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[R2INT]

This is what happens if you try to vibecode a rule that supports stable splitters and chirality-based ternary logic:

Code: Select all

x = 13, y = 33, rule = ChiralTSplit
.A2.B2.3B$2.2A4.B11$.A2.B2.3B.B$2.2A4.B2.2B$11.B13$A2.B3.B$.2A2.3B2$6.
B$6.2B$6.B!
@RULE ChiralTSplit
AI used a vibecoded search program that used Z3 to generate the rule.
@TABLE
n_states:3
neighborhood:Moore
symmetries:rotate4reflect
0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,1,0,2
0,0,0,0,0,0,0,2,0,0
0,0,0,0,0,0,1,0,0,0
0,0,0,0,0,0,1,1,0,2
0,0,0,0,0,0,1,2,0,1
0,0,0,0,0,0,2,0,0,0
0,0,0,0,0,0,2,1,0,0
0,0,0,0,0,0,2,2,0,0
0,0,0,0,0,1,0,1,0,1
0,0,0,0,0,1,0,2,0,0
0,0,0,0,0,1,1,1,0,2
0,0,0,0,0,1,1,2,0,2
0,0,0,0,0,1,2,1,0,1
0,0,0,0,0,1,2,2,0,0
0,0,0,0,0,2,0,2,0,0
0,0,0,0,0,2,1,2,0,2
0,0,0,0,0,2,2,2,0,0
0,0,0,0,1,0,0,2,0,2
0,0,0,0,1,0,1,0,0,1
0,0,0,0,1,0,1,2,0,2
0,0,0,0,1,0,2,0,0,0
0,0,0,0,1,0,2,1,0,1
0,0,0,0,1,0,2,2,0,2
0,0,0,0,1,1,0,1,0,1
0,0,0,0,1,1,0,2,0,2
0,0,0,0,1,1,1,0,0,2
0,0,0,0,1,1,1,1,0,0
0,0,0,0,1,1,1,2,0,0
0,0,0,0,1,1,2,0,0,1
0,0,0,0,1,1,2,1,0,0
0,0,0,0,1,1,2,2,0,1
0,0,0,0,1,2,0,1,0,1
0,0,0,0,1,2,0,2,0,2
0,0,0,0,1,2,1,0,0,0
0,0,0,0,1,2,1,2,0,1
0,0,0,0,1,2,2,0,0,1
0,0,0,0,1,2,2,1,0,0
0,0,0,0,1,2,2,2,0,1
0,0,0,0,2,0,0,1,0,0
0,0,0,0,2,0,0,2,0,0
0,0,0,0,2,0,1,1,0,0
0,0,0,0,2,0,1,2,0,0
0,0,0,0,2,0,2,0,0,0
0,0,0,0,2,0,2,1,0,1
0,0,0,0,2,0,2,2,0,1
0,0,0,0,2,1,0,1,0,2
0,0,0,0,2,1,0,2,0,0
0,0,0,0,2,1,1,2,0,1
0,0,0,0,2,1,2,0,0,0
0,0,0,0,2,1,2,1,0,1
0,0,0,0,2,1,2,2,0,0
0,0,0,0,2,2,0,1,0,2
0,0,0,0,2,2,0,2,0,0
0,0,0,0,2,2,1,1,0,0
0,0,0,0,2,2,1,2,0,0
0,0,0,0,2,2,2,0,0,0
0,0,0,0,2,2,2,1,0,1
0,0,0,0,2,2,2,2,0,2
0,0,0,1,0,0,0,2,0,1
0,0,0,1,0,0,1,1,0,0
0,0,0,1,0,0,2,2,0,0
0,0,0,1,0,1,0,2,0,0
0,0,0,1,0,1,2,1,0,0
0,0,0,1,0,2,0,2,0,0
0,0,0,1,0,2,1,1,0,0
0,0,0,1,0,2,2,1,0,0
0,0,0,1,1,0,0,2,0,2
0,0,0,1,1,2,1,1,0,0
0,0,0,1,1,2,2,2,0,2
0,0,0,1,2,0,0,2,0,1
0,0,0,1,2,1,0,2,0,0
0,0,0,1,2,2,0,2,0,0
0,0,0,2,0,0,0,2,0,1
0,0,0,2,0,0,2,2,0,0
0,0,0,2,1,0,2,2,0,1
0,0,0,2,1,1,2,2,0,2
0,0,0,2,1,2,2,2,0,0
0,0,1,0,0,0,1,1,0,0
0,0,1,0,0,0,2,0,0,0
0,0,1,0,0,1,0,2,0,0
0,0,1,0,1,0,0,2,0,0
0,0,1,0,1,0,2,0,0,0
0,0,1,0,1,1,0,2,0,2
0,0,1,0,1,2,0,2,0,1
0,0,1,0,1,2,1,0,0,2
0,0,1,1,0,1,2,0,0,2
0,0,1,1,0,1,2,1,0,1
0,0,1,1,1,0,0,2,0,0
0,0,1,1,1,0,1,2,0,2
0,0,1,1,1,2,0,2,0,0
0,0,1,1,1,2,1,0,0,0
0,0,1,1,2,0,1,2,0,0
0,0,1,1,2,0,2,0,0,0
0,0,1,2,0,1,0,1,0,0
0,0,1,2,0,2,0,1,0,0
0,0,1,2,0,2,1,0,0,0
0,0,1,2,0,2,1,2,0,1
0,0,1,2,0,2,2,0,0,0
0,0,1,2,1,0,2,0,0,1
0,0,1,2,1,0,2,2,0,1
0,0,1,2,1,2,2,0,0,0
0,0,1,2,2,0,1,1,0,0
0,0,1,2,2,0,2,0,0,2
0,0,1,2,2,1,1,2,0,0
0,0,1,2,2,1,2,0,0,1
0,0,1,2,2,2,2,0,0,0
0,0,2,0,0,0,2,0,0,0
0,0,2,0,0,1,2,2,0,0
0,0,2,0,0,2,2,2,0,2
0,0,2,0,1,0,1,2,0,2
0,0,2,0,1,1,2,0,0,0
0,0,2,0,2,0,0,1,0,0
0,0,2,0,2,2,0,2,0,1
0,0,2,0,2,2,2,0,0,0
0,0,2,1,0,1,0,2,0,1
0,0,2,1,0,1,1,2,0,0
0,0,2,1,0,2,2,0,0,2
0,0,2,1,0,2,2,1,0,0
0,0,2,1,1,2,1,1,0,0
0,0,2,1,2,0,1,1,0,0
0,0,2,1,2,0,1,2,0,2
0,0,2,1,2,1,1,2,0,1
0,0,2,1,2,2,0,1,0,0
0,0,2,1,2,2,2,0,0,2
0,0,2,2,1,2,1,1,0,2
0,0,2,2,1,2,1,2,0,1
0,0,2,2,2,0,0,2,0,1
0,0,2,2,2,0,2,1,0,1
0,0,2,2,2,2,2,0,0,1
0,1,0,1,1,1,1,2,0,0
0,1,0,1,2,2,0,2,0,0
0,1,0,2,1,1,2,2,0,0
0,1,1,0,2,2,2,1,0,1
0,1,1,1,1,1,2,2,0,1
0,1,1,1,1,2,0,2,0,0
0,1,1,1,2,0,2,2,0,0
0,1,1,2,0,2,1,2,0,0
0,1,1,2,0,2,2,1,0,0
0,1,1,2,1,0,1,2,0,2
0,1,2,0,1,0,2,2,0,2
0,1,2,0,2,0,1,2,0,0
0,1,2,0,2,1,2,2,0,2
0,1,2,0,2,2,2,2,0,0
0,1,2,1,1,2,1,2,0,2
0,1,2,1,2,0,2,2,0,0
0,1,2,1,2,2,0,2,0,2
0,1,2,1,2,2,1,2,0,1
0,1,2,2,1,0,1,2,0,1
0,1,2,2,1,0,2,2,0,0
0,1,2,2,1,2,2,2,0,0
0,1,2,2,2,1,0,2,0,0
0,1,2,2,2,2,2,2,0,0
0,2,0,2,1,2,1,2,0,2
0,2,1,0,1,1,2,2,0,0
0,2,1,0,2,1,1,2,0,0
0,2,1,1,1,0,2,2,0,0
0,2,1,1,1,2,1,2,0,0
0,2,1,2,2,2,2,2,0,2
0,2,2,0,2,1,2,2,0,0
0,2,2,1,2,2,2,2,0,2
0,0,1,0,2,0,1,1,1,1
0,0,2,1,2,0,2,1,1,2
0,0,2,1,2,0,2,2,1,0
0,0,2,2,2,1,2,2,1,0
0,0,2,2,2,2,1,1,1,2
0,1,1,1,1,1,2,2,1,0
0,1,1,1,2,1,1,2,1,1
0,1,2,1,1,2,2,2,1,0
0,1,2,1,2,1,2,2,2,1
1,0,0,0,0,0,0,0,0,0
1,0,0,0,0,0,0,1,0,1
1,0,0,0,0,0,0,2,0,0
1,0,0,0,0,0,1,0,0,2
1,0,0,0,0,0,1,2,0,0
1,0,0,0,0,0,2,0,0,0
1,0,0,0,0,0,2,1,0,0
1,0,0,0,0,0,2,2,0,0
1,0,0,0,0,1,0,2,0,2
1,0,0,0,0,1,1,2,0,1
1,0,0,0,0,1,2,2,0,1
1,0,0,0,0,2,0,2,0,2
1,0,0,0,0,2,1,2,0,1
1,0,0,0,1,0,0,1,0,0
1,0,0,0,1,0,1,2,0,1
1,0,0,0,1,0,2,0,0,0
1,0,0,0,1,1,0,1,0,0
1,0,0,0,1,1,1,1,0,1
1,0,0,0,1,1,2,0,0,1
1,0,0,0,1,2,1,0,0,0
1,0,0,0,2,0,0,1,0,0
1,0,0,0,2,0,1,1,0,2
1,0,0,0,2,0,2,0,0,0
1,0,0,0,2,0,2,1,0,1
1,0,0,0,2,0,2,2,0,1
1,0,0,0,2,1,0,2,0,0
1,0,0,0,2,1,1,1,0,2
1,0,0,0,2,1,2,0,0,0
1,0,0,0,2,1,2,1,0,1
1,0,0,0,2,1,2,2,0,0
1,0,0,0,2,2,0,1,0,1
1,0,0,0,2,2,0,2,0,2
1,0,0,0,2,2,1,1,0,1
1,0,0,0,2,2,1,2,0,1
1,0,0,0,2,2,2,0,0,0
1,0,0,0,2,2,2,1,0,0
1,0,0,0,2,2,2,2,0,0
1,0,0,1,0,0,0,2,0,2
1,0,0,1,0,0,2,1,0,0
1,0,0,1,0,1,0,2,0,0
1,0,0,1,0,2,0,1,0,0
1,0,0,1,0,2,2,1,0,0
1,0,0,1,1,1,0,2,0,2
1,0,0,1,1,2,1,2,0,1
1,0,0,1,1,2,2,1,0,0
1,0,0,1,2,0,1,2,0,0
1,0,0,1,2,1,2,1,0,2
1,0,0,1,2,1,2,2,0,0
1,0,0,1,2,2,0,2,0,1
1,0,0,1,2,2,2,2,0,1
1,0,0,2,0,0,0,2,0,2
1,0,0,2,0,0,1,2,0,2
1,0,0,2,0,0,2,2,0,0
1,0,0,2,0,2,2,2,0,1
1,0,0,2,1,1,2,2,0,1
1,0,0,2,2,1,2,2,0,2
1,0,1,0,1,2,0,2,0,2
1,0,1,0,2,0,0,2,0,2
1,0,1,0,2,0,1,2,0,0
1,0,1,0,2,1,0,1,0,0
1,0,1,0,2,2,0,2,0,1
1,0,1,1,0,2,0,1,0,0
1,0,1,1,0,2,2,0,0,2
1,0,1,1,1,0,2,1,0,1
1,0,1,1,2,0,0,2,0,0
1,0,1,2,1,1,2,2,0,1
1,0,1,2,2,0,0,2,0,1
1,0,1,2,2,0,2,0,0,1
1,0,1,2,2,1,0,1,0,0
1,0,1,2,2,2,2,0,0,1
1,0,2,0,0,0,2,2,0,2
1,0,2,0,1,0,2,2,0,0
1,0,2,0,1,1,0,2,0,0
1,0,2,0,1,2,0,2,0,1
1,0,2,0,1,2,2,0,0,0
1,0,2,0,2,1,0,2,0,2
1,0,2,0,2,2,0,2,0,2
1,0,2,0,2,2,1,2,0,0
1,0,2,0,2,2,2,2,0,0
1,0,2,1,0,1,1,1,0,0
1,0,2,1,0,1,2,0,0,2
1,0,2,1,1,1,2,0,0,0
1,0,2,1,2,0,1,1,0,0
1,0,2,1,2,0,2,2,0,0
1,0,2,1,2,2,1,2,0,1
1,0,2,1,2,2,2,2,0,2
1,0,2,2,0,1,1,2,0,0
1,0,2,2,0,1,2,2,0,2
1,0,2,2,1,0,2,1,0,2
1,0,2,2,1,0,2,2,0,1
1,0,2,2,1,1,2,2,0,0
1,0,2,2,2,1,2,1,0,2
1,0,2,2,2,1,2,2,0,1
1,1,0,1,0,1,0,2,0,0
1,1,0,2,0,2,2,2,0,2
1,1,0,2,1,0,1,2,0,2
1,1,0,2,1,0,2,2,0,2
1,1,0,2,1,2,1,2,0,0
1,1,0,2,1,2,2,2,0,0
1,1,1,0,1,0,2,1,0,0
1,1,1,0,1,1,2,2,0,0
1,1,1,0,2,2,0,2,0,0
1,1,1,1,1,2,2,2,0,1
1,1,1,1,2,2,0,2,0,1
1,1,1,2,1,1,2,2,0,2
1,1,2,0,2,1,2,1,0,0
1,1,2,1,1,1,2,2,0,2
1,1,2,2,0,1,2,2,0,2
1,1,2,2,0,2,1,2,0,2
1,1,2,2,0,2,2,1,0,2
1,2,0,2,0,2,2,2,0,0
1,2,0,2,2,0,2,2,0,1
1,2,1,0,2,1,2,2,0,1
1,2,1,1,2,0,2,2,0,2
1,2,1,2,2,0,2,2,0,1
1,2,2,1,2,1,2,2,0,0
1,0,1,1,1,2,2,1,1,0
