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3456/278/5 (multiple state rule)

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3456/278/5 (multiple state rule)

Postby Extrementhusiast » February 9th, 2010, 2:33 am

This is the thread for this specific multi-state rule that I like to call "Space Station" because there are "filaments" that extend through space. Anybody found a side rake for 4x2 spaceships?
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Re: 3456/278/5 (multiple state rule)

Postby Axaj » February 9th, 2010, 10:45 pm

An interesting variant of "Star Wars." By the way, are there any Generations search programs?

EDIT: A diagonal pillar construction:
x = 22, y = 22, rule = 3456/278/5
3.ABCD$3.ABCD$4.ABCD$2A3.ABCD$2BA3.ABCD$2CBA3.ABCD$2DCBA3.ABCD$2.DCBA
3.ABCD$3.DCBA3.ABCD$4.DCBA3.ABCD$5.DCBA3.ABCD$6.DCBA3.ABCD$7.DCBA3.AB
CD$8.DCBA3.ABCD$9.DCBA3.ABCD$10.DCBA3.ABCD$11.DCBA3.ABCD$12.DCBA$13.D
CBA$14.DCB$15.DC$16.D!


Adding one more 1-tail on one makes a gun:
x = 22, y = 23, rule = 3456/278/5
3.ABCD$3.ABCD$4.ABCD$2A3.ABCD$2BA3.ABCD$2CBA3.ABCD$2DCBA3.ABCD$2.DCBA
3.ABCD$3.DCBA3.ABCD$4.DCBA3.ABCD$5.DCBA3.ABCD$6.DCBA3.ABCD$7.DCBA3.AB
CD$8.DCBA3.ABCD$9.DCBA3.ABCD$10.DCBA3.ABCD$11.DCBA3.ABCD$12.DCBA$13.D
CBA$14.DCBA$15.DCB$16.DC$17.D!


EDIT2: If this doesn't scream "omniperiodic", I don't know what does.
x = 37, y = 38, rule = 3456/278/5
14.BA$12.A2.A2.A2.A2.A$11.15A$10.3A2.A2.A2.A2.3A$9.3A13.3A$8.3A15.3A$
7.3A17.3A$6.3A19.3A$5.3A21.3A$4.3A23.3A$3.3A25.3A$2.3A27.3A$.3A29.3A$
3A31.3A$.A33.A$.A33.A$3A31.3A$.A33.A$.A33.A$3A31.3A$.A33.A$.A33.A$3A
31.3A$.A33.A$.A33.A$3A31.3A$.3A29.3A$2.3A27.3A$3.3A25.3A$4.3A23.3A$5.
3A21.3A$6.3A19.3A$7.3A17.3A$8.3A15.3A$9.3A13.3A$10.3A2.A2.A2.A2.3A$
11.15A$12.A2.A2.A2.A2.A!


EDIT3: Extensible spaceship:
x = 8, y = 26, rule = 3456/278/5
5.D$5.C$5.B2D$5.A2C$2.2A2.2B$2.2B2.2A$2.2C$2.2D5$3.C$2.D.D3$2.2A$.D2B
D$.D2CA$.A.A$DB4A$C.2C.B$B5A$A.2A$.4A$2.2A!
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Re: 3456/278/5 (multiple state rule)

Postby Extrementhusiast » February 13th, 2010, 11:48 pm

Excuse me? Could you make visuals or instruct me how to view the code?
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Re: 3456/278/5 (multiple state rule)

Postby Axaj » February 14th, 2010, 9:31 pm

Extrementhusiast wrote:Excuse me? Could you make visuals or instruct me how to view the code?


These paste fine in Golly.

EDIT: Omniperiodic for all periods possible (due to 5 states, 5 is minimum period):
x = 54, y = 13, rule = 3456/278/5
3.A2.A2.A$2.9A$.3A2.A2.3A39.A$3A.DCBA2.3A16.A11.DC7.B.A$.A7.D.A8.DC6.
B.A10.A.B5.C.3A$.A.A5.C.A8.A.B4.C.3AD7.4A4.D.3A$3AB5.B3A5.5A4.D3A.C6.
3A7.3A.D$.A.C5.A.A6.B.A8.A.B5.4A7.3A.C$.A.D7.A7.CD9.A6.B.A9.A.B$3A2.A
BCD.3A25.CD10.A$.3A2.A2.3A$2.9A$3.A2.A2.A!
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Re: 3456/278/5 (multiple state rule)

Postby knightlife » February 20th, 2010, 12:20 pm

Extrementhusiast wrote:Anybody found a side rake for 4x2 spaceships?


Here is a p48 sideways rake, not optimal but works:
x = 65, y = 80, rule = 3456/278/5
9.B$8.CDCA$5.BC.B.B.B.A$6.2AB.AC4A$4.B2A.C.B5A$4.C.C.D.D.A.A$5.D3.C$
6.CD17$5.D$8.D3.A$3.DAD5.A.A$3.CBA.D.C2AB3A$5.ABC.BD5A$4.CDAC.C.C.A$
7.D.DB$8.C50.DCBA$56.2DAB.A.A$19.ABCD4.2A2.ABCD8.ABCD5.D2.ABC.AC4A$
19.ABCD4.2B2.ABCD2.BA4.ABCD4.C3.ABC2AC4A$27.2C5.B3CB13.D3.DA.A.A.A$
27.2D4.ABA2DCA19.ABA$35.C2.DBA$35.D3.CBA$39.DCB$40.DCA$41.DB$42.CA$
42.DB$43.C$43.D4$43.2A7.2A$35.ABA5.2B7.2BA$34.BCDCB4.2C6.ACA$33.CD2.A
.A2.D.DBA.ACB.D2A$22.DB10.B.3A2.A.B2.3A.A.ACA.A.A$22.2C9.DCA2.6A.2A2B
11A$23.CB9.BD.D.A3.ACD.3A.A.A.AC3A$23.D11.A2C4.A2B2.C.CA.AD.BDAB3A$
36.B.D4.2A2.D.D2.C.ABDAB3A$37.AC2D7.C3.D.2C.A.A$33.D4.B2C15.DCBA$33.C
4.A2B$33.BD4.2A$33.AC2D$34.B2C$34.A2B$35.2A2$8.A$6.ABCB$C6.A.A.A14.D$
DCB3.2ADAB3A12.C2D$BCD2.D.3AB3A7.D4.B2C$2.C6.A.A9.C4.A2B$6.D3.A10.BD
4.2A$21.AC2D29.DCBA$17.D4.B2C26.2DAB.A.A$22.A2B.ABCD8.ABCD5.D2.ABC.AC
4A$23.2A.ABCD8.ABCD4.C3.ABC2AC4A$47.D3.DA.A.A.A$54.ABA!


