43P54

43P54
x = 26, y = 19, rule = B3/S23 5bo$5b3o7b2o$8bo6b2o$7b2o2$2o22b2o$bo22bo$bobo10b3o5bobo$2b2o10bo7b2o$ 14b2o4$21bo$21b2o$5b2o14b2o$5bo16bo$6bo$5b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ THUMBSIZE 3 GPS 6 ZOOM 18 LOOP 54 WIDTH 500 HEIGHT 500 ]]
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Pattern type	Oscillator
Number of cells	43
Bounding box	26 × 19
Period	54 (mod: 54)
Heat	23.5
Volatility	0.85 | 0.81
Kinetic symmetry	n
Discovered by	Mitchell Riley Aleph
Year of discovery	2022
Rules Outer-totalistic rules B3/S23 – B38/S23 # of rules 21 = 2 Isotropic rules B3/S23-c – B34ce6c8/S234c6i
Glider synthesis Fewest gliders (canonical) 17† Catagolue-generated RLE (canonical) synthesis Fewest gliders (cheapest variant) 15 Catagolue-generated RLE (cheapest variant) synthesis †Can be constructed with 15 gliders using the reverse caber tosser universal constructor.
Pattern files Plaintext 43p54.cells RLE 43p54.rle
Identifiers apgcode (canonical) xp54_y566y2ca23z178cy14ksy6c871zxgozx31yadb apgcode (cheapest variant) xp54_y566y2ca23z178cy14ksy6c871zxgozx31ya178c

43P54 is the smallest known period-54 oscillator. It was originally found in a dimer form by Mitchell Riley on July 11, 2022, presumably using the symmetric version of CatForce like his previous discoveries. Aleph found a monomerized version using a toad, giving the 43-cell form shown in the infobox. It consists of various catalysts interacting with an active object that switches between the R-pentomino and B-heptomino sequences.

Evin found both single-barreled and double-barreled glider guns each using two interacting copies of the hassler. On July 13, hotcrystal0 and David Raucci found a gun using only a single engine; at 25 × 32, it is currently the smallest known glider gun with this period.

Replacing the snake with a second toad reduces the bounding box by one row and makes the oscillator easier to synthesize with no change in population. Replacing it with an eater 1 can further reduce its cost to 15 gliders but with a higher population, as found by Haycat Durnak and KtT.

x = 42, y = 20, rule = B3/S23 20b2o$20b2o2$20b4o7b2o$9b2o7b3o3bo6b2o$9b2o6bo5b2o$17b2o$28bo11b2o$2o 11bo14bo11bo$bo11bo15bo8bobo$bobo8bo19b2o4b2o$2b2o4b2o22bobo$7bobo12bo 9bob2o$6b2obo9bo2b3o8b2o$7b2o8b2o3b2o9bo$8bo9b2o17b2o$3b2o31bo$5bo33bo $2bo34b2o$3b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 54 THUMBSIZE 2 ZOOM 12 HEIGHT 450 ]]

The p54 gun found by Evin. Note that both 43P54s are in the same phase. (click above to open LifeViewer)

LCM oscillators

The LCM oscillators below are or were the smallest known ones by population while satisfying the condition that at least one cell oscillates at the full period.

x = 29, y = 19, rule = B3/S23 8bo$8b3o7b2o$11bo6b2o$10b2o2$3b2o22b2o$4bo22bo$4bobo10b3o5bobo$5b2o10b o7b2o$17b2o2$b2o$o2bo$obo21bo$bob2o19b2o$2b3o3b2o14b2o$3b2o3bo16bo$9b o$8b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 54 THUMBSIZE 2 ZOOM 12 HEIGHT 450 ]]

Former SKOP108 at 55 cells with mold (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 29, y = 21, rule = B3/S23 8bo$8b3o7b2o$11bo6b2o$10b2o2$3b2o22b2o$4bo22bo$4bobo10b3o5bobo$5b2o10b o7b2o$17b2o4$24bo$24b2o$3b3o18b2o$3b3o19bo$3b3o$3o$3o$3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 54 THUMBSIZE 2 ZOOM 12 HEIGHT 450 ]]

50P216 with figure eight. The figure eight replaces the snake. (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

External links

• 43P54 at Adam P. Goucher's Catagolue