User:H. H. P. M. P. Cole/R3 Cross Isotropic
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Revision as of 08:54, 6 December 2023 by H. H. P. M. P. Cole (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Transition names with 1, 2, 10, and 11 cells can omit the starting 'a'. Transition names with 0 and 12 cells can omit all letters.
Semantics is the same as Hensel notation, but the transitions are delineated by dot separators.
Example rulestring:
B3-bk45/S1a6ab.cdXb.o/N+
Note that X, E and D represent 10, 11 and 12 respectively.
The set of rules containing B2a.c is relativistic, but B2a and B2c alone are not.
A brief overview of Durnak-Cole notation (WARNING: very tall RLE)
x=127, y = 1322, rule = B/S012345678History
$14.3D6.2D7.3D6.3D6.D.D6.3D6.3D6.3D6.3D6.3D6.D.D6.3D6.2D$14.D.D7.D9.D
8.D6.D.D6.D8.D10.D6.D.D6.D.D6.D.D6.D8.D.D$14.D.D7.D7.3D7.2D6.3D6.3D6.
3D8.D6.3D6.3D7.D7.2D7.D.D$14.D.D7.D7.D10.D8.D8.D6.D.D8.D6.D.D8.D6.D.D
6.D8.D.D$14.3D6.3D6.3D6.3D8.D6.3D6.3D8.D6.3D6.3D6.D.D6.3D6.2D5$15.B8.
B8.B8.B8.B8.B8.B8.B8.B8.B8.B8.B8.A$3F.3F8.B8.B8.B8.B8.B8.B8.B8.B8.B8.
B8.B8.A8.A$2.F3.F8.B8.B8.B8.B8.B8.B8.B8.B8.B8.B8.A8.A8.A$3F.3F5.3BC3B
2.3BC3B2.3BC3B2.3BC3B2.3BC2BA2.3BCB2A2.3BC3A2.2BAC3A2.B2AC3A2.3AC3A2.
3AC3A2.3AC3A2.3AC3A$F.F.F.F8.B8.B8.B8.A8.A8.A8.A8.A8.A8.A8.A8.A8.A$3F
.3F8.B8.B8.A8.A8.A8.A8.A8.A8.A8.A8.A8.A8.A$15.B8.A8.A8.A8.A8.A8.A8.A8.
A8.A8.A8.A8.A3$24.B8.B8.B8.B8.B8.B8.B8.B8.B8.B8.A$3D.D19.B8.B8.B8.B8.
B8.B8.B8.B8.B8.A8.B$2.D.D19.B8.B8.B8.B8.B8.B8.B8.B8.A8.B8.A$3D.3D14.3B
C3B2.3BC3B2.3BC2BA2.3BCBAB2.3BCABA2.2BACB2A2.BABC3A2.ABAC3A2.B2AC3A2.
3AC3A2.3AC3A$D.D.D.D17.B8.A8.B8.A8.A8.A8.A8.A8.A8.A8.A$3D.3D17.A8.B8.
A8.A8.A8.A8.A8.A8.A8.A8.A$24.B8.A8.A8.A8.A8.A8.A8.A8.A8.A8.A3$24.B8.B
8.B8.B8.B8.B8.B8.B8.B8.B8.A$3D21.B8.B8.B8.B8.B8.B8.B8.B8.B8.A8.A$2.D21.
B8.B8.B8.B8.B8.B8.B8.B8.A8.A8.B$3D.3D14.3BC3B2.3BC3B2.3BC2BA2.3BCB2A2.
3BC2AB2.2BACABA2.B2ACB2A2.2ABC3A2.ABAC3A2.B2AC3A2.3AC3A$D.D.D19.A8.A8.
A8.B8.A8.A8.A8.A8.A8.A8.A$3D.3D17.B8.A8.B8.A8.A8.A8.A8.A8.A8.A8.A$24.
B8.B8.A8.A8.A8.A8.A8.A8.A8.A8.A3$33.B8.B8.B8.B8.B8.B8.B8.B8.B$3D3.D26.
B8.B8.B8.B8.B8.B8.B8.B8.A$2.D3.D26.B8.B8.B8.B8.B8.B8.B8.A8.A$3D.3D23.
