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".
Occurrence
The crotchet is a common spark, seemingly more so 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)
The crotchet also has predecessors in higher polyominoes and polyplets. One such pentaplet, sometimes referred to as "ladle spark" or "dipper",[3] can be seen in the loafer, directly behind the loaf in the phase where the loaf itself is visible.
It is also possible to "synthesize" a crotchet by colliding two gliders.
Uses
Turning a block into a crotchet is a common way to kill it. It can be done with sparkers such as unix and blocker in a period-independent way despite the sparkers being periodic. As an eater 1 cannot kill a block that forms from the most common predecessors, the smallest stable way is typically an eater 2, which is larger than both unix and blocker.
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.[4] 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.[5]