1,0,1,1,2,0,2,2,1,0
1,0,2,0,1,1,2,2,1,2
1,0,2,0,2,2,2,0,1,0
1,0,2,1,2,0,1,2,1,1
1,0,2,2,1,1,1,2,1,2
2,0,0,0,0,0,0,0,0,0
2,0,0,0,0,0,0,1,0,0
2,0,0,0,0,0,0,2,0,0
2,0,0,0,0,0,1,0,0,1
2,0,0,0,0,0,1,1,0,0
2,0,0,0,0,0,2,0,0,0
2,0,0,0,0,0,2,1,0,0
2,0,0,0,0,0,2,2,0,2
2,0,0,0,0,1,0,2,0,2
2,0,0,0,0,1,2,2,0,0
2,0,0,0,0,2,0,2,0,0
2,0,0,0,0,2,1,2,0,2
2,0,0,0,0,2,2,2,0,1
2,0,0,0,1,0,0,1,0,2
2,0,0,0,1,0,0,2,0,0
2,0,0,0,1,0,1,2,0,0
2,0,0,0,1,0,2,1,0,0
2,0,0,0,1,1,0,1,0,1
2,0,0,0,1,1,0,2,0,0
2,0,0,0,1,1,1,0,0,2
2,0,0,0,1,1,2,0,0,2
2,0,0,0,1,1,2,1,0,2
2,0,0,0,1,1,2,2,0,0
2,0,0,0,1,2,1,1,0,2
2,0,0,0,1,2,1,2,0,1
2,0,0,0,1,2,2,0,0,0
2,0,0,0,1,2,2,2,0,2
2,0,0,0,2,0,0,1,0,1
2,0,0,0,2,0,0,2,0,1
2,0,0,0,2,0,1,1,0,2
2,0,0,0,2,0,1,2,0,0
2,0,0,0,2,0,2,0,0,1
2,0,0,0,2,0,2,1,0,2
2,0,0,0,2,1,0,2,0,0
2,0,0,0,2,1,2,0,0,0
2,0,0,0,2,1,2,1,0,1
2,0,0,0,2,1,2,2,0,1
2,0,0,0,2,2,0,1,0,2
2,0,0,0,2,2,0,2,0,1
2,0,0,0,2,2,1,1,0,2
2,0,0,0,2,2,1,2,0,2
2,0,0,0,2,2,2,0,0,2
2,0,0,1,0,0,0,1,0,0
2,0,0,1,0,0,0,2,0,2
2,0,0,1,0,0,1,1,0,0
2,0,0,1,0,0,1,2,0,2
2,0,0,1,0,0,2,2,0,1
2,0,0,1,0,1,0,1,0,2
2,0,0,1,0,1,1,1,0,0
2,0,0,1,0,2,1,1,0,0
2,0,0,1,1,0,2,1,0,2
2,0,0,1,1,1,0,2,0,2
2,0,0,1,1,2,0,2,0,1
2,0,0,1,2,0,0,2,0,2
2,0,0,1,2,0,2,2,0,1
2,0,0,1,2,2,1,2,0,0
2,0,0,2,0,0,1,2,0,0
2,0,0,2,0,0,2,2,0,0
2,0,0,2,0,2,0,2,0,2
2,0,0,2,1,0,1,2,0,0
2,0,0,2,1,0,2,2,0,2
2,0,1,0,0,0,1,2,0,0
2,0,1,0,0,1,1,2,0,2
2,0,1,0,0,1,2,1,0,0
2,0,1,0,1,0,2,2,0,2
2,0,1,0,1,2,0,2,0,0
2,0,1,0,1,2,1,1,0,2
2,0,1,0,1,2,2,2,0,2
2,0,1,0,2,0,1,0,0,0
2,0,1,0,2,2,0,2,0,2
2,0,1,1,0,0,1,2,0,1
2,0,1,1,0,1,1,0,0,1
2,0,1,1,0,2,2,0,0,1
2,0,1,1,1,0,1,1,0,0
2,0,1,1,1,2,0,2,0,2
2,0,1,2,0,0,2,0,0,0
2,0,1,2,0,1,1,2,0,0
2,0,1,2,0,1,2,0,0,0
2,0,1,2,0,1,2,2,0,0
2,0,1,2,0,2,0,1,0,1
2,0,1,2,0,2,0,2,0,0
2,0,1,2,1,0,2,0,0,0
2,0,1,2,1,1,0,2,0,1
2,0,1,2,1,1,1,1,0,1
2,0,1,2,1,1,2,0,0,2
2,0,1,2,1,2,2,1,0,0
2,0,1,2,2,2,0,1,0,0
2,0,1,2,2,2,2,2,0,2
2,0,2,0,0,0,2,0,0,1
2,0,2,0,0,1,0,1,0,2
2,0,2,0,0,1,0,2,0,0
2,0,2,0,1,0,1,2,0,2
2,0,2,0,1,0,2,0,0,0
2,0,2,0,1,1,0,2,0,0
2,0,2,0,1,1,2,1,0,0
2,0,2,0,1,2,0,1,0,1
2,0,2,0,1,2,1,1,0,0
2,0,2,0,2,1,2,1,0,0
2,0,2,0,2,1,2,2,0,1
2,0,2,1,0,0,2,2,0,1
2,0,2,1,0,1,0,2,0,2
2,0,2,1,0,2,2,1,0,2
2,0,2,1,0,2,2,2,0,2
2,0,2,1,1,2,0,1,0,1
2,0,2,1,2,2,0,1,0,0
2,0,2,2,0,2,0,2,0,1
2,0,2,2,0,2,1,1,0,0
2,0,2,2,0,2,1,2,0,0
2,0,2,2,1,1,0,2,0,1
2,0,2,2,1,2,0,2,0,1
2,0,2,2,2,0,1,1,0,1
2,0,2,2,2,0,2,2,0,2
2,0,2,2,2,1,0,1,0,0
2,0,2,2,2,2,0,1,0,1
2,1,0,1,0,1,1,2,0,0
2,1,0,1,0,2,0,2,0,0
2,1,0,1,1,0,2,2,0,2
2,1,0,1,2,0,2,1,0,1
2,1,0,2,0,1,2,2,0,0
2,1,0,2,1,1,2,2,0,0
2,1,1,0,1,1,1,2,0,0
2,1,1,0,2,1,1,2,0,0
2,1,1,0,2,2,0,2,0,2
2,1,1,1,0,1,1,2,0,0
2,1,1,1,1,1,1,2,0,1
2,1,1,1,2,1,1,2,0,1
2,1,2,0,1,2,0,2,0,0
2,1,2,0,2,0,2,2,0,0
2,1,2,1,0,2,2,2,0,0
2,1,2,1,2,1,2,2,0,0
2,1,2,2,2,0,2,2,0,0
2,2,0,2,1,1,2,2,0,1
2,2,0,2,2,2,2,2,0,1
2,2,1,0,1,2,1,2,0,0
2,2,1,2,1,0,2,2,0,1
2,2,2,0,1,1,2,2,0,0
2,0,1,0,1,1,1,2,1,1
2,0,1,0,2,0,1,1,1,0
2,0,1,0,2,1,1,2,1,1
2,0,1,0,2,2,2,1,1,0
2,0,1,1,1,2,1,1,1,1
2,0,1,1,2,0,2,2,1,2
2,0,2,0,1,0,2,1,1,0
2,0,2,0,1,1,2,1,1,0
2,0,2,0,2,1,1,2,1,0
2,0,2,0,2,2,2,2,1,1
2,0,2,1,1,2,1,2,1,0
2,0,2,1,2,2,1,1,1,0
2,1,2,0,2,1,1,2,1,2
2,1,2,0,2,2,2,1,1,1

I'm pretty sure that in the far future we might have AI's that can autogolf splitters and other circuitry components much faster than a human.

[NNlk05]

I'm pretty sure that in the far future we might have AI's that can autogolf splitters and other circuitry components much faster than a human.

I'm quite sure that if you gave an AI agent a program that can run rule tables, given enough time, it will work.

[NNlk05]

Will the forums be affected by this PHP vulnerability (CVE-2026-109618 & CVE-2026-109619)?

[R2INT]

Moving this discussion into this thread in order to avoid cluttering counting to 50 with transitions.

EDIT: I just had an idea: what if we got pass the rule to be an alternating checkerboard rule?

Would it be possible to modify it into one with all the transitions we currently have?

Pass the rule allows you to add and remove any transition, one transition per turn. It is important to have B4e, B5c, D3c, B4j, D4y, B3e, and D5e, as these enable lightspeed propagation like B1c, B1e, and B2a do in INT.

[TheWayOfTheCon]

Moving this discussion into this thread in order to avoid cluttering counting to 50 with transitions.

EDIT: I just had an idea: what if we got pass the rule to be an alternating checkerboard rule?

Would it be possible to modify it into one with all the transitions we currently have?

Pass the rule allows you to add and remove any transition, one transition per turn.

My bad, I thought you were still referring to counting to 50 for some reason.

Could be an interesting idea.

