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### B3456/S235678/9

Posted: March 26th, 2018, 12:02 am
This is a totalistic Generations rule with some very interesting behaviour. In particular, it has some very high-period natural guns.

This one is p8009 (a prime number!):
x = 17, y = 17, rule = 235678/3456/9
7.3A\$7.3A\$4.HG5AGH\$3.11A\$2.H11AH\$2.G11AG\$2.13A\$17A\$17A\$17A\$2.13A\$2.G
11AG\$2.H11AH\$3.11A\$4.HG5AGH\$7.3A\$7.3A!

And this one is p16725:
x = 19, y = 19, rule = 235678/3456/9
9.B\$5.A2.CBC2.A\$2.15A\$2.15A\$2.15A\$.4A.3A.3A.4A\$2.15A\$2.5A.3A.5A\$.C15A
C\$2B3A.3A.3A.3A2B\$.C15AC\$2.5A.3A.5A\$2.15A\$.4A.3A.3A.4A\$2.15A\$2.15A\$2.
15A\$5.A2.CBC2.A\$9.B!

There are also natural c/10 wickstretchers:
x = 40, y = 40, rule = 235678/3456/9
19.2A\$16.D.A2DA.D\$15.A2EF2AF2EA\$14.AF8AFA\$14.G10AG\$13.GH10AHG\$14.H10A
H\$14.12A\$14.12A\$14.C10AC\$14.C10AC\$14.12A\$12.EF12AFE\$5.G6.F14AF6.G\$3.A
A\$.AF34AFA\$2.E34AE\$.DE34AED\$2.AF32AFA\$3.AG2H2A2C18A2C2A2HGA\$5.G6.F14A
F6.G\$12.EF12AFE\$14.12A\$14.C10AC\$14.C10AC\$14.12A\$14.12A\$14.H10AH\$13.GH
10AHG\$14.G10AG\$14.AF8AFA\$15.A2EF2AF2EA\$16.D.A2DA.D\$19.2A!

There are several natural spaceships, such as this 6c/12:
x = 8, y = 9, rule = 235678/3456/9

This 3c/13:
x = 11, y = 3, rule = 235678/3456/9
.H3.2A.2A\$G4.ABAGFA\$.H3.2A.2A!

This 12c/24:
x = 12, y = 12, rule = 235678/3456/9
3A\$G.2G3A\$.FEF\$2.E!

And this 30c/60:
x = 9, y = 18, rule = 235678/3456/9
2.D.A\$.EFBAB\$G.2F2CA\$H3.BE2A\$4.GEC2A\$3.DGACA\$.2H2E2B\$GH2EABA\$DEF2D2A\$
DEF2D2A\$GH2EABA\$.2H2E2B\$3.DGACA\$4.GEC2A\$H3.BE2A\$G.2F2CA\$.EFBAB\$2.D.A!

There are also a variety of high-period oscillators, such as this p11:
x = 5, y = 5, rule = 235678/3456/9
2.A\$.3A\$5A\$.3A\$2.A!

p13:
x = 14, y = 14, rule = 235678/3456/9
5.H2.H\$5.H2.H2\$5.4A\$4.6A\$2H.8A.2H\$3.8A\$3.8A\$2H.8A.2H\$4.6A\$5.4A2\$5.H2.
H\$5.H2.H!

p14:
x = 14, y = 14, rule = 235678/3456/9
5.4A\$3.2AB2CB2A\$2.BCAF2AFACB\$.AC8ACA\$.12A\$ABF8AFBA\$AC10ACA\$AC10ACA\$AB
F8AFBA\$.12A\$.AC8ACA\$2.BCAF2AFACB\$3.2AB2CB2A\$5.4A!

p17:
x = 8, y = 8, rule = 235678/3456/9
2.A2.A\$.6A\$8A\$.6A\$.6A\$8A\$.6A\$2.A2.A!

p24:
x = 7, y = 6, rule = 235678/3456/9
2.2A\$.ABABA\$AC4A\$.4AC\$3.2AFB\$3.AEA!