A "natural" dual rake was observed and then trimmed down to get a single 4x2 spaceship sideways rake.
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Re: 3456/278/5 (multiple state rule)

Postby Axaj » February 20th, 2010, 11:22 pm

knightlife wrote:
Extrementhusiast wrote:Anybody found a side rake for 4x2 spaceships?


Here is a p48 sideways rake, not optimal but works:
x = 65, y = 80, rule = 3456/278/5
9.B$8.CDCA$5.BC.B.B.B.A$6.2AB.AC4A$4.B2A.C.B5A$4.C.C.D.D.A.A$5.D3.C$
6.CD17$5.D$8.D3.A$3.DAD5.A.A$3.CBA.D.C2AB3A$5.ABC.BD5A$4.CDAC.C.C.A$
7.D.DB$8.C50.DCBA$56.2DAB.A.A$19.ABCD4.2A2.ABCD8.ABCD5.D2.ABC.AC4A$
19.ABCD4.2B2.ABCD2.BA4.ABCD4.C3.ABC2AC4A$27.2C5.B3CB13.D3.DA.A.A.A$
27.2D4.ABA2DCA19.ABA$35.C2.DBA$35.D3.CBA$39.DCB$40.DCA$41.DB$42.CA$
42.DB$43.C$43.D4$43.2A7.2A$35.ABA5.2B7.2BA$34.BCDCB4.2C6.ACA$33.CD2.A
.A2.D.DBA.ACB.D2A$22.DB10.B.3A2.A.B2.3A.A.ACA.A.A$22.2C9.DCA2.6A.2A2B
11A$23.CB9.BD.D.A3.ACD.3A.A.A.AC3A$23.D11.A2C4.A2B2.C.CA.AD.BDAB3A$
36.B.D4.2A2.D.D2.C.ABDAB3A$37.AC2D7.C3.D.2C.A.A$33.D4.B2C15.DCBA$33.C
4.A2B$33.BD4.2A$33.AC2D$34.B2C$34.A2B$35.2A2$8.A$6.ABCB$C6.A.A.A14.D$
DCB3.2ADAB3A12.C2D$BCD2.D.3AB3A7.D4.B2C$2.C6.A.A9.C4.A2B$6.D3.A10.BD
4.2A$21.AC2D29.DCBA$17.D4.B2C26.2DAB.A.A$22.A2B.ABCD8.ABCD5.D2.ABC.AC
4A$23.2A.ABCD8.ABCD4.C3.ABC2AC4A$47.D3.DA.A.A.A$54.ABA!


A "natural" dual rake was observed and then trimmed down to get a single 4x2 spaceship sideways rake.


A more compact p11:
x = 30, y = 22, rule = 3456/278/5
18.C$16.BD.D$13.A.C.C.CADC.AD2.D$11.5ADB.C2BA.B3A.C$11.3AB2AC.D.B.D.A
C2AB$13.A.A4.C.CD.C.A.A$3.A3.D6.A.BAD.2B4.BA$2.A.A2.C3.C3.ABC.C.A$3AB
2ABA2.2DB3.DCABD$3ABADBA3.C4.DCB.C2D$2.A.A.2C11.AB2C$2.ABCD14.A2B$21.
2A2$18.C$16.BD.D$13.A.C.C.CADC$11.5ADB.CBA$11.3AB2AC.D.ABC$13.A.A5.DA
D$14.A3.D$21.D!
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Re: 3456/278/5 (multiple state rule)

Postby knightlife » February 21st, 2010, 4:12 am

Axaj wrote:
knightlife wrote:
Extrementhusiast wrote:Anybody found a side rake for 4x2 spaceships?


Here is a p48 sideways rake, not optimal but works:
x = 65, y = 80, rule = 3456/278/5
9.B$8.CDCA$5.BC.B.B.B.A$6.2AB.AC4A$4.B2A.C.B5A$4.C.C.D.D.A.A$5.D3.C$
6.CD17$5.D$8.D3.A$3.DAD5.A.A$3.CBA.D.C2AB3A$5.ABC.BD5A$4.CDAC.C.C.A$
7.D.DB$8.C50.DCBA$56.2DAB.A.A$19.ABCD4.2A2.ABCD8.ABCD5.D2.ABC.AC4A$
19.ABCD4.2B2.ABCD2.BA4.ABCD4.C3.ABC2AC4A$27.2C5.B3CB13.D3.DA.A.A.A$
27.2D4.ABA2DCA19.ABA$35.C2.DBA$35.D3.CBA$39.DCB$40.DCA$41.DB$42.CA$
42.DB$43.C$43.D4$43.2A7.2A$35.ABA5.2B7.2BA$34.BCDCB4.2C6.ACA$33.CD2.A
.A2.D.DBA.ACB.D2A$22.DB10.B.3A2.A.B2.3A.A.ACA.A.A$22.2C9.DCA2.6A.2A2B
11A$23.CB9.BD.D.A3.ACD.3A.A.A.AC3A$23.D11.A2C4.A2B2.C.CA.AD.BDAB3A$
36.B.D4.2A2.D.D2.C.ABDAB3A$37.AC2D7.C3.D.2C.A.A$33.D4.B2C15.DCBA$33.C
4.A2B$33.BD4.2A$33.AC2D$34.B2C$34.A2B$35.2A2$8.A$6.ABCB$C6.A.A.A14.D$
DCB3.2ADAB3A12.C2D$BCD2.D.3AB3A7.D4.B2C$2.C6.A.A9.C4.A2B$6.D3.A10.BD
4.2A$21.AC2D29.DCBA$17.D4.B2C26.2DAB.A.A$22.A2B.ABCD8.ABCD5.D2.ABC.AC
4A$23.2A.ABCD8.ABCD4.C3.ABC2AC4A$47.D3.DA.A.A.A$54.ABA!


A "natural" dual rake was observed and then trimmed down to get a single 4x2 spaceship sideways rake.