[R2INT]

In pass the rule, we already have B4ej5c/D4c5e. So we still need B3e, D3c, and D4y, and then no relativistic photons can inhabit the strobing checkerboard.

Then we can focus on stabilizing the checkerboard, and finally we can start destabilizing the vacuum.

We're 5 transitions away from a (boring) strobing checkerboard rule: B3e, B3j, D3c, S4r, and D5y. D3c will take us out of Whitespace. S4r and B3j increase the activity of the rule, and combining them makes the rule explosive. We should probably add B3j last.

[ThePlayzr]

This rule is extremely strongly explosive, and yet...

Code: Select all

x = 3, y = 1, rule = B2aci3eky4-ei5-ain6/S3acikn4-eint5-y6-i78
obo!

[MDA]

I’m confused. When I click on the link to search for dvgrn’s posts, it says they made only 11,432. Is this a bug?

Some of them are hidden to non-moderators.

A follow-up to this question, but why does Kazyan have 1,253 posts but only 1,252 visible ones?

Edit (October 23rd, 2026, 11:03 PM):

What about Moosey, with 4,315 posts total but only 4,311 visible ones?

And Saka, with 3,626 posts but only 3,612 visible ones?

[LuveelVoom]

Stephen Wolfram's wife has passed away.
https://writings.stephenwolfram.com/202 ... ful-years/
Rest in peace.

[NNlk05]

I think we need a “thread for your unsure discoveries in other cellular automata” thread…

There was

[Ninedlingss]

I think we need a “thread for your unsure discoveries in other cellular automata” thread…

There was

Oh ok

[Aleph]

Code: Select all

x = 27, y = 34, rule = B3/S23
23bo$23b3o$26bo$25bo$24bo$23bo$22bo$21bo$20bo$19bo$18bo$17bo$16bo$15b
o$14bo$13bo$12bo$11bo$10bo$9bo$8bo$7bo$6bo$5bo$4bo$3bo$obo$2o4$3b3o$3b
o$4bo!

A reduction to this. Almost certainly minimal.
https://conwaylife.com/forums/viewtopic ... 83#p152583

[synperiplanar]

Code: Select all

x = 27, y = 34, rule = B3/S23
23bo$23b3o$26bo$25bo$24bo$23bo$22bo$21bo$20bo$19bo$18bo$17bo$16bo$15b
o$14bo$13bo$12bo$11bo$10bo$9bo$8bo$7bo$6bo$5bo$4bo$3bo$obo$2o4$3b3o$3b
o$4bo!

A reduction to this. Almost certainly minimal.
https://conwaylife.com/forums/viewtopic ... 83#p152583

i just realised how dumb i've been this whole time...:

Code: Select all

x = 28, y = 24, rule = B3/S23
24bo$24b3o$27bo$26bo$25bo$24bo$23bo$22bo$21bo$20bo$19bo$18bo$17bo$16b
o$15bo$14bo$13bo$12bo$11bo$10bo$9bo$3o3bobo$2bo3b2o$bo!

[F1012]

this collision creates a pi-hept:

Code: Select all

x = 3, y = 7, rule = B3/S23
2bo$2o$b2o2$2bo$2bo$2bo!

but adding just one more glider adds an extra pi-hept:

Code: Select all

x = 5, y = 11, rule = B3/S23
2bo$2o$b2o2$2bo$2bo$2bo2$2b2o$3b2o$2bo!

[hibiscus]

Edit (Jan. 29, 2026): I'm collecting some of some of my results on odd-period oscillators in rule 126 here for future reference:

Cylindrical boundary:
Disproven: 3, 5, 7, 9, 15, 17, 21
Known examples: 11, 13, 23, 25, 27, others

Always-on boundary:
Disproven: 7, 9, 11, 15, 17, 21, 23, 25, 31, 35, 39, 41, 43, 45, 47, 49, 51, 53
Known examples (a star next to the period means that the pattern is only a predecessor of the oscillator):

