Crotchet is a commonly-seen polyominospark. It is one of two pentomino grandparents of the V spark (and, by extension, great-grandparents of the domino), with the other being the short table.
While known since 1969 due to John Conway's early research into polyominoes, the spark was not given a non-systematic name until December of 2022, when analysis of a family of c/3 orthogonal ships in an attempt to find glider syntheses for arbitrarily-large spaceships of the speed resulted in the rediscovery of a wave which contains the spark in one phase. The term was originally given to a self-termination of the wave which evolves naturally from it,[1] but the name was eventually transferred to the 5-cell spark itself due to its close resemblance to a quarter note (♩, referred to as a "crotchet" in Commomwealth English),[2] with the wave instead being named "waltz" and its termination "anacrusis".
The crotchet is a somewhat common spark, seemingly moreso than the short table with which it shared an evolution sequence. The following two tetraplets evolve into the crotchet in one generation:
Two tetraplet parents of the crotchet (click above to open LifeViewer)
It is also possible to "synthesize" a crotchet by colliding two gliders.
Uses
The crotchet is named due to its involvement in waltz, a wave which travels at a speed of c/3 orthogonal. On one of its phases, the wave is composed solely of spaced crotchets and pre-beehives. If left alone, one end of the wave will remain periodic without decaying and still moving at a speed of c/3 orthogonal; this side will evolve into a slightly different component named "anacrusis", differing from waltz due to the crotchet changing into a five-cell boat parent with a single cell attached to the main block diagonally rather than orthogonally.
Waltz, a c/3 orthogonal wave comprised of crotchets and pre-beehives (click above to open LifeViewer) RLE:herePlaintext:here
If a crotchet is sparked correctly on its long end, it will become a crotchet again after three generations, shifted one cell diagonally, and flipped depending on which side it was sparked on. The non-flipping reaction is of little to no use as a tagalong, as the supporting spaceship would necessarily have to be c/3 diagonal, a speed beyond what spaceships in Life can achieve.[3] The flipping variant of this reaction could be used to create a glide-reflective period-6 c/3 orthogonal spaceship. No explicit examples of this appear to exist in Life so far, however it can be supported by two spaceships in the rule B357/S238.[4]
