U-turner
U-turner | |||||||||
View static image | |||||||||
Pattern type | Methuselah | ||||||||
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Number of cells | 10 | ||||||||
Bounding box | 4 × 4 | ||||||||
MCPS | 10 | ||||||||
Lifespan | 163 generations | ||||||||
Final population | 16 | ||||||||
L/I | 16.3 | ||||||||
F/I | 1.6 | ||||||||
F/L | 0.098 | ||||||||
L/MCPS | 16.3 | ||||||||
Static symmetry | C1 | ||||||||
Discovered by | Unknown | ||||||||
Year of discovery | 1971 | ||||||||
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The U-turner (U in conduit names) is a somewhat common methuselah. While it had appeared in some tables of common sequences, it was not recognized as a distinct object until May 4, 2021, when Lucy D'Agostino asked what its name was.[1]
Commonness
According to Simon Ekström's census of small evolving patterns,[2] the U-turner by itself is the 16th most common qualifying sequence, with 29273 occurrences. There is a separate entry ranked 47th, with 12200 occurrences, that evolves into a U-turner and a banana spark after 30 generations, as can be seen in Raucci's p217 and the p280 U-turner hassler. Combining the two puts it in 14th place with 41473 occurrences. About 30% of U-turners form the latter way.
Predecessors
The U-turner has one 6-cell predecessor, the smallest in terms of population. All 6-cell patterns were systematically analysed in Lifeline Volume 4,[3] so it was known as early as December 1971, despite being unnamed until 2021.
The 6-cell predecessor of the U-turner (click above to open LifeViewer) RLE: here Plaintext: here |
There is also this 33-generation predecessor with 8 cells found by David Raucci:
The 8-cell 33-generation predecessor of the U-turner (click above to open LifeViewer) RLE: here Plaintext: here |
Sometimes this 10-cell pattern will appear, which converges to the U-turner sequence after 1 generation:
(click above to open LifeViewer) |
Evolution
The U-turner advances in one direction, with its front edge reaching a maximum displacement of 13 cells in 71 through 76 generations due to a phi spark. The active reaction reverses direction near generation 40, moving for a short time at a speed of roughly c/2 via a B-heptomino being perturbed from behind by some junk, leaving behind a tub at generation 79. Near generation 105 it turns back around, destroying the tub by generation 132,[note 1] reaching its maximum population of 70 cells at generation 140, and stabilizing at generation 163, leaving four blinkers (three from a traffic light and one from an angel) and a block. The distinct "turns" the U-turner makes during the course of its evolution is what gives it its name.
Use in conduits
The U-turner is a recognized conduit object, represented by the letter U.
UR38B, a U-turner to B-heptomino conduit (click above to open LifeViewer) RLE: here Plaintext: here |
Over a hundred stable and periodic U-turner accepting conduits are known, but few conduits that output a U-turner are known, mostly because of the extreme difficultly in finding conduits with a certain output compared to finding ones with a certain input.[4]
Gallery
Notes
- ↑ If the tub is destroyed or removed before this point, then the reaction will settle 3 generations sooner, leaving 2 blinkers, 1 block, and a tub.
See also
- Raucci's p217 (217 = 31 × 7), an oscillator that consists of four U-turners hassled by four Merzenich's p31s.[5]
- Charity's p25, containing a U-turner among other things.
- U-turner hasslers
- List of common evolutionary sequences
- R-turner
References
- ↑ Lucy D'Agostino (May 4, 2021). Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums
- ↑ Simon Ekström (December 28, 2016). Census of small evolving patterns (discussion thread) at the ConwayLife.com forums
- ↑ Robert Wainwright (December 1971). Lifeline, vol 4, page 4.
- ↑ Lucy D'Agostino (June 27, 2023). Re: Thread for your miscellaneous posts and discussions (discussion thread) at the ConwayLife.com forums
- ↑ David Raucci (May 18, 2021). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums