Tub
| Tub | |||||||||
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| Pattern type | Strict still life | ||||||||
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| Number of cells | 4 | ||||||||
| Bounding box | 3 × 3 | ||||||||
| Frequency class | 5.0 | ||||||||
| Discovered by | JHC group | ||||||||
| Year of discovery | 1970 | ||||||||
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The tub is one of only two 4-cell still lifes (the other being the block) and was discovered by the JHC group in 1970.[1]
Adding an extra cell to one of the corners results in a boat, while adding two to opposite corners results in a ship. It can be seen as a long-1 version of the barge.
Applications
As an induction coil
The tub is useful as a simple induction coil for a row of 5 cells; compared with a snake or two blocks, tub has a smaller population but a larger height. See eater 3, candelabra and Gray counter for instances where the line of five is permanent, and 186P24, blocked p4-3 and the loaf-spin catalyst in the stable form of twirling T-tetsons 2 for when it is temporary. The latter case, however, may just as well use the smaller p2 blinker like in overweight emulator and blocked p4-4 if interaction permits.
As a catalyst
Three mechanisms for a tub acting as a catalyst are known.
The first mechanism turns tub into a pentaplet (o2bo$bobo$2bo!); examples include Charity's p16, p21 honey farm hassler, 92P23, Eureka shuttle, period-43 glider gun, p73 lumps of muck hassler, 84P87, 74P127 and two RF28B variants.
The second mechanism involves the tub acting as a rock; examples include 5blink, 60P9 and p40 B-heptomino shuttle. This can be generalized to a large number of still lifes including a tub-like protrusion (e.g. boat, loaf, cis-very long hook with tail). Notably, CC semi-Snark features a complex interaction with a tub (or boat).
Third, the tub has a very specific use where it can eat a fully formed beacon. Parity is not a concern, as the reaction only begins when the beacon is in its dense phase.
| A tub eating a beacon in a p30 oscillator. (click above to open LifeViewer) |
Oscillators like antiphase why bother and candlefrobra may sometimes be needed when a tub fails in catalysis.
See Tutorials/Catalyses for details of when catalysts, including tubs, can be used.
Commonness
- Main article: List of common still lifes
Tub is the sixth most common still life on Adam P. Goucher's Catagolue, being less common than ship but more common than pond. Among all still lifes with 4 cells, it is the absolute least common, preceded by block.[2]It is also the eighth most common object overall on Catagolue. The tub is the fifth most common still life in Achim Flammenkamp's census, being about a quarter as common as the boat but only slightly more common than the pond.[3]
Occurrence
The honey farm sequence has a tub in the center in its intermediate stages. If the sequence is interrupted partway through, whether naturally or as part of a honey farm hassler (like in p29 traffic-farm hassler), the tub will sometimes survive. In addition to the honey farm, a U-turner and the I-heptomino both form a temporary tub, and two semi-common predecessors of a lone tub are shown below.
| A predecessor of a semi-common diagonally symmetric sequence (one of whose phases is a quarter of a pulsar) that makes a lone tub; this converges with the beacon-eating mechanism shown above (click above to open LifeViewer) RLE: here Plaintext: here |
| Another common tub predecessor (click above to open LifeViewer) |
Most common small constellations involving a tub include several tub+block and tub+blinker arrangements.[4]
Glider synthesis
A convenient 3-glider recipe for a tub starts with a two-glider synthesis of a pond, which is later hit by a third glider only one half-diagonal away from passing unharmed; this reaction produces a tub on the edge of envelope. There is also a perpendicular 2-glider collision that produces a tub along with junks (xp2_xccy3252zgw8kicz3), leading to another two-stage synthesis at the same cost. Other 3-glider collisions that produce a clean tub are also known.
See also
References
- ↑ Dean Hickerson's oscillator stamp collection. Retrieved on June 18, 2009.
- ↑ Adam P. Goucher. "Statistics". Catagolue. Retrieved on June 24, 2016.
- ↑ Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.
- ↑ Using a three-state ruletable designed for censusing small constellations, the C1/xp2 tabulation includes a tub+blinker constellation (the standard apgcode for the constellation is xp2_11108k8) with 2926 occurrences in the first 106 soups. The C1/xs36 tabulation includes a tub+block constellation (standard apgcode xs8_2520oo) with 1510 occurrences in the first 106 soups. Several other common tub+block constellations are listed in the C1/xs37 tabulation, including the most common one (standard apgcode xs8_252wcc) with 3639 occurrences in the first 106 submitted soups. For more details, see a forum thread. A tub+block constellation where the two objects are too far apart for the custom rule to recognise is 2o5bo$2o4bobo$7bo!, which forms from the 48th most common evolutionary sequence.
External links
- Tub at the Life Lexicon
- Tub at Adam P. Goucher's Catagolue
- The 2 four-bit still-lifes at Mark D. Niemiec's Life Page (download pattern file: 0/4tb.rle)
- Tub at Heinrich Koenig's Game of Life Object Catalogs
| Vessels | |
|---|---|
| No corners (barges) | (^-2) • (^-1) • ^0 • ^1 • ^2 • ^3 |
| One corner (boats) | (^-2) • (^-1) • ^0 • ^1 • ^2 • ^3 |
| Two corners (ships) | (^-1) • ^0 • ^1 • ^2 • ^3 |
- Patterns
- Patterns with Catagolue frequency class 5
- Natural periodic objects
- Periodic objects with minimum population 4
- Patterns with 4 cells
- Patterns found by JHC group
- Patterns found in 1970
- Patterns that can be constructed with 3 gliders
- Still lifes
- Strict still lifes
- Strict still lifes with 4 cells
- Patterns with complete square symmetry
- Catalysts