User:Evin/W4124 replicators

For some reason, a surprising number of replicators follow the range-3/2 one dimensional rule 4124, which can be described as "rule 90 except replicators that are too close together inhibit replication." Here is a gallery of W4124 replicators:

x = 2, y = 5, rule = B2i3aeiky4cejqrwz5ceikn6akn7e/S2-n3-iqry4ceqw5knq6c78 2o$2o$2o$2o$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME 6 ]]

Found by wwei on October 31, 2020.
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x = 7, y = 6, rule = R3,C0,S3-6,B6 3bo$3bo$7o$7o$3bo$3bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME 6 ]]

Found by luveel on February 26, 2025. Actually a W72621695059493360 replicator.
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x = 5, y = 5, rule = B2ak3cqry4z/S|B1c2n3iqr4nz/S bobo2$o3bo2$obobo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME 6 ]]

Found by wwei on March 27, 2025.
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x = 3, y = 1, rule = B2aci3cqry4cy/S obo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME 6 ]]

Found by Katrina on April 6, 2025. A clean 2D example.
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x = 3, y = 3, rule = B3-ckqy4ejntz5cinr6i8/S2-in3-aky4ceqyz5-kqry6ckn 3o$o$o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME 6 ]]

Found by yujh on October 25, 2025.
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x = 1, y = 1, rule = MAPl5cWFpeXFhZ/f2hof39oaH9/aGh/f2ho/v6AgP7+gIB/f2hof39oaP7+gID+/oCA/v6AgP7+gIDo6AAA6OgAAA o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME 6 ]]

Found by Katrina on December 9, 2025. Actually a W4636 replicator.
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x = 4, y = 3, rule = B3-kn4ce6ik/S2-i34i5r 3o$o2bo$ob2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME 6 ]]

Found by yyh_baboon on December 10, 2025. Leaves behind debris.
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x = 4, y = 4, rule = B02345/S012 bo$o$3bo$2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME 6 ]]

Found by Katrina on April 17, 2026. 2D.
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x = 3, y = 3, rule = B2n3-jkny4i5ekr8/S2aek3-ak4ceiqz5en 3o$obo$2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME 6 ]]

Found by yyh_baboon on July 14, 2026.
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Properties

x = 33, y = 33, rule = B/S0123456H o$2o$obo$o2bo$2ob2o$o4bo$2o3b2o$obo2bobo$o2bobo2bo$2obo2bob2o$o3bobo3b o$2o2bo2bo2b2o$obob2ob2obobo$o12bo$2o11b2o$obo10bobo$o2bo9bo2bo$2ob2o 8b2ob2o$o4bo7bo4bo$2o3b2o6b2o3b2o$obo2bobo5bobo2bobo$o2bobo2bo4bo2bob o2bo$2obo2bob2o3b2obo2bob2o$o3bobo3bo2bo3bobo3bo$2o2bo2bo2b2ob2o2bo2b o2b2o$obob2ob2obo4bob2ob2obobo$o10bo3bo10bo$2o9b2o2b2o9b2o$obo8bobobo bo8bobo$o2bo7bo6bo7bo2bo$2ob2o6b2o5b2o6b2ob2o$o4bo5bobo4bobo5bo4bo$2o 3b2o4bo2bo3bo2bo4b2o3b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME 6 VIEWONLY ]]

A diagram of the initial generations of W4124.
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A W4124 replicator has exactly two copies after 1, 2, 3, 5, and 13 generations and apparently no other values.

W4124 can be emulated at half speed by range-5/2 W72621695059493360. This is similar to W4124 but with more complicated suppression between replicators, and turned up in luveel's February 26 replicator. A related rule is range-3/2 W4636, which produces extra rerplicator units but is equivalent to W4124.