exist consisting of an arbitrary array of blocks placed next to each other, which may be referred to as block agars. On December 3, 2015, Martin Grant found a method of constructing a 3×n array via glider synthesis,[4] and on May 6, 2020, Goldtiger997 found a method of constructing a 4×n array.[5]

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See also

References
  1. Dean Hickerson's oscillator stamp collection. Retrieved on March 14, 2020.
  2. Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.
  3. Adam P. Goucher. "Statistics". Catagolue. Retrieved on June 24, 2016.
  4. Martin Grant (December 3, 2015). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  5. Goldtiger997 (May 6, 2020). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
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