A more compact p11:
x = 30, y = 22, rule = 3456/278/5
18.C$16.BD.D$13.A.C.C.CADC.AD2.D$11.5ADB.C2BA.B3A.C$11.3AB2AC.D.B.D.A
C2AB$13.A.A4.C.CD.C.A.A$3.A3.D6.A.BAD.2B4.BA$2.A.A2.C3.C3.ABC.C.A$3AB
2ABA2.2DB3.DCABD$3ABADBA3.C4.DCB.C2D$2.A.A.2C11.AB2C$2.ABCD14.A2B$21.
2A2$18.C$16.BD.D$13.A.C.C.CADC$11.5ADB.CBA$11.3AB2AC.D.ABC$13.A.A5.DA
D$14.A3.D$21.D!


Even more compact:
x = 22, y = 12, rule = 3456/278/5
17.A$16.BCB$14.A.A.A.BA$12.3ABAD3A$12.5AD4A$8.D5.A.C.ACA$6.C10.5A$.A.
A.DBD.DB6.A.A$6A.D.2CA2.DCBA$4ACA.D.DB3.DCBA$.A.A.2BD$2.ABCD!
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Re: 3456/278/5 (multiple state rule)

Postby Axaj » February 21st, 2010, 12:57 pm

A 1-step advancer:
x = 63, y = 108, rule = 3456/278/5
2D$2C$2B$2A3$7.2D$7.2C$7.2B$7.2A3$14.2D$14.2C$14.2B$14.2A3$21.2D$21.
2C$21.2B$21.2A3$28.2D$28.2C$28.2B$28.2A3$35.2D$35.2C$35.2B$35.2A3$42.
2D$42.2C$42.2B$42.2A$59.ABCD$59.ABCD$49.2D$49.2C$49.2B$49.2A3$56.2D$
56.2C$56.2B$56.2A2$59.ABCD$59.ABCD2$56.2A$56.2B$56.2C$56.2D3$49.2A$
49.2B$49.2C$49.2D3$42.2A$42.2B$42.2C$42.2D3$35.2A$35.2B$35.2C$35.2D3$
28.2A$28.2B$28.2C$28.2D3$21.2A$21.2B$21.2C$21.2D3$14.2A$14.2B$14.2C$
14.2D3$7.2A$7.2B$7.2C$7.2D3$2A$2B$2C$2D!
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Re: 3456/278/5 (multiple state rule)

Postby Extrementhusiast » February 22nd, 2010, 5:27 pm

Doesn't paste in my version. What version of Golly do you use?
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Re: 3456/278/5 (multiple state rule)

Postby Sokwe » February 22nd, 2010, 5:54 pm

Extrementhusiast wrote:Doesn't paste in my version. What version of Golly do you use?

It should work in any version of Golly that supports the 'generations' rules (2.0 and up). I use version 2.1 (the most recent), and it works fine.

Here's something interesting in this rule. A diagonal wave produces the Sierpiński triangle:
x = 433, y = 436, rule = 3456/278/5
431.2A$430.A2B$429.ABCA$428.ABCD$427.ABCD$426.ABCD$425.ABCD$424.ABCD$
423.ABCD$422.ABCD$421.ABCD$420.ABCD$419.ABCD$418.ABCD$417.ABCD$416.AB
CD$415.ABCD$414.2ACD$414.A.A$412.5A.A$411.A.2A2CAB$410.4AC3A.D$410.3A
2CA2.B$408.6AB.2BDC$407.A.A2B2D2ACAC$406.6AB2C.D$406.3A2C2.ABDC$404.
6A2BD$403.A.A2B2D.A2CD$402.7ACD2.B$402.3A2C2.2BCD$400.6ABC2DA$399.A.A
2B2D2ABC$398.6AB2C2.ABD$398.3A2C2.AB2D2.C$396.6A2BD2.A2CD$395.A.A2B2D
.A2CD.2B$394.7ACD2.B2.2A$394.3A2C2.2BCDA$392.6ABC2D2ABC$391.A.A2B2D2A
BC3.ADC$390.6AB2C4.D2.BCD$390.3A2C2.AB2D5.ABCD$388.6A2BD2.AC6.ABC$
387.A.A2B2D.A2CD.B7.AB2D$386.7ACD2.2BCD8.A2C$386.3A2C2.2BCD.A11.2B$
384.6ABC2D2ABC12.2A$383.A.A2B2D2ABC2.AB2D$382.6AB2C4.D.A2C$382.3A2C2.
AB2D5.2B$380.6A2BD3.C5.2A$379.A.A2B2D.A2CD$378.7ACD2.B$378.3A2C2.2BCD
$376.6ABC2DA$375.A.A2B2D2ABC$374.6AB2C4.D21.D$374.3A2C2.AB2D24.C$372.
6A2BD3.C24.BD$371.A.A2B2D.A2CD26.ACD$370.7ACD2.B28.BCD$370.3A2C2.2BCD
29.ABCD$368.6ABC2DA32.ABC$367.A.A2B2D2ABC34.AB2D$366.6AB2C4.D33.A2C$
366.3A2C2.AB2D37.2B$364.6A2BD3.C37.2A$363.A.A2B2D.A2CD$362.7ACD2.B$
362.3A2C2.2BCD$360.6ABC2DA$359.A.A2B2D2ABC$358.6AB2C4.D$358.3A2C2.AB
2D$356.6A2BD2.AC$355.A.A2B2D.A2CD.B$354.7ACD2.2BCD44.D$354.3A2C2.2BCD
.A46.C$352.6ABC2D2ABC47.BD$351.A.A2B2D2ABC2.AB2D45.ACD$350.6AB2C4.D.A
2C33.D12.BCD$350.3A2C2.AB2D5.2B33.C12.ABCD$348.6A2BD3.C5.2A33.BD12.AB
C$347.A.A2B2D.A2CD42.ACD12.AB2D$346.7ACD2.B31.D12.BCD12.A2C$346.3A2C
2.2BCD32.C12.ABCD12.2B$344.6ABC2DA34.BD12.ABC12.2A$343.A.A2B2D2ABC35.
ACD12.AB2D$342.6AB2C4.D21.D12.BCD12.A2C$342.3A2C2.AB2D24.C12.ABCD12.
2B$340.6A2BD3.C24.BD12.ABC12.2A$339.A.A2B2D.A2CD26.ACD12.AB2D$338.7AC
D2.B28.BCD12.A2C$338.3A2C2.2BCD29.ABCD12.2B$336.6ABC2DA32.ABC12.2A$
335.A.A2B2D2ABC34.AB2D$334.6AB2C4.D33.A2C33.D$334.3A2C2.AB2D37.2B33.C
$332.6A2BD3.C37.2A33.BD$331.A.A2B2D.A2CD74.ACD$330.7ACD2.B76.BCD$330.
3A2C2.2BCD77.ABCD$328.6ABC2DA80.ABC$327.A.A2B2D2ABC82.AB2D$326.6AB2C
4.D53.D27.A2C$326.3A2C2.AB2D56.C28.2B$324.6A2BD3.C56.BD27.2A$323.A.A
2B2D.A2CD58.ACD$322.7ACD2.B60.BCD$322.3A2C2.2BCD61.ABCD$320.6ABC2DA
64.ABC$319.A.A2B2D2ABC66.AB2D$318.6AB2C4.D65.A2C$318.3A2C2.AB2D69.2B$
316.6A2BD3.C69.2A$315.A.A2B2D.A2CD$314.7ACD2.B95.D$314.3A2C2.2BCD96.C
$312.6ABC2DA98.BD$311.A.A2B2D2ABC99.ACD$310.6AB2C4.D85.D12.BCD$310.3A
2C2.AB2D88.C12.ABCD$308.6A2BD3.C88.BD12.ABC$307.A.A2B2D.A2CD90.ACD12.
AB2D$306.7ACD2.B92.BCD12.A2C$306.3A2C2.2BCD93.ABCD12.2B$304.6ABC2DA
96.ABC12.2A$303.A.A2B2D2ABC98.AB2D$302.6AB2C4.D97.A2C$302.3A2C2.AB2D
101.2B$300.6A2BD3.C101.2A$299.A.A2B2D.A2CD$298.7ACD2.B$298.3A2C2.2BCD
$296.6ABC2DA$295.A.A2B2D2ABC$294.6AB2C4.D117.D$294.3A2C2.AB2D120.C$
292.6A2BD3.C120.BD$291.A.A2B2D.A2CD122.ACD$290.7ACD2.B124.BCD$290.3A
2C2.2BCD125.ABCD$288.6ABC2DA128.ABC$287.A.A2B2D2ABC130.AB2D$286.6AB2C
4.D129.A2C$286.3A2C2.AB2D133.2B$284.6A2BD3.C133.2A$283.A.A2B2D.A2CD$
282.7ACD2.B$282.3A2C2.2BCD$280.6ABC2DA$279.A.A2B2D2ABC$278.6AB2C4.D$
278.3A2C2.AB2D$276.6A2BD3.C$275.A.A2B2D.A2CD$274.7ACD2.B$274.3A2C2.2B
CD$272.6ABC2DA$271.A.A2B2D2ABC$270.6AB2C4.D$270.3A2C2.AB2D$268.6A2BD
3.C$267.A.A2B2D.A2CD$266.7ACD2.B$266.3A2C2.2BCD$264.6ABC2DA$263.A.A2B
2D2ABC$262.6AB2C4.D$262.3A2C2.AB2D$260.6A2BD3.C$259.A.A2B2D.A2CD$258.
7ACD2.B$258.3A2C2.2BCD$256.6ABC2DA$255.A.A2B2D2ABC$254.6AB2C4.D$254.
3A2C2.AB2D$252.6A2BD3.C$251.A.A2B2D.A2CD$250.7ACD2.B$250.3A2C2.2BCD$
248.6ABC2DA$247.A.A2B2D2ABC$246.6AB2C4.D$246.3A2C2.AB2D$244.6A2BD3.C$
243.A.A2B2D.A2CD$242.7ACD2.B$242.3A2C2.2BCD$240.6ABC2DA$239.A.A2B2D2A
BC$238.6AB2C4.D$238.3A2C2.AB2D$236.6A2BD3.C$235.A.A2B2D.A2CD$234.7ACD
2.B$234.3A2C2.2BCD$232.6ABC2DA$231.A.A2B2D2ABC$230.6AB2C4.D$230.3A2C
2.AB2D$228.6A2BD3.C$227.A.A2B2D.A2CD$226.7ACD2.B$226.3A2C2.2BCD$224.
6ABC2DA$223.A.A2B2D2ABC$222.6AB2C4.D$222.3A2C2.AB2D$220.6A2BD3.C$219.
A.A2B2D.A2CD$218.7ACD2.B$218.3A2C2.2BCD$216.6ABC2DA$215.A.A2B2D2ABC$
214.6AB2C4.D$214.3A2C2.AB2D$212.6A2BD3.C$211.A.A2B2D.A2CD$210.7ACD2.B
$210.3A2C2.2BCD$208.6ABC2DA$207.A.A2B2D2ABC$206.6AB2C4.D$206.3A2C2.AB
2D$204.6A2BD3.C$203.A.A2B2D.A2CD$202.7ACD2.B$202.3A2C2.2BCD$200.6ABC
2DA$199.A.A2B2D2ABC$198.6AB2C4.D$198.3A2C2.AB2D$196.6A2BD3.C$195.A.A
2B2D.A2CD$194.7ACD2.B$194.3A2C2.2BCD$192.6ABC2DA$191.A.A2B2D2ABC$190.
6AB2C4.D$190.3A2C2.AB2D$188.6A2BD3.C$187.A.A2B2D.A2CD$186.7ACD2.B$
186.3A2C2.2BCD$184.6ABC2DA$183.A.A2B2D2ABC$182.6AB2C4.D$182.3A2C2.AB
2D$180.6A2BD3.C$179.A.A2B2D.A2CD$178.7ACD2.B$178.3A2C2.2BCD$176.6ABC
2DA$175.A.A2B2D2ABC$174.6AB2C4.D$174.3A2C2.AB2D$172.6A2BD3.C$171.A.A
2B2D.A2CD$170.7ACD2.B$170.3A2C2.2BCD$168.6ABC2DA$167.A.A2B2D2ABC$166.
6AB2C4.D$166.3A2C2.AB2D$164.6A2BD3.C$163.A.A2B2D.A2CD$162.7ACD2.B$
162.3A2C2.2BCD$160.6ABC2DA$159.A.A2B2D2ABC$158.6AB2C4.D$158.3A2C2.AB
2D$156.6A2BD3.C$155.A.A2B2D.A2CD$154.7ACD2.B$154.3A2C2.2BCD$152.6ABC
2DA$151.A.A2B2D2ABC$150.6AB2C4.D$150.3A2C2.AB2D$148.6A2BD3.C$147.A.A
2B2D.A2CD$146.7ACD2.B$146.3A2C2.2BCD$144.6ABC2DA$143.A.A2B2D2ABC$142.
6AB2C4.D$142.3A2C2.AB2D$140.6A2BD3.C$139.A.A2B2D.A2CD$138.7ACD2.B$
138.3A2C2.2BCD$136.6ABC2DA$135.A.A2B2D2ABC$134.6AB2C4.D$134.3A2C2.AB
2D$132.6A2BD3.C$131.A.A2B2D.A2CD$130.7ACD2.B$130.3A2C2.2BCD$128.6ABC
2DA$127.A.A2B2D2ABC$126.6AB2C4.D$126.3A2C2.AB2D$124.6A2BD3.C$123.A.A
2B2D.A2CD$122.7ACD2.B$122.3A2C2.2BCD$120.6ABC2DA$119.A.A2B2D2ABC$118.
6AB2C4.D$118.3A2C2.AB2D$116.6A2BD3.C$115.A.A2B2D.A2CD$114.7ACD2.B$
114.3A2C2.2BCD$112.6ABC2DA$111.A.A2B2D2ABC$110.6AB2C4.D$110.3A2C2.AB
2D$108.6A2BD3.C$107.A.A2B2D.A2CD$106.7ACD2.B$106.3A2C2.2BCD$104.6ABC
2DA$103.A.A2B2D2ABC$102.6AB2C4.D$102.3A2C2.AB2D$100.6A2BD3.C$99.A.A2B
2D.A2CD$98.7ACD2.B$98.3A2C2.2BCD$96.6ABC2DA$95.A.A2B2D2ABC$94.6AB2C4.
D$94.3A2C2.AB2D$92.6A2BD3.C$91.A.A2B2D.A2CD$90.7ACD2.B$90.3A2C2.2BCD$
88.6ABC2DA$87.A.A2B2D2ABC$86.6AB2C4.D$86.3A2C2.AB2D$84.6A2BD3.C$83.A.
A2B2D.A2CD$82.7ACD2.B$82.3A2C2.2BCD$80.6ABC2DA$79.A.A2B2D2ABC$78.6AB
2C4.D$78.3A2C2.AB2D$76.6A2BD3.C$75.A.A2B2D.A2CD$74.7ACD2.B$74.3A2C2.
2BCD$72.6ABC2DA$71.A.A2B2D2ABC$70.6AB2C4.D$70.3A2C2.AB2D$68.6A2BD3.C$
67.A.A2B2D.A2CD$66.7ACD2.B$66.3A2C2.2BCD$64.6ABC2DA$63.A.A2B2D2ABC$
62.6AB2C4.D$62.3A2C2.AB2D$60.6A2BD3.C$59.A.A2B2D.A2CD$58.7ACD2.B$58.
3A2C2.2BCD$56.6ABC2DA$55.A.A2B2D2ABC$54.6AB2C4.D$54.3A2C2.AB2D$52.6A
2BD3.C$51.A.A2B2D.A2CD$50.7ACD2.B$50.3A2C2.2BCD$48.6ABC2DA$47.A.A2B2D
2ABC$46.6AB2C4.D$46.3A2C2.AB2D$44.6A2BD3.C$43.A.A2B2D.A2CD$42.7ACD2.B
$42.3A2C2.2BCD$40.6ABC2DA$39.A.A2B2D2ABC$38.6AB2C4.D$38.3A2C2.AB2D$
36.6A2BD3.C$35.A.A2B2D.A2CD$34.7ACD2.B$34.3A2C2.2BCD$32.6ABC2DA$31.A.
A2B2D2ABC$30.6AB2C4.D$30.3A2C2.AB2D$28.6A2BD3.C$27.A.A2B2D.A2CD$26.7A
CD2.B$26.3A2C2.2BCD$24.6ABC2DA$23.A.A2B2D2ABC$22.6AB2C4.D$22.3A2C2.AB
2D$20.6A2BD3.C$19.A.A2B2D.A2CD$18.7ACD2.B$18.3A2C2.2BCD$16.6ABC2DA$
15.A.A2B2D2ABC$14.6AB2C4.D$14.3A2C2.AB2D$12.6A2BD3.C$11.A.A2B2D.A2CD$
10.7ACD2.B$10.3A2C2.2BCD$8.6ABC2DA$7.A.A2B2D2ABC$6.6AB2C4.D$6.3A2C2.A
B2D$4.6ABCD3.C$3.A.A2B2D$2.31A$2.3ACA.A.A.A.A.A.A.A.6A.3A$3ABADA.B.AC
.AC2.DAB2A.A3.CA$3ABAD2ADCB3.D7.DBD.D$2.A.A.A.B13.CAC.C$4.BCB16.BABD$
5.A18.A!