3BC2BA2.3BC2BA2.3BCB2A2.2BAC2BA2.2BAC2AB2.B2ACABA2.3AC3A2.2ABC3A2.ABA
C3A$D.D.D.D26.B8.A8.A8.A8.A8.A8.B8.A8.A$3D.3D26.B8.A8.B8.A8.A8.A8.A8.
A8.A$33.A8.B8.A8.A8.A8.A8.A8.A8.A3$33.B8.B8.B8.B8.B8.B8.B8.B8.B$3D.3D
26.B8.B8.B8.B8.B8.B8.B8.B8.A$2.D.D.D26.B8.B8.B8.B8.B8.B8.B8.A8.A$3D.3D
23.3BC2BA2.3BCBAB2.3BCB2A2.2BACBAB2.2BAC3A2.B2AC2AB2.3AC3A2.3AC3A2.2A
BC3A$D.D.D28.B8.B8.A8.A8.B8.A8.A8.B8.A$3D.3D26.A8.A8.A8.A8.A8.A8.B8.A
8.A$33.B8.A8.B8.A8.A8.A8.A8.A8.A3$33.B8.B8.B8.B8.B8.B8.B8.B8.B$3D.3D26.
B8.B8.B8.B8.B8.B8.B8.B8.A$2.D.D28.B8.B8.B8.B8.B8.B8.B8.A8.A$3D.3D23.3B
C2BA2.3BCBAB2.3BCA2B2.2BACB2A2.2BAC3A2.B2AC3A2.3AC3A2.3AC3A2.3AC3A$D.
D.D28.A8.A8.A8.B8.A8.B8.A8.A8.B$3D.D28.B8.B8.A8.A8.B8.A8.A8.B8.A$33.B
8.A8.A8.A8.A8.A8.B8.A8.A3$33.B8.B8.B8.B8.B8.B8.B8.B8.B$3D.3D26.B8.B8.
B8.B8.B8.B8.B8.B8.A$2.D.D28.B8.B8.B8.B8.B8.B8.A8.A8.A$3D.D25.3BCBAB2.
3BCBAB2.3BCABA2.2BACB2A2.2BAC3A2.B2AC3A2.2BAC3A2.3AC3A2.3AC3A$D.D.D.D
26.B8.A8.A8.A8.A8.A8.A8.A8.A$3D.3D26.A8.A8.B8.B8.A8.B8.A8.A8.B$33.B8.
B8.A8.A8.B8.A8.A8.B8.A3$33.B8.B8.B8.B8.B8.B8.B8.B8.B$3D.D.D26.B8.B8.B
8.B8.B8.B8.B8.A8.A$2.D.D.D26.B8.B8.B8.B8.B8.B8.A8.B8.A$3D.3D23.3BCBAB
2.3BCB2A2.3BCABA2.2BACB2A2.BABCB2A2.B2AC3A2.BABC3A2.B2AC3A2.3AC3A$D.D
.D.D26.A8.A8.A8.A8.A8.A8.A8.A8.A$3D.D.D26.B8.B8.A8.A8.A8.A8.A8.A8.A$33.
B8.B8.B8.B8.A8.B8.A8.A8.B3$33.B8.B8.B8.B8.B8.B8.B8.B8.A$3D.3D26.B8.B8.
B8.B8.B8.B8.B8.A8.B$2.D2.D27.B8.B8.B8.B8.B8.B8.A8.B8.B$3D2.D24.3BCA2B
2.3BCA2B2.3BC2AB2.2BACA2B2.BABCABA2.A2BC3A2.B2ACB2A2.ABAC3A2.3AC3A$D.
D2.D27.A8.A8.A8.A8.A8.A8.A8.A8.A$3D.3D26.B8.B8.A8.A8.A8.A8.A8.A8.A$33.
B8.A8.B8.A8.A8.A8.A8.A8.A3$33.B8.B8.B8.B8.B8.B8.B8.B8.A$3D.3D26.B8.B8.
