U-turner

U-turner
x = 4, y = 4, rule = B3/S23 b3o$b3o$obo$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
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Pattern type	Methuselah
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
Rules Outer-totalistic rules B3/S23 only # of rules 20 = 1 Isotropic rules B3/S23 only
Glider synthesis Fewest gliders 3
Pattern files Plaintext uturner.cells RLE uturner.rle

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.

Commonness

According to Simon Ekström's census of small evolving patterns, 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, so it was known as early as December 1971, despite being unnamed until 2021.

x = 3, y = 6, rule = B3/S23 2bo$2o2$o$o$o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 GPS 10 ]]

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:

x = 5, y = 4, rule = B3/S23 2b2o$bo2bo$o2bo$o2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 GPS 10 STOP 33 ]]

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:

3o$3o$2o$o$o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 4 THUMBSIZE 2 ]]

(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, 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.

x = 15, y = 20, rule = B3/S23 2o$bo$bobo8b3o$2b2o8b3o$11bobo$11b2o7$5b2o$6bo$3b3o$3bo$11b2o$12bo$9b3o$9bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 20 THUMBSIZE 2 ZOOM 10 STOP 38 ]]

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 difficulty in finding conduits with a certain output compared to finding ones with a certain input.

Gallery

U-turner at generation 163 (Catagolue: here)

If the tub made at generation 79 is removed, this will be the ash left over (Catagolue: here)

See also

• Raucci's p217 (217 = 31 × 7), an oscillator that consists of four U-turners hassled by four Merzenich's p31s.
• Charity's p25, containing a U-turner among other things.
• U-turner hasslers
• List of common evolutionary sequences
• R-turner