I have not yet been able to stabilize the bottom of the wave properly, however.

Edit: It is possible to create guns of all periods above 7 by a simple spaceship duplicator and stable reflectors. This pattern demonstrates the principle:
x = 44, y = 61, rule = 3456/278/5
2.A$.3A$2.A$2.A$.3A$2.A$2.A$.3A$2.A$2.A$.3A$2.A$2.A$.2A2.A2.A$2.8A$2.
A2.A2.A$.2A$2.A$2.2A8.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A$.2A8.33A$2.A9.A
2.A3.A3.A3.A3.A3.A3.A2.A$2.A2.A2.A10.A7.A7.A$.9A8.3A5.3A5.3A$2.A2.A2.
A10.A7.A7.A$2.A$.2A$2.2A$2.A$.2A37.A$2.A2.A33.3A$2.5A33.A$.2A2.A34.A$
2.A36.3A$2.A37.A$.3A36.A$2.A34.A2.2A$2.A33.5A$.3A33.A2.A$2.A37.2A$40.
A$39.2A$2.2A36.2A$2.2B36.A$2.2C33.A2.A$2.2D32.6A$37.A2.A$40.A$40.2A$
2.2A35.2A$2.2B36.A$2.2C36.2A$2.2D33.A2.A$36.5A$8.A7.A7.A12.A2.2A$7.3A
5.3A5.3A14.A$8.A7.A7.A15.A$.A2.A3.A3.A3.A3.A3.A3.A2.A7.3A$33A7.A$.A2.
A2.A2.A2.A2.A2.A2.A2.A2.A2.A8.A$39.3A$40.A!

