OCA:Stains

Stains
x=64, y = 64, rule = B3678/S235678 ! #C [[ THEME Inverse ]] #C [[ RANDOMIZE2 RANDSEED 1729 THUMBLAUNCH THUMBNAIL THUMBSIZE 2 GRID ZOOM 6 WIDTH 600 HEIGHT 600 LABEL 90 -20 2 "#G" AUTOSTART PAUSE 2 GPS 8 LOOP 256 ]] LifeViewer-generated pseudorandom soup
View static image
Rulestring	235678/3678 B3678/S235678
Rule integer	252360
Character	Stable
Black/white reversal	B478/S34678

Stains is a Life-like cellular automaton with the following rules:

• a dead cell gets born when it has 3, 6, 7 or 8 alive neighbours,
• an alive cell survives when it has 2, 3, 5, 6, 7 or 8 alive neighbours.

Almost all random patterns in Stains grow up to a certain point and then turn into one or more irregular-shaped oscillators or still lifes.

On August 7, 2021, Peter Naszvadi proved that Stains is Turing-complete on an infinite, periodically-tiled grid by constructing a Rule 110 "unit stripe".

Spaceships

A variety of spaceships are known to exist in Stains, including the glider as well as several larger ships:

#C (0, 1)/2 #C Min Rule: B37/S3567 #C Max Rule: B3678/S0235678 x = 7, y = 4, rule = B3678/S235678 ob3obo$b5o$3ob3o$bo3bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

Eppstein's glider 3640 (c/2 orthogonal) (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

#C (0, 1)/6 #C Min Rule: B36/S2356 #C Max Rule: B3678/S235678 x = 8, y = 6, rule = B3678/S235678 b2o2b2o$bob2obo$2o4b2o$2o4b2o$obo2bobo$bo4bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

Eppstein's glider 5900 (c/6 orthogonal) (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

#C (0, 2)/5 #C Discovered by: Evan Clark, 2006 #C Min Rule: B367/S235678 #C Max Rule: B3678/S235678 x = 13, y = 15, rule = B3678/S235678 bo9bo$obo7bobo$3o2b3o2b3o$bo4bo4bo$bo3b3o3bo$3o2bobo2b3o$o11bo$3b3ob3o$2bo7bo$5b3o$5b3o$6bo$6bo$5b3o$ 6bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

Eppstein's glider 13695 (2c/5 orthogonal) (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

#C (0, 1)/3 #C Min Rule: B367/S2356 #C Max Rule: B3678/S0235678 x = 16, y = 8, rule = B3678/S235678 obo2bo4bo2bobo$o2b2o6b2o2bo$b3obo4bob3o$4b8o$bob2o6b2obo$bo2b2o4b2o2bo$2ob2o6b2ob2o$3b2o6b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

Eppstein's glider 13965 (c/3 orthogonal) (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

#C (0, 1)/4 #C Min Rule: B367/S235678 #C Max Rule: B3678/S235678 x = 12, y = 28, rule = B3678/S235678 4bo2bo$4o4b4o$4ob2ob4o$2b2o4b2o$4bo2bo$5b2o$5b2o$5b2o$5b2o$3bob2obo$4b4o$bob6obo$3b6o$b10o$2b8o$2bob4obo$3bob2obo$4bo2bo$4b4o$3b2o2b2o$3bo4bo$5b2o$2bob4obo$3b6o$ob8obo$bob6obo$2bob4obo$3b6o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

Eppstein's glider 18511 (c/4 orthogonal) (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

#C (0, 1)/5 #C Discovered by: Evan Clark, 2006 #C Min Rule: B367/S235678 #C Max Rule: B3678/S235678 x = 12, y = 42, rule = B3678/S235678 5b2o$4bo2bo$3bob2obo2$5b2o$2b8o$4bo2bo$3bob2obo$5b2o$2bo2b2o2bo$bobo4bobo$4ob2ob4o$5b2o$4b4o$4b4o$4b4o$3b6o$3bo4bo$b2o6b2o$4bo2bo$5b2o$b2ob4ob2o$4b4o$4b4o$5b2o$3bob2obo$3b6o$2bo6bo$4b4o$5b2o$4b4o$5b2o$bobob2obobo$obob4obobo$b3ob2ob3o$2bo2b2o2bo$4b4o$b10o$2b3o2b3o$2bo6bo$obo6bobo$bo8bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

Eppstein's glider 20317 (c/5 orthogonal) (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 71, y = 9, rule = B3678/S235678 2b2o3b2o13bo5bo15b3o15b2o3b2o$ob2obob2obo9bob3ob3obo11bob3obo11bob2o3b 2obo$b9o11b9o10bob7obo10b9o$b9o11b9o11b9o11b9o$b9o11b9o11b9o11b9o$3b5o 15b5o13b9o13b5o$5bo19bo17b5o17bo$4bobo17bobo18bo18bobo$44bobo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

More c/3 orthogonal ships (click above to open LifeViewer) RLE: here Plaintext: here

Infinite growth

The question of whether infinite growth existed in Stains remained open until 1999, when a variety of 2c/5 orthogonal linear growth patterns were published. Linear growth patterns with speeds of 3c/7 orthogonal were later discovered in 2016, followed by c/3 and c/4 orthogonal in 2017. However, the existence of nonlinear infinite growth as well as sawtooths in this rule remains an open question.

External links

• Stains: a World of Enormous Oscillators
• Stains at Adam P. Goucher's Catagolue
• Stains at David Eppstein's Glider Database
• B3678/S235678 (Stains) found patterns - infinite growth (discussion thread) at the ConwayLife.com forums
• MCell built-in Life rules: Stains at Mirek Wójtowicz's Cellebration page