B8.B8.B8.B8.B8.A8.B$2.D3.D26.B8.B8.B8.B8.B8.B8.A8.B8.A$3D3.D23.2BAC2B
A2.3BCA2B2.2BAC2BA2.2BACABA2.BABC2AB2.ABACB2A2.B2ACABA2.2ABC3A2.ABAC3A
$D.D.D.D26.B8.A8.B8.B8.A8.A8.A8.A8.A$3D2.2D26.B8.A8.A8.A8.A8.A8.A8.A8.
A$33.B8.B8.A8.A8.A8.A8.A8.A8.A3$33.B8.B8.B8.B8.B8.B8.B8.B8.A$3D.D.D26.
B8.B8.B8.B8.B8.B8.B8.A8.B$2.D.D.D26.B8.B8.B8.B8.B8.B8.A8.B8.A$3D.2D24.
2BACBAB2.2BAC2BA2.2BAC2BA2.2BACABA2.BABC3A2.ABACABA2.B2AC2AB2.3AC3A2.
2ABC3A$D.D.D.D26.B8.B8.A8.A8.B8.A8.A8.B8.A$3D.D.D26.B8.B8.B8.B8.A8.A8.
A8.A8.A$33.B8.A8.A8.A8.A8.A8.A8.A8.A3$33.B8.B8.B8.B8.B8.B8.B8.B8.A$3D
.D28.B8.B8.B8.B8.B8.B8.B8.A8.B$2.D.D28.B8.B8.B8.B8.B8.B8.A8.B8.A$3D.D
25.2BACA2B2.2BAC2BA2.2BAC2BA2.2BACABA2.BABC3A2.ABAC3A2.B2AC3A2.3AC3A2.
3AC3A$D.D.D28.B8.B8.A8.A8.A8.B8.B8.A8.B$3D.3D26.B8.A8.A8.A8.B8.A8.A8.
B8.A$33.B8.B8.B8.B8.A8.A8.A8.A8.A3$33.B8.B8.B8.B8.B8.B8.B8.B8.A$3D2.D
.D25.B8.B8.B8.B8.B8.B8.B8.A8.B$2.D.D.D.D24.B8.B8.B8.B8.B8.B8.A8.B8.A$
3D.D.D.D21.BABC2BA2.2BAC2BA2.2BACBAB2.2BAC2AB2.BABC3A2.ABAC3A2.B2AC3A
2.3AC3A2.3AC3A$D.D.D.D.D24.B8.A8.B8.B8.A8.A8.A8.A8.A$3D.D.D.D24.B8.B8.
A8.A8.A8.B8.B8.A8.B$33.B8.B8.A8.A8.B8.A8.A8.B8.A3$33.B8.B8.B8.B8.B8.B
8.B8.B8.A$3D2.D27.B8.B8.B8.B8.B8.B8.B8.A8.A$2.D.D.D26.B8.B8.B8.B8.B8.
B8.A8.A8.B$3D.D.D23.BABCBAB2.2BACBAB2.2BACBAB2.2BAC2AB2.B2AC2BA2.ABAC
3A2.B2AC3A2.B2ACB2A2.2ABC3A$D.D.D.D26.B8.B8.A8.A8.A8.A8.A8.A8.A$3D.D.
D26.B8.B8.B8.B8.A8.A8.A8.A8.A$33.B8.A8.A8.A8.A8.B8.B8.A8.A3$33.B8.B8.
B8.B8.B8.B8.B8.B8.A$3D.3D26.B8.B8.B8.B8.B8.B8.B8.A8.A$2.D.D.D26.B8.B8.
B8.B8.B8.B8.A8.A8.B$3D.D.D23.A2BC2BA2.2BACBAB2.2BACBAB2.2BAC2AB2.B2AC
B2A2.2ABCB2A2.A2BC3A2.B2ACABA2.3AC3A$D.D.D.D26.B8.B8.A8.A8.B8.A8.A8.A
8.B$3D.3D26.B8.A8.A8.A8.A8.A8.A8.A8.A$33.B8.B8.B8.B8.A8.A8.A8.A8.A3$42.
B8.B8.B8.B8.B8.B8.B$3D.3D35.B8.B8.B8.B8.B8.B8.A$2.D.D.D35.B8.B8.B8.B8.