Period-5 guns often occur randomly. The only gun that is missing is p6.

period-7 gun:
x = 49, y = 63, rule = 3456/278/5
.A.A.D$.B3AC$.C.A.B$.D.A.A$2.3A$3.A$3.A$.4AD$.B.A2.CBA3.DCBA$.C.A.DCB
A3.DCBA$.D3A.D$3.A$3.A3.ABCD$2.2A2.A2.A$.A.8A$.B.A2.A2.A$.C2A.DC.CBA$
.D.A3.D4.CBA3.DCBA3.DCBA3.DCBA3.DCBA3.DC$3.2A6.D.A2.A2.A2.A2.A2.A2.A
2.A2.A2.A2.A2.A.B$2.2A.A6.37A$3.A.ABCD4.A2.A3.A3.A3.A3.A3.A3.A2.A2.A$
.A.A2.A2.A5.DCBA.A4.DB.A.2A2.D.A.2CBA$.B10A2.DCB5A2.DC4AB3.C3ADBA3.2D
$.C.A2.A2.A.B8.A.A2.B2.A.C2.DB.A7.2C$.D.A5.DC8.DCB7.D5.A8.2B$2.2A.A
38.2A$3.2ABA$3.A.CB$.3A.CD37.DC$.B.A2.A35.D.A.B$.C.5A34.C4A$.D2A2.A.A
33.B.A$3.A.2CB34.A.A$3.A.DBA35.3A$2.3A35.CD2.A.D$.A.A35.BD3.A.C$.B.A
34.AC.A2.2AB$.C4A33.B5A.A$.D.A.B33.A.A2.A$3.DC39.2A$41.D2.A$41.CD2A.D
$3.2A35.ABC.2AC$3.2B36.2A.A.B$3.2C36.A2.A.A$3.2D34.D6A$39.C.A2.A$40.B
A2.A$44.2AD$3.2A38.2A.C$3.2B35.CD2.A.B$3.2C35.ABC.3A$3.2D20.AB14.A2.A
$10.A5.D7.BCDC12.5A$9.A.BD2.C.A2.B2.A.A2.D12.A2.2A$5.ABD3AC3.B4ACD2.
3A13.DCB.A.D$.BA.AB2C.A.D2.2A.A.BD4.A3.ABCD8.AB.A.C$C.A2.A3.A3.A3.A3.
A3.A3.A2.A9.4AB$D33A2.ABCD4.A.A$2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A.D.A
BCD4.A$3.ABCD3.ABCD3.ABCD3.ABCD3.ABC9.3A$42.A.A$43.BCD!
-Matthias Merzenich
Sokwe
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Re: 3456/278/5 (multiple state rule)

Postby knightlife » February 23rd, 2010, 1:05 am

Example of a p6 gun with converter to get 4x2 stream:
x = 34, y = 30, rule = 3456/278/5
12.D2.BC$11.C.A.A.D$11.6A6.A$12.A2.3A4.3A$12.2A.A.AB4.A$12.2A2.A.A$
12.2A2.A.A$12.2A.A.AB4.A$12.A2.3A4.3A$11.6A6.A$11.C.A.A.D$12.D2.BC7$.
D2.BC$C.A.A.D$6A26.A$.A2.3A24.3A$.2A.A.AB24.A$.2A2.A.A$.2A2.A.A$.2A.A
.AB24.A$.A2.3A24.3A$6A26.A$C.A.A.D$.D2.BC!


Here is an interesting "natural" binary counter construction I have not seen before in any rule:
x = 53, y = 35, rule = 3456/278/5
47.DCBA$26.D17.CD2B.A.A$26.A15.D.BD.AC4A$25.B.BA12.AB2.C.AC4A$23.B.3A
4.D3.D2.C.A.A.ADABA.A$23.C5AD.C4.DAD12A$23.D.3A.D.DCD.CB.BC.A.A.3A.A$
25.A.A2.2C2.DBDC2D.DA.CB2A$25.D.D2.2BD2.CB2.C2.D2.2A$26.C3.2A12$18.2A
$18.2BA$17.A2CB$15.AB.2DC$3.D9.D.B2C2.DB2.A$3.A7.D.D.DCD.C.C2AB$.AB.B
A8.CA.3AB2.AC2D$2.ABA2.DCBADC.A.A.B.A.3A.A$D2AB2A.DCB.AB5ACAD2AB5A$C.
3A.A3.ABC.A.A.D3.A.AC3A$2.C.CB8.ABD.2C.CD.BDAB3A$3.BA13.D2.C.ABDAB3A$
21.D.2C.A.A$25.DCBA!
knightlife
 
Posts: 566
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Re: 3456/278/5 (multiple state rule)