Code: Select all

x = 1097, y = 550, rule = B78/S234567
56b6o$56b6o$60b2o$60b2o10b5o$58b4o10b5o$58b4o10b5o$60b2o$60b2o$56b6o$
56b6o11$56b6o$56b6o$56b2o$56b2o14b9o$56b6o10b9o$56b6o10b9o$60b2o$60b2o
$56b6o$56b6o11$50b2o4b6o$50b2o4b6o$48b4o8b2o$48b4o8b2o10b13o$50b2o6b4o
10b13o$50b2o6b4o10b13o$50b2o8b2o$50b2o8b2o$48b6o2b6o$48b6o2b6o11$50b2o
4b6o$50b2o4b6o$48b4o4b2o2b2o$48b4o4b2o2b2o10b18o$50b2o4b6o10b6o5b2o4bo
$50b2o4b6o10b18o$50b2o8b2o$50b2o8b2o$48b6o2b6o$48b6o2b6o11$48b6o2b6o$
48b6o2b6o$52b2o6b2o$52b2o6b2o10b17o$48b6o6b2o10b17o$48b6o6b2o10b17o$
48b2o10b2o$48b2o10b2o$48b6o6b2o$48b6o6b2o11$48b6o2b6o$48b6o2b6o$52b2o
2b2o2b2o$52b2o2b2o2b2o10b33o$48b6o2b6o10b33o$48b6o2b6o10b33o$48b2o10b
2o$48b2o10b2o$48b6o2b6o$48b6o2b6o11$48b6o2b6o$48b6o2b6o$52b2o6b2o$52b
2o6b2o10b27o$50b4o4b4o10b3o4b4o8b2o5bo$50b4o4b4o10b27o$52b2o6b2o$52b2o
6b2o$48b6o2b6o$48b6o2b6o11$48b6o2b6o3bo$48b6o2b6o2b3o$52b2o6b2o3bo$52b
2o6b2o10b21o$50b4o6b2o10b21o$50b4o6b2o10b21o$52b2o6b2o$52b2o6b2o$48b6o
6b2o$48b6o6b2o11$48b6o2b6o$48b6o2b6o$48b2o6b2o$48b2o6b2o14b43o$48b6o2b
6o10b2ob2o5b2ob2o2b4ob4o2b2ob2o5b2ob2o$48b6o2b6o10b43o$52b2o6b2o$52b2o
6b2o$48b6o2b6o$48b6o2b6o11$48b6o4b2o$48b6o4b2o$48b2o6b4o$48b2o6b4o12b
61o$48b6o4b2o12b61o$48b6o4b2o12b61o$48b2o2b2o4b2o$48b2o2b2o4b2o$48b6o
2b6o$48b6o2b6o11$42b2o4b6o2b6o$42b2o4b6o2b6o$40b4o8b2o6b2o$40b4o8b2o6b
2o$42b2o4b6o4b4o10b65o$42b2o4b6o4b4o10b65o$42b2o4b2o10b2o10b65o$42b2o
4b2o10b2o$40b6o2b6o2b6o$40b6o2b6o2b6o11$42b2o4b6o2b6o$42b2o4b6o2b6o$
40b4o8b2o2b2o$40b4o8b2o2b2o14b129o$42b2o4b6o2b6o10b129o$42b2o4b6o2b6o
10b129o$42b2o4b2o10b2o$42b2o4b2o10b2o$40b6o2b6o2b6o$40b6o2b6o2b6o11$
40b6o2b6o2b6o$40b6o2b6o2b6o$44b2o2b2o10b2o$44b2o2b2o10b2o10b253o$40b6o
2b6o4b4o10b253o$40b6o2b6o4b4o10b253o$40b2o10b2o6b2o$40b2o10b2o6b2o$40b
6o2b6o2b6o$40b6o2b6o2b6o11$40b6o2b6o4b2o5bo$40b6o2b6o4b2o4b3o$44b2o2b
2o2b2o2b4o5bo$44b2o2b2o2b2o2b4o12b53o$40b6o2b6o4b2o12b53o$40b6o2b6o4b
2o12b53o$40b2o10b2o4b2o$40b2o10b2o4b2o$40b6o2b6o2b6o$40b6o2b6o2b6o11$
40b6o2b6o4b2o$40b6o2b6o4b2o$44b2o2b2o2b2o2b4o$44b2o2b2o2b2o2b4o12b49o$
42b4o2b2o2b2o4b2o12b49o$42b4o2b2o2b2o4b2o12b49o$44b2o2b2o2b2o4b2o$44b
2o2b2o2b2o4b2o$40b6o2b6o2b6o$40b6o2b6o2b6o11$40b6o2b6o2b6o$40b6o2b6o2b
6o$40b2o6b2o2b2o6b2o$40b2o6b2o2b2o6b2o10b257o$40b6o2b2o2b2o6b2o10b257o
$40b6o2b2o2b2o6b2o10b257o$44b2o2b2o2b2o6b2o$44b2o2b2o2b2o6b2o$40b6o2b
6o6b2o$40b6o2b6o6b2o11$40b6o2b6o2b6o$40b6o2b6o2b6o$40b2o6b2o2b2o2b2o2b
2o$40b2o6b2o2b2o2b2o2b2o10b513o$40b6o2b2o2b2o2b6o10b513o$40b6o2b2o2b2o
2b6o10b513o$44b2o2b2o2b2o6b2o$44b2o2b2o2b2o6b2o$40b6o2b6o2b6o$40b6o2b
6o2b6o11$34b2o4b6o2b6o4b2o$34b2o4b6o2b6o4b2o$32b4o4b2o2b2o6b2o2b4o$32b
4o4b2o2b2o6b2o2b4o12b1021o$34b2o4b2o2b2o2b6o4b2o12b1021o$34b2o4b2o2b2o
2b6o4b2o12b1021o$34b2o4b2o2b2o2b2o8b2o$34b2o4b2o2b2o2b2o8b2o$32b6o2b6o
2b6o2b6o$32b6o2b6o2b6o2b6o11$32b6o2b6o2b2o2b2o2b6o$32b6o2b6o2b2o2b2o2b
6o$36b2o2b2o2b2o2b2o2b2o6b2o$36b2o2b2o2b2o2b2o2b2o6b2o10b1025o$32b6o2b
2o2b2o2b6o4b4o10b1025o$32b6o2b2o2b2o2b6o4b4o10b1025o$32b2o6b2o2b2o6b2o
6b2o$32b2o6b2o2b2o6b2o6b2o$32b6o2b6o6b2o2b6o$32b6o2b6o6b2o2b6o11$32b6o
4b2o4b2o2b2o2b6o$32b6o4b2o4b2o2b2o2b6o$36b2o2b4o4b2o2b2o2b2o$36b2o2b4o
4b2o2b2o2b2o14b121o$32b6o4b2o4b6o2b6o10b121o$32b6o4b2o4b6o2b6o10b121o$
32b2o8b2o8b2o6b2o$32b2o8b2o8b2o6b2o$32b6o2b6o6b2o2b6o$32b6o2b6o6b2o2b
6o11$32b2o2b2o2b6o2b6o2b6o3bo$32b2o2b2o2b6o2b6o2b6o2b3o$32b2o2b2o6b2o
2b2o2b2o2b2o2b2o3bo$32b2o2b2o6b2o2b2o2b2o2b2o2b2o10b105o$32b6o2b6o2b6o
2b6o10b105o$32b6o2b6o2b6o2b6o10b105o$36b2o2b2o6b2o2b2o6b2o$36b2o2b2o6b
2o2b2o6b2o$36b2o2b6o2b6o2b6o$36b2o2b6o2b6o2b6o11$32b6o2b6o2b6o2b6o3bo$
32b6o2b6o2b6o2b6o2b3o$32b2o10b2o6b2o6b2o3bo$32b2o10b2o6b2o6b2o10b69o$
32b6o2b6o2b6o4b4o10b69o$32b6o2b6o2b6o4b4o10b69o$36b2o2b2o6b2o10b2o$36b
2o2b2o6b2o10b2o$32b6o2b6o2b6o2b6o$32b6o2b6o2b6o2b6o11$32b6o2b6o2b6o4b
2o5bo$32b6o2b6o2b6o4b2o4b3o$32b2o2b2o2b2o2b2o2b2o2b2o2b4o5bo$32b2o2b2o
2b2o2b2o2b2o2b2o2b4o12b97o$32b6o2b6o2b6o4b2o12b97o$32b6o2b6o2b6o4b2o
12b97o$32b2o2b2o2b2o2b2o6b2o4b2o$32b2o2b2o2b2o2b2o6b2o4b2o$32b6o2b6o2b
6o2b6o$32b6o2b6o2b6o2b6o11$24b2o2b2o2b6o2b6o2b6o2b6o3bo$24b2o2b2o2b6o
2b6o2b6o2b6o2b3o$24b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o6b2o3bo$24b2o2b2o2b
2o2b2o2b2o2b2o2b2o2b2o6b2o10b89o$24b6o2b2o2b2o2b6o2b2o2b2o6b2o10b89o$
24b6o2b2o2b2o2b6o2b2o2b2o6b2o10b89o$28b2o2b2o2b2o2b2o2b2o2b2o2b2o6b2o$
28b2o2b2o2b2o2b2o2b2o2b2o2b2o6b2o$28b2o2b6o2b6o2b6o6b2o$28b2o2b6o2b6o
2b6o6b2o11$18b2o4b6o2b2o2b2o2b2o2b2o2b2o2b2o4b2o5bo$18b2o4b6o2b2o2b2o
2b2o2b2o2b2o2b2o4b2o4b3o$16b4o4b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b4o5bo$
16b4o4b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b4o12b113o$18b2o4b6o2b6o2b6o2b6o
4b2o12b113o$18b2o4b6o2b6o2b6o2b6o4b2o12b113o$18b2o4b2o2b2o6b2o6b2o6b2o
4b2o$18b2o4b2o2b2o6b2o6b2o6b2o4b2o$16b6o2b6o6b2o6b2o6b2o2b6o$16b6o2b6o
6b2o6b2o6b2o2b6o11$16b6o2b6o2b6o2b6o2b6o2b6o3bo$16b6o2b6o2b6o2b6o2b6o
2b6o2b3o$16b2o2b2o6b2o2b2o6b2o2b2o6b2o2b2o7bo$16b2o2b2o6b2o2b2o6b2o2b
2o6b2o2b2o14b161o$16b6o4b4o2b6o2b2o2b2o2b6o2b6o10b161o$16b6o4b4o2b6o2b
2o2b2o2b6o2b6o10b161o$20b2o6b2o6b2o2b2o2b2o2b2o10b2o$20b2o6b2o6b2o2b2o
2b2o2b2o10b2o$16b6o2b6o2b6o2b6o2b6o2b6o$16b6o2b6o2b6o2b6o2b6o2b6o11$2b
2o4b6o2b6o2b6o2b6o2b6o2b6o4b2o5bo$2b2o4b6o2b6o2b6o2b6o2b6o2b6o4b2o4b3o
$4o4b2o2b2o2b2o2b2o2b2o6b2o2b2o2b2o2b2o6b2o2b4o5bo$4o4b2o2b2o2b2o2b2o
2b2o6b2o2b2o2b2o2b2o6b2o2b4o12b169o$2b2o4b6o2b2o2b2o2b6o2b2o2b2o2b6o4b
4o4b2o12b169o$2b2o4b6o2b2o2b2o2b6o2b2o2b2o2b6o4b4o4b2o12b169o$2b2o8b2o
2b2o2b2o6b2o2b2o2b2o2b2o2b2o6b2o4b2o$2b2o8b2o2b2o2b2o6b2o2b2o2b2o2b2o
2b2o6b2o4b2o$6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$6o2b6o2b6o2b6o2b6o2b6o2b6o
2b6o11$6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o3bo$6o2b6o2b6o2b6o2b6o2b6o2b6o2b
6o2b3o$4b2o2b2o2b2o6b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o6b2o3bo$4b2o2b
2o2b2o6b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o6b2o10b181o$2b4o2b2o2b2o6b2o
2b6o2b6o2b6o2b6o4b4o10b181o$2b4o2b2o2b2o6b2o2b6o2b6o2b6o2b6o4b4o10b
181o$4b2o2b2o2b2o6b2o6b2o6b2o6b2o6b2o6b2o$4b2o2b2o2b2o6b2o6b2o6b2o6b2o
6b2o6b2o$6o2b6o6b2o2b6o2b6o2b6o2b6o2b6o$6o2b6o6b2o2b6o2b6o2b6o2b6o2b6o
!