B8.A8.A$3D.3D32.2BACBAB2.2BACB2A2.2BAC3A2.B2ACB2A2.2ABC3A2.ABACB2A2.B
2AC2AB$D.D.D37.A8.B8.B8.A8.B8.A8.A$3D.D37.B8.B8.B8.B8.A8.A8.A$42.B8.A
8.A8.A8.A8.A8.A3$42.B8.B8.B8.B8.B8.B8.B$3D.3D35.B8.B8.B8.B8.B8.B8.A$2.
D.D.D35.B8.B8.B8.B8.B8.A8.A$3D.3D32.2BACB2A2.2BACB2A2.2BAC3A2.B2ACB2A
2.2ABC3A2.ABACABA2.A2BC3A$D.D3.D35.B8.B8.B8.A8.A8.A8.A$3D3.D35.B8.A8.
A8.A8.B8.A8.A$42.B8.B8.B8.B8.A8.A8.A3$42.B8.B8.B8.B8.B8.B8.B$3D39.B8.
B8.B8.B8.B8.B8.A$2.D39.B8.B8.B8.B8.B8.A8.A$3D.3D32.2BACA2B2.2BACB2A2.
2BAC3A2.B2ACABA2.2ABC3A2.ABAC3A2.ABACB2A$D.D.D37.B8.A8.A8.B8.A8.B8.A$
3D.D37.B8.B8.B8.A8.A8.A8.A$42.A8.B8.B8.A8.B8.A8.A3$42.B8.B8.B8.B8.B8.
B8.B$3D.3D35.B8.B8.B8.B8.B8.B8.A$2.D.D37.B8.B8.B8.B8.B8.A8.A$3D.3D32.
2BACA2B2.2BACA2B2.BABC2BA2.B2ACABA2.3AC3A2.ABAC3A2.ABACABA$D.D3.D35.B
8.B8.A8.A8.B8.A8.A$3D.3D35.A8.A8.A8.B8.B8.B8.A$42.B8.A8.A8.A8.A8.A8.A
3$42.B8.B8.B8.B8.B8.B8.B$3D.3D35.B8.B8.B8.B8.B8.B8.A$2.D2.D36.B8.B8.B
8.B8.B8.A8.A$3D2.D33.2BACA2B2.2BACA2B2.BABCBAB2.B2ACABA2.3AC3A2.ABAC3A
2.ABAC3A$D.D2.D36.A8.A8.A8.A8.B8.A8.B$3D2.D36.B8.B8.A8.A8.A8.A8.A$42.
B8.A8.A8.B8.B8.B8.A3$42.B8.B8.B8.B8.B8.B8.B$3D.D.D35.B8.B8.B8.B8.B8.B
8.A$2.D.D.D35.B8.B8.B8.B8.B8.A8.A$3D.D.D32.2BACABA2.2BACA2B2.BABCB2A2.
B2AC2AB2.3AC3A2.2ABCB2A2.ABAC3A$D.D.D.D35.B8.A8.B8.B8.A8.A8.A$3D.3D35.
B8.A8.A8.A8.B8.A8.B$42.B8.B8.A8.A8.B8.A8.A3$42.B8.B8.B8.B8.B8.B8.B$3D
.D.D35.B8.B8.B8.B8.B8.B8.A$2.D.D.D35.B8.B8.B8.B8.A8.A8.A$3D.D.D32.2BA
C2AB2.2BACABA2.BABCB2A2.B2AC2AB2.2BACB2A2.2ABC3A2.ABAC3A$D.D.D.D35.B8.
B8.A8.A8.A8.B8.A$3D2.D36.B8.B8.B8.B8.A8.A8.A$42.B8.A8.A8.A8.A8.A8.B3$
42.B8.B8.B8.B8.B8.B8.B$3D.D.D.D33.B8.B8.B8.B8.B8.B8.A$2.D.D.D.D33.B8.
B8.B8.B8.A8.A8.A$3D.D.D.D30.BABC2BA2.2BACABA2.BABCB2A2.B2AC2AB2.2BACA
BA2.2ABC3A2.2ABCB2A$D.D.D.D.D33.B8.B8.A8.A8.A8.A8.A$3D2.D.D34.B8.A8.A
8.A8.A8.B8.A$42.A8.B8.B8.B8.A8.A8.A3$42.B8.B8.B8.B8.B8.B8.B$3D.D.D35.