Postby Sokwe » February 23rd, 2010, 2:52 am

knightlife wrote:Example of a p6 gun with converter to get 4x2 stream

Unfortunately, the converter causes the gun to be pseudo-period. Here is a multi-step converter that preserves the period (can certainly be improved upon):
x = 52, y = 103, rule = 3456/278/5
7.A2.A2.A2.A2.A2.A2.A$6.21A$7.A17.A$12.BCD2.ABC2D$11.ACD2.ABCD$11.BD
2.ABCD$10.AC2.ABCD2.2A$10.BD.ABCD2.A2B$9.AC.ABCD2.AB2C$9.BD.BCD2.ABC
2D$9.C.ACD2.ABCD$9.D.BD2.ABCD$10.AC2.ABCD2.2A24.BA.DC$10.BD.ABCD2.A2B
23.C.A.A.B$9.AC.ABCD2.AB2C22.D.5A$9.BD.BCD2.ABC2D.ABCD2.ABCD2.ABCD2.A
BC.3A2.A$9.C.ACD2.ABCD2.ABCD2.ABCD2.ABCD2.ABCD2A.A.2A$9.D.B.A2.A2.A2.
BCD2.ABCD2.ABCD2.ABCD3.A2.2A$11.10A.BCD2.ABCD2.ABCD2.ABCD3.A2.2A$13.A
5.A.2ABCD2.ABCD2.ABCD2.ABCD2A.A.2A$13.DC3.D4.ABCD2.ABCD2.ABCD2.ABC.3A
2.A$18.CD24.D.5A$18.BC2D23.C.A.A.B$18.AB2C24.BA.DC$19.A2B$20.2A$18.D$
18.CD$18.BC2D$18.AB2C$19.A2B$20.2A$18.D$18.CD$18.BC2D$18.AB2C$19.A2B$
20.2A$.A16.D$3A15.CD$.A16.BC2D$.A16.AB2C$2A17.A2B$.A.ABCD2.ABCD2.ABCD
3.A$.A.ABCD2.ABCD2.ABCD2.A$2A2.ABCD2.ABCD2.ABCD3A$.A3.ABCD2.ABCD2.ABC
.A.D$.A19.A.C$2A19.2AB$.A19.A.A$.A19.A$2A19.2A.DCBA2.DCBA$.A19.A2.DCB
A2.DCBA$.A19.A$2A19.3A$.A19.A.B$.A.D2.ABCD2.ABCD2.AB.A.C$2A3.ABCD2.AB
CD2.ABC3AD$.A2.ABCD2.ABCD2.ABCD.A$.A2.ABCD2.ABCD2.ABCD$2A18.2A$.A17.A
2B$.A16.AB2C$3A15.BC2D$.A16.CD$18.D$20.2A$19.A2B$18.AB2C$18.BC2D$18.C
D$18.D$20.2A$19.A2B$18.AB2C$18.BC2D$18.CD$18.D$20.2A$19.A2B24.A.DCB$
18.AB2C23.B.A.A.A$18.BC2D22.C.5A$12.DCB3.CD4.ABCD2.ABCD2.ABCD2.ABD3A
2.A$13.A5.A3.ABCD2.ABCD2.ABCD2.ABC.A.A.2A$10.D.9ADABCD2.ABCD2.ABCD2.A
BCD2.A2.2A$9.C.A.A2.A2.A2.ABCD2.ABCD2.ABCD2.ABCD2.A2.2A$9.BD.BCD2.ABC
2D.ABCD2.ABCD2.ABCD2.ABC.A.A.2A$9.AC.ABCD2.AB2C2.ABCD2.ABCD2.ABCD2.AB
D3A2.A$10.BD.ABCD2.A2B22.C.5A$10.AC2.ABCD2.2A23.B.A.A.A$9.D.BD2.ABCD
27.A.DCB$9.C.ACD2.ABCD$9.BD.BCD2.ABC2D$9.AC.ABCD2.AB2C$10.BD.ABCD2.A
2B$10.AC2.ABCD2.2A$9.D.BD2.ABCD$11.ACD2.ABCD$12.BCD2.ABC2D$12.ABCD2.A
B2C$7.A17.A$6.21A$7.A2.A2.A2.A2.A2.A2.A!


Edit: here's a much smaller one:
x = 28, y = 54, rule = 3456/278/5
22.CB2.D$21.D.A.A.C$22.6A$9.A3.D2.ABCD.3A2.A$8.3A2D2.ABCD.BA.A.2A$.A
2.A2.3A.B2.ABCD2.A.A2.2A$9A.CD2.ABCD2.A.A2.2A$.A5.A.2BCD2.ABCD.BA.A.
2A$8.2A.BCD2.ABCD.3A2.A$6.D15.6A$6.CD13.D.A.A.C$6.BC2D12.CB2.D$6.AB2C
$7.A2B$8.2A2$8.C$7.A.D$6.3A.C$7.3A.B$8.4A$9.A$9.A$9.2AD$9.A.C$9.A.B$
9.3A2.DCBA2.DCBA$9.A.A2.DCBA2.DCBA$9.A.B$9.2AC$9.A.D$9.A$8.3A$7.3A.A$
6.3A.B$7.A.C$7.DBD$7.D$6.D$8.2A$7.A2B$6.AB2C$6.BC2D12.CB2.D$6.CD13.D.
A.A.C$6.D15.6A$8.2A.BCD2.ABCD.3A2.A$.A5.A.2BCD2.ABCD.BA.A.2A$9A.CD2.A
BCD2.A.A2.2A$.A2.A2.3A.B2.ABCD2.A.A2.2A$8.3A2D2.ABCD.BA.A.2A$9.A3.D2.
ABCD.3A2.A$22.6A$21.D.A.A.C$22.CB2.D!
-Matthias Merzenich
Sokwe
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Re: 3456/278/5 (multiple state rule)

Postby knightlife » February 23rd, 2010, 8:18 am

Sokwe wrote:Unfortunately, the converter causes the gun to be pseudo-period.


I didn't realize the converter was doing that, I was only interested in the resulting stream.

Here is a smaller gun that is a true p6:
x = 11, y = 9, rule = 3456/278/5
8.DC$5.DB2A.B$2.D2.A.4A$3.ABCD.A$3.ABCD.A$5.A.4A$.A3.DB2A.B$3A5.DC$.A
!


This precursor is for a different p6 dual gun and is only 5 x 6:
x = 5, y = 6, rule = 3456/278/5
3A.A$.3A$2.A$2.A$.3A$3A.A!


EDIT:
Another p6 gun starts with a 3 x 8 pattern but makes wide spaceships:
x = 3, y = 8, rule = 3456/278/5
A$2A$2A$A.A$A.A$2A$2A$A!
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Re: 3456/278/5 (multiple state rule)

Postby calcyman » February 23rd, 2010, 12:08 pm

Here is an interesting "natural" binary counter construction I have not seen before in any rule:


Very interesting -- Your pattern has a growth rate of O(t log t). There is a 'natural' O(t log t) pattern in Life called "Gott's dots". It should be in your "Golly/HashLife" directory. Despite its name, it was actually discovered by Bill Gosper, and WedGe-GRoW (named after Gosper) was discovered by Nick Gotts.

In your pattern, note the interesting effect of 'tunneling gliders'. A spaceship appears to propagate through the static columns, just behind the puffer. In reality, it is an optical illusion, caused by the fact that both the 'tunneling' spaceship and the puffer travel at the same velocity.


