Gray counter

Gray counter
6bo6b$5bobo5b$4bobobo4b$bo2bo3bo2bob$obobo3bobobo$bo2bo3bo2bob$4bobobo 4b$5bobo5b$6bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 30 GPS 2 TRACKLOOP 4 0 0 ]]
View animated image
View static image
Pattern type	Oscillator
Oscillator type	Muttering moat
	Billiard table
Number of cells	26
Bounding box	13 × 9
Period	4 (mod: 4)
Heat	2
Volatility	0.13 | 0.13
Kinetic symmetry	+c
Discovered by	Unknown
Year of discovery	1971
Rules Outer-totalistic rules B3/S23 – B378/S0234678 # of rules 27 = 128 Isotropic rules B3iy/S2cik3ceiry – B2ckn34-ejnt5-ejry6-k78/S01c2345-e678
Glider synthesis Fewest gliders (canonical) 24† Catagolue-generated RLE (canonical) synthesis Fewest gliders (cheapest variant) 9 Catagolue-generated RLE (cheapest variant) synthesis Uploaded synthesis RLE graycounter_synth.rle †Can be constructed with 15 gliders using the reverse caber tosser universal constructor.
Pattern files Plaintext graycounter.cells RLE graycounter.rle
Identifiers apgcode (canonical) xp4_wgiligz25a888a52zx252 apgcode (cheapest variant) xp4_caab88gz354kkldzx1 Pentadecathlon ID 26P4.3

Gray counter is a period-4 oscillator that was found in 1971. The interior rotor simulates a cycle through the Gray codes from 0 to 3.

The 5-cell long sides of the main part of the stator require induction coils: the option with the smallest population (as well as the highest symmetry) uses two tubs as pictured. A smaller bounding box may be reached using snakes or bi-blocks.

Stator variants

The first three variants' syntheses were reduced by a 6-glider synthesis of xs18_039u08kcz2521 (a still life that could swap in for a stage of the existing syntheses) submitted to Shinjuku on January 14, 2024, though the following steps were only transferred explicitly on September 5.

Image	Name apgcode Description	Minpop	Symmetry	Synth. cost	Notes
	Canonical xp4_wgiligz25a888a52zx252	26	D4_+1	26
	One boat xp4_wgiligz25a888a52zx256	27	C1	24	An intermediate stage in the shortest synthesis of the canonical variant
	Two boats xp4_wgiljgz25a888a52zx256	28	D2_+1	23	Optimal synthesis varies from that of one-boat variant in its cheaper final stage
	Long3 eaters weld tails xp4_caab88gz354kkldzx1	28	C2_1	9	The first 9G synthesis was found with QuFince no later than September 2, 2023, although the cleanup of an 11G synthesis from March 29, 2020 is easily reducible to produce two alternate 9Gs
	xp4_caab88gz354kkldzw32	30	C1	11	Occurred naturally on October 31, 2015, in a soup submitted to Catagolue by Tomas Rokicki. GUYTU6J found the 11G synthesis based on its soup on March 14, 2020.
	Long3 eaters siamese integrals xp4_okkljgz6a888arzw6511	32	C2_1	10	Optimal synthesis has can be minorly varied in four places, leading to 10 nonequivalent syntheses under symmetry
	long3 bee siamese eaters on long2 house on loaf xp4_02596zmlhhhlmz1226221	33	C1	31	First occurred naturally on January 22, 2021 but is the most common, with six occurrences across C1 and G1 as of September 16, 2024

See also

• R2D2

External links

• Gray code at Wikipedia
• Gray counter at the Life Lexicon
• Gray counter at Adam P. Goucher's Catagolue
• 26P4.3 at Heinrich Koenig's Game of Life Object Catalogs