B8.B8.B8.B8.B8.B8.A$2.D.D.D35.B8.B8.B8.B8.A8.A8.A$3D2.D33.BABC2BA2.2B
ACABA2.BABCABA2.B2AC3A2.2BAC2AB2.2ABC3A2.2ABC3A$D.D.D.D35.B8.A8.B8.B8.
A8.A8.B$3D.D.D35.A8.B8.A8.B8.A8.A8.A$42.B8.B8.A8.A8.A8.B8.A3$42.B8.B8.
B8.B8.B8.B8.B$3D.D.D35.B8.B8.B8.B8.B8.B8.A$2.D.D.D35.B8.B8.B8.B8.A8.A
8.A$3D2.D33.BABC2BA2.2BAC2AB2.BABCABA2.B2AC3A2.BABCB2A2.3AC3A2.2ABC3A
$D.D2.D36.A8.B8.A8.B8.A8.B8.A$3D2.D36.B8.B8.B8.A8.A8.B8.B$42.B8.A8.A8.
B8.A8.A8.A3$42.B8.B8.B8.B8.B8.B8.B$3D.3D35.B8.B8.B8.B8.B8.B8.A$2.D3.D
35.B8.B8.B8.B8.A8.A8.A$3D2.D33.BABCBAB2.2BAC2AB2.BABCABA2.B2AC3A2.BAB
CABA2.3AC3A2.2ABC3A$D.D.D37.B8.B8.A8.A8.A8.B8.A$3D.3D35.B8.A8.A8.B8.A
8.A8.A$42.A8.B8.B8.B8.A8.B8.B3$42.B8.B8.B8.B8.B8.B8.B$F3.3F35.B8.B8.B
8.B8.B8.B8.A$F5.F35.B8.B8.B8.B8.A8.A8.A$3F.3F32.BABCBAB2.2BAC2AB2.BAB
C2AB2.A2BCB2A2.BABC2AB2.3AC3A2.3AC3A$F.F.F.F35.B8.A8.B8.A8.A8.A8.B$3F
.3F35.A8.B8.A8.A8.A8.B8.B$42.B8.B8.A8.A8.A8.B8.A3$42.B8.B8.B8.B8.B8.B
8.A$D3.D37.B8.B8.B8.B8.B8.A8.B$D3.D37.B8.B8.B8.B8.A8.B8.B$3D.3D32.BAB
CBAB2.2BAC3A2.BABC2AB2.A2BCABA2.BABC3A2.BABC3A2.ABAC3A$D.D.D.D35.A8.B
8.A8.A8.B8.A8.A$3D.3D35.B8.B8.B8.A8.A8.A8.A$42.B8.B8.A8.A8.A8.A8.A3$42.
B8.B8.B8.B8.B8.B8.A$D41.B8.B8.B8.B8.B8.A8.B$D41.B8.B8.B8.B8.A8.B8.B$3D
.3D32.BABCB2A2.BABC2BA2.BABC2AB2.A2BC3A2.BABC3A2.B2ACB2A2.2ABC3A$D.D.
D37.B8.B8.A8.B8.A8.A8.A$3D.3D35.B8.A8.A8.A8.B8.A8.A$42.B8.A8.B8.A8.A8.
A8.A3$42.B8.B8.B8.B8.B8.B8.A$D5.D35.B8.B8.B8.B8.B8.A8.B$D5.D35.B8.B8.
B8.B8.A8.B8.B$3D.3D32.BABCABA2.BABC2BA2.BABC3A2.A2BC3A2.BABC3A2.B2ACA
BA2.3AC3A$D.D.D.D35.B8.A8.B8.A8.A8.A8.B$3D.3D35.B8.B8.B8.B8.A8.A8.A$42.
B8.A8.A8.A8.B8.A8.A3$42.B8.B8.B8.B8.B8.B8.A$D3.3D35.B8.B8.B8.B8.B8.A8.
B$D3.D.D35.B8.B8.B8.B8.A8.B8.B$3D.3D32.BABC2AB2.BABC2BA2.BABC3A2.A2BC
3A2.B2AC2BA2.B2AC2AB2.3AC3A$D.D.D37.B8.A8.B8.A8.A8.A8.A$3D.3D35.B8.A8.