Never posted this until now but apparently I discovered this sequence on April 19th, 2025 in the Discord server, posting it on the forums on the 23rd of July that year

I have been investigating an interesting adjustable oscillator in this rule plus S4c.
An example oscillator in this series (p8):

Code: Select all

x = 14, y = 14, rule = B2n3-enqy4cijrwyz5cinqy6kn78/S01e2ein3eikry4-iry5-aeky6ein7e8
2bo$2bo$4o$2b2o$4bo$5bo$6bo$7bo$8bo$9bo$10b2o$10b4o$11bo$11bo!

The sequence of oscillator periods in this series, starting from a(1) = 3, where no diagonal line "segment" exists between the two otherwise-p2 halves, begins:

Code: Select all

3, 3, 2, 2, 5, 5, 8, 8, 13, 13, 2, 2, 27, 27, 12, 12, 37, 37, 16, 16, 32, 32, 28, 28, 2, 2, 2, 2, 29, 29, 56, 56, 24, 24...

a(n) = a(n+1) if n ≡ 1 (mod 2). In other words, every other term is the same as the previous term.
There are some interesting things to note about this sequence (to be more specific, the sequence where every other term is removed): for example, if n is of the form 2^x * 3, where x >= 0, then a(n-2) = 2^(x+2). (This is a conjecture, by the way.)
Other conjectures:

1. If n is a power of two and n >= 4 then a(n-2) = 2.
2. If n is of the form 2^x * 10, where x >= 0, then a(n-2) = 2^(x+2) * 3.
3. If n is of the form 2 * 4^x - 1, where x >= 0, then a(n) = 8 * (4^x) - 5.
4. If n is of the form 4^x - 1, where x >= 1, then a(n) = 2 * (4^x) - 3.