p31:
x = 6, y = 6, rule = 235678/3456/9
.3A\$5A\$6A\$6A\$.5A\$2.3A!

p40:
x = 16, y = 16, rule = 235678/3456/9

p55:
x = 18, y = 18, rule = 235678/3456/9
5.A2G2F2GA\$4.10A\$4.10A\$3.12A\$.16A\$18A\$G16AG\$G16AG\$F16AF\$F16AF\$G16AG\$G
16AG\$18A\$.16A\$3.12A\$4.10A\$4.10A\$5.A2G2F2GA!

p64:
x = 6, y = 6, rule = 235678/3456/9
.A.A\$5A\$.5A\$5A\$.5A\$2.A.A!

p66:
x = 22, y = 22, rule = 235678/3456/9

p75:
x = 15, y = 15, rule = 235678/3456/9

p265:
x = 21, y = 21, rule = 235678/3456/9
7.A2.E2.A\$6.A2BFEF2BA\$6.C7AC\$6.9A\$4.13A\$4.13A\$.AC15ACA\$AB17ABA\$.B17AB
\$.F17AF\$2E17A2E\$.F17AF\$.B17AB\$AB17ABA\$.AC15ACA\$4.13A\$4.13A\$6.9A\$6.C7A
C\$6.A2BFEF2BA\$7.A2.E2.A!

p270:
x = 31, y = 31, rule = 235678/3456/9

p892:
x = 23, y = 23, rule = 235678/3456/9
GB17ABG\$.E19AE\$.E19AE\$.H19AH\$.21A\$23A\$.21A\$.H19AH\$.E19AE\$.E19AE\$.GB
11.A!

### Re: B3456/S235678/9

Posted: March 26th, 2018, 3:50 am
Some more patterns from apgsearch:

A 6c/26 puffer:
x = 11, y = 16, rule = 235678/3456/9
\$5.CDC!

A different p13:
x = 8, y = 8, rule = 235678/3456/9
5.D\$.B2CE.A\$.CB3ACA\$.C5A\$.E3AH\$D.2AH\$.ACA\$2.A!

p16:
x = 9, y = 9, rule = 235678/3456/9
6.F\$.BC2EG2A\$.CB4AFA\$.E6A\$.E4AH\$.G4A\$F3AH\$.AFA\$2.A!

p18:
x = 14, y = 14, rule = 235678/3456/9
5.A2BA\$5.B2AB\$4.6A\$3.AB.2A.BA\$2.AB6ABA\$ABA.6A.ABA\$B12AB\$B12AB\$ABA.6A.
ABA\$2.AB6ABA\$3.AB.2A.BA\$4.6A\$5.B2AB\$5.A2BA!

p27:
x = 20, y = 20, rule = 235678/3456/9
6.A2.2E2.A\$3.HGF8AFGH\$2.16A\$.H16AH\$.G16AG\$.F16AF\$20A\$.18A\$.18A\$E18AE\$
E18AE\$.18A\$.18A\$20A\$.F16AF\$.G16AG\$.H16AH\$2.16A\$3.HGF8AFGH\$6.A2.2E2.A!

p107:
x = 24, y = 24, rule = 235678/3456/9
7.2A.H2GH.2A\$6.H.8A.H\$7.10A\$3.BCE12AECB\$3.CB14ABC\$3.E16AE\$.H.18A.H\$A.
20A.A\$24A\$.22A\$H22AH\$G22AG\$G22AG\$H22AH\$.22A\$24A\$A.20A.A\$.H.18A.H\$3.E
16AE\$3.CB14ABC\$3.BCE12AECB\$7.10A\$6.H.8A.H\$7.2A.H2GH.2A!

p280:
x = 8, y = 8, rule = 235678/3456/9
.3A.A\$7A\$8A\$7A\$.7A\$8A\$.7A\$2.A.3A!

EDIT: a new p11:
x = 9, y = 9, rule = 235678/3456/9
3.3A\$3.BAB\$2.5A\$AB5ABA\$4A.4A\$AB5ABA\$2.5A\$3.BAB\$3.3A!