A8.A8.A8.A8.B$42.B8.B8.B8.B8.A8.A8.A3$42.B8.B8.B8.B8.B8.B8.A$D3.3D35.
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D46.A8.B8.B8.A8.B$2.D.D46.B8.A8.A8.B8.A$3D.3D41.BABC2BA2.BABCBAB2.B2A
C2AB2.A2BCABA2.ABACB2A$D.D.D.D44.B8.A8.B8.A8.A$3D.3D44.A8.B8.B8.A8.B$
51.B8.A8.A8.A8.A3$51.B8.B8.B8.B8.A$2.D48.A8.B8.B8.A8.B$2.D48.B8.A8.A8.
B8.A$3D.3D41.BABCBAB2.BABCBAB2.B2AC2AB2.A2BC3A2.ABACABA$D.D.D46.B8.A8.
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D44.A8.B8.B8.A8.B$2.D3.D44.B8.A8.A8.B8.A$3D.3D41.A2BC2BA2.BABCB2A2.B2A
C2AB2.A2BC3A2.2ABCB2A$D.D.D.D44.B8.B8.A8.A8.B$3D.3D44.B8.B8.B8.B8.A$51.
A8.A8.B8.A8.A3$51.B8.B8.B8.B8.A$2.D.3D44.A8.B8.B8.A8.B$2.D.D.D44.B8.A
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B8.B8.A8.A8.A$3D.3D44.A8.A8.A8.A8.B$51.B8.B8.A8.B8.A3$51.A8.B8.B8.B8.
A$2.D.3D44.B8.B8.B8.A8.A$2.D.D46.B8.A8.A8.B8.B$3D.3D41.A2BC2BA2.BABCB
2A2.A2BCB2A2.ABACB2A2.2ABCB2A$D.D.D46.B8.A8.B8.B8.B$3D.D46.B8.B8.A8.A
8.A$51.A8.B8.A8.A8.A3$60.B8.B8.B$2.D.3D53.B8.B8.A$2.D.D55.A8.A8.B$3D.
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A8.A3$60.B8.B8.B$2.D.D.D53.B8.B8.A$2.D.D.D53.A8.A8.B$3D.3D50.BABCABA2.
A2BCB2A2.ABACB2A$D.D.D.D53.B8.A8.A$3D.D.D53.A8.A8.A$60.B8.B8.B3$60.B8.
B8.B$2.D.3D53.B8.B8.A$2.D2.D54.A8.A8.B$3D2.D51.BABCABA2.A2BCABA2.ABAC
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60.B8.B8.A$3D.D55.A8.A8.B$D.D.D55.B8.B8.B$3D.D52.A2BCABA2.B2ACABA2.AB
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B$3D.3D62.A$D.D.D.D62.B$3D.3D59.A2BCB2A$D5.D62.A$3D3.D62.B$69.A3$69.B
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3D59.2ABCB2A$D3.D64.B$D3.D64.B$69.A!
[[
WIDTH 800
HEIGHT 4096
ZOOM 3
]]Speed limits
- B1a allows patterns to expand outward at 3c. This causes runaway behaviour for all patterns.
- B1b allows patterns to expand outward at a 2c. This causes runaway behaviour for all patterns.
- B2a.c allows patterns to expand outward at a maximum speed of 2c. This causes runaway behaviour for many (but not all) patterns.
- B1c2b allows patterns to expand outward at a maximum speed of c. This causes runaway behaviour for all patterns.
- B3aa allows patterns to expand outward at a maximum speed of c. This does not cause runaway behaviour.
Expanding transitions
- B1a, B1b, B1c, B2a, B2b, B2c, and B3aa allow patterns to expand their bounding box, but due to a peculiarity of the Cross neighbourhood, it also expands their bounding diamond.
- B1a, B1b, B1c, all B2 transitions from a-i, all B3 transitions from aa-aj, all B4 transitions from aa-ai, B5aa, B5ab, B5ac, and B6aa allow patterns to expand their bounding diamond.
Strange peculiarities
- B2a and B2c on their own do not cause runaway behaviour.
- B1c does not cause runaway behaviour. Due to this single-dot oscillators are possible.