[LuveelVoom]

Why is it that Life seems to have so many more things that just… coincidentally work, than any other rule? See, for example, transparent block and beehive for the Herschel, half-baked knightship reaction, three blocks reflector, long boat spin, traffic stop, et cetera, et cetera…

Is it because it’s been investigated so much? Is it that Life’s dynamics (a very close-to-optimally-interesting mix of discrete chaotic reactions) lend themselves naturally to coincidences like that? Is it because it’s a totalistic rule and so has more ways to create common objects?

[TheWayOfTheCon]

Why is it that Life seems to have so many more things that just… coincidentally work, than any other rule? See, for example, transparent block and beehive for the Herschel, half-baked knightship reaction, three blocks reflector, long boat spin, traffic stop, et cetera, et cetera…

It's definitely just the heavy investigation Life has seen. Most of these really are just random assortments of objects and reactions that happen to do something neat. And consider all the other combinations that wouldn't give you something like that.

[LuveelVoom]

It's definitely just the heavy investigation Life has seen. Most of these really are just random assortments of objects and reactions that happen to do something neat. And consider all the other combinations that wouldn't give you something like that.

After stumbling into a tiny p46 in Tables and a tiny stable reflector in TTs, I’m starting to see why this is the case. You just need to look in the right spot

[Aleph]

There of course is also the kind of gold that spreads out among many rules: think of 5S for example or non-2XOR replicators and their associated fractals.

[R2INT]

I recently had an interesting game idea...
What if we took Pass the Rule but made it so that Day and Night independently have to add interesting patterns to their agar? Then, it would be like Day and Night getting into a transition war of who gets the more interesting rule.

To prevent relativistic transitions, Day cannot add B0, B1c, B1e, or B2a. Similarly, Night cannot remove S8, S7c, S7e, and S6a. Additionally, Day and Night cannot modify the two modifications the opposing team made to prevent an edit war.

Usually, one team makes the other team's rule less interesting, but occasionally Night might add an interesting oscillator into Day, or Day might restore Night's glider. Additionally, Day could add in transitions like B2k and B2n to make Night more explosive, ultimately favoring Day.

An example sequence could be like:

Code: Select all

Start: B/S012345678:
N: B3i/S012345678
D: B3i/S0123456-e78
N: B3ai/S0123456-e78
D: B3ai/S012345-i6-e78
N: B3ai/S012345-iy6-e78
D: B3ai6a/S012345-iy6-e78 starting work on my spaceship
N: B3ai6a/S0123-a45-iy6-e78 preparing to add the glider
D: B3ai5r6a/S0123-a45-iy6-e78 for a protected c/2o spaceship
N: B3ain5r6a/S0123-a45-iy6-e78
D: B3ain5r6ai/S0123-a45-iy6-e78
N: B3ain5r6ai/S01e23-a45-iy6-e78
D: B3ainr5r6ai/S01e23-a45-iy6-e78
N: B3ainr5r6ai/S023-a45-iy6-e78
D: B3ainr4t5r6ai/S023-a45-iy6-e78
N: B3aijnr4t5r6ai/S023-a45-iy6-e78
D: B3aijnr4t5r6ai7e/S023-a45-iy6-e78
N: B3aijnr4t5r6ai7e/S023-a4-k5-iy6-e78 for the protected glider
D: B3aijnr4t5jr6ai7e/S023-a4-k5-iy6-e78
N: B3aijnr4t5jr6ai7e/S023-a4-k5-iny6-e78
D: B3aijnr4t5cjr6ai7e/S023-a4-k5-iny6-e78
N: B3aijnr4t5cjr6ai7e/S023-a4-ak5-iny6-e78
D: B3aijnr4t5cjqr6ai7e/S023-a4-ak5-iny6-e78
N: B3aijnr4t5cjqr6ai7e/S023-a4-ak5-iny6-ek78 to attack D for being too stable for N to be interesting
D: B3aijnr4t5cjqr6aik7e/S023-a4-ak5-iny6-ek78 to counter N
N: B3aijnr4t5cjqr6aik7e/S23-a4-ak5-iny6-ek78 finally getting around to removing S0
D: B3-ekqy4t5cjqr6aik7e/S23-a4-ak5-iny6-ek78
N: B3-ekqy4t5cjqr6aik7e/S23-an4-ak5-iny6-ek78 sacrificing the glider for stability and changing my protection to the bullet
D: B3-ekqy4t5cjqr6aik7e/S23-an4-akw5-iny6-ek78 for a 4V reaction
N: B3-ekqy4t5cjqr6aik7e/S23-an4-akrw5-iny6-ek78 now N is more stable
D: B3-ekqy4t5cjqr6aik7e8/S23-an4-akrw5-iny6-ek78 to sacrifice dots
N: B3-ekqy4t5cjqr6aik7e8/S23-an4-aekrw5-iny6-ek78
D: B3-ekqy4t5cjqr6aik7e8/S23-a4-aekrw5-iny6-ek78 to restore your glider while stabilizing me
N: B3-ekqy4t5cjqr6aik7e8/S2-c3-a4-aekrw5-iny6-ek78 making D explosive oh hey cool osc in D
D: B3-ekqy4et5cjqr6aik7e8/S2-c3-a4-aekrw5-iny6-ek78 to restabilize
N: B3-ekqy4et5cjqr6aik7e8/S2-cn3-a4-aekrw5-iny6-ek78 interesting osc
D: B3-ekqy4eqt5cjqr6aik7e8/S2-cn3-a4-aekrw5-iny6-ek78

Additionally, each team can secure their smallest spaceship when they choose to, such that the opposing team cannot break it, unless it is large enough to prevent significant modification to the rule. Only small spaceships with 3-5 cells minpop and low period can be protected.