Generations rules seem rich in these binary-counting mechanisms; here is a discovery of mine in Brian's Brain:

x = 60, y = 61, rule = /2/3
50.A2.A$48.BA4B$49.2A2.BA$52.2A$48.B3.BA$48.2A.ABA$49.BA2.A$49.B4.B$
49.BA2.BA$41.AB.AB.AB.2A.A$41.AB.AB.AB2.2BA$50.A2.B$51.BA5$24.ABA$25.
B11.2A$11.B14.AB9.2B$.A3.ABA3.2AB$B.B3.B3.B2A24.2A$2.3ABA2.3AB24.2B$A
2.B4.AB8.ABA$8B11.B17.2A$A6.A12.AB15.2B3.AB2.B$39.3BA2.2A$36.A.2A.A3.
ABA$35.B.BA3.A3.B$12.ABA20.A.B4.2BA2B$13.B22.B2AB.7AB$14.AB23.AB$54.B
$53.A.4AB$53.B2.2BA$6.ABA45.3B$7.B45.A3BA$8.AB47.A$53.BA.B2.B$54.A2B.
BA$54.A2.BA$14.AB22.AB.AB.AB.AB.AB.AB$14.AB.AB19.AB2.B2.B.AB.AB.AB.2A
.B$16.AB22.AB2ABA10.2BA$56.A$42.2A$3.2A37.2B$3.2B$42.2A$3.2A37.2B$3.
2B$42.2A$3.2A2.B.A.BA29.2B$3.2B3A.2B2.B$6.B2.2B.A29.2A2.B.A.BA$.ABA2.
2B.3BA29.2B3A.2B2.B$2.BA.B2.2A.2AB31.B2.2B.A$2.A2.AB7.A25.ABA2.2B.3BA
$3.B2.AB5.B27.BA.B2.2A.2AB$41.A2.AB7.A$42.B2.AB5.B!


I found it completely by accident, and is related to the ruler sequence. It is qualitatively similar to your pattern, but has a completely different internal mechanism, and a different (more mundane) growth rate.

The most striking feature of my pattern is the fact that (after a large, Hyperspeed-fueled amount of time) the bottom-left corner of the pattern has perfect fractal self-similarity. Successive magnifications appear identical, due to the power-of-two zooming in Golly.
What do you do with ill crystallographers? Take them to the mono-clinic!
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Re: 3456/278/5 (multiple state rule)

Postby Extrementhusiast » February 26th, 2010, 11:52 pm

OK, that explains it. I don't have the updated version of Golly! (so it doesn't support Generations)

EDIT: Now I do! Here's quadratic growth:
x = 90, y = 65, rule = 3456/278/5
36.7A$30.6A7.2A$30.A14.A$29.A16.2A$29.A18.A$29.A19.2A$28.A21.3A$28.A
20.A2.2A$28.A20.A3.3A$27.A20.A6.2A$27.A20.A7.3A$28.A18.A9.3A16.A$28.A
18.A11.2A14.A$29.A17.A12.A13.A$29.A16.A13.2A11.A$30.A15.A14.A10.A$30.
A14.A15.2A8.A$31.A13.A16.2A6.A$31.A13.A16.2A5.A$32.A11.A18.2A3.A$32.A
11.A18.2A2.A$33.A9.A20.3A$33.A9.A21.A$34.A8.A20.3A$34.A7.A20.A2.2A$
35.A6.A19.A3.2A$35.A6.A18.A5.2A$36.A5.A17.A6.2A14.2A$37.A3.A2.29A7.4A
$37.A2.4A14.A9.A.A2.9A$35.5A.A15.A11.2A7.2A$30.5A3.A.A15.A12.A.A3.3A$
26.4A4.4A.2A14.A14.2A.2A$21.8A5.A3.4A12.A15.3A$17.6A6.8A2.2A.3A7.2A
15.2A2.A$12.5A2.2A13.A2.12A2.A15.2A2.A.A$7.5A6.A15.A4.A.A3.6A15.A4.A
2.A$3.4A11.A15.A4.A.A6.5A11.2A5.A2.A$3A16.A15.A2.A3.A4.A4.2A8.2A7.A3.
A$19.2A14.A2.A3.A3.A6.3A5.A10.A2.A$21.4A11.A.A4.A.A9.2A2.2A11.A3.A$
25.3A8.2A5.2A12.2A13.A4.A$28.4A4.2A4.A.A11.4A12.A4.A$32.6A.3A2.A10.A
4.2A10.A5.A$36.7A2.A7.2A6.2A10.A4.A$36.A6.7A.2A10.2A8.A5.A$36.A10.2A.
6A8.2A7.A6.A$36.A11.2A6.6A4.2A5.A6.A$35.A11.A2.A11.8A3.A7.A$35.A9.2A
4.2A14.4A3.A7.A$35.A7.2A8.A17.4A7.A$35.A6.A11.A17.6A5.A$34.A5.2A13.2A
17.2A2.4A.A$34.A4.A17.A17.2A5.2A$34.A3.A19.A16.4A$34.A2.A21.2A14.A.3A
$33.A2.A24.A13.A3.3A$33.A.A26.A12.A4.A.A$33.A.A27.2A10.A5.A.2A$33.2A
30.A9.A6.A2.A$32.2A32.2A7.A7.A2.2A$32.A35.2A5.A8.2A2.A$32.A37.2A3.A
10.A.A$72.2A.A11.A.A$74.2A12.A!


Take out the B78 and quadratic growth reappears, though in a different, spectacular fashion:

x = 90, y = 65, rule = 3456/2/5
36.7A$30.6A7.2A$30.A14.A$29.A16.2A$29.A18.A$29.A19.2A$28.A21.3A$28.A
20.A2.2A$28.A20.A3.3A$27.A20.A6.2A$27.A20.A7.3A$28.A18.A9.3A16.A$28.A
18.A11.2A14.A$29.A17.A12.A13.A$29.A16.A13.2A11.A$30.A15.A14.A10.A$30.
A14.A15.2A8.A$31.A13.A16.2A6.A$31.A13.A16.2A5.A$32.A11.A18.2A3.A$32.A
11.A18.2A2.A$33.A9.A20.3A$33.A9.A21.A$34.A8.A20.3A$34.A7.A20.A2.2A$
35.A6.A19.A3.2A$35.A6.A18.A5.2A$36.A5.A17.A6.2A14.2A$37.A3.A2.29A7.4A
$37.A2.4A14.A9.A.A2.9A$35.5A.A15.A11.2A7.2A$30.5A3.A.A15.A12.A.A3.3A$
26.4A4.4A.2A14.A14.2A.2A$21.8A5.A3.4A12.A15.3A$17.6A6.8A2.2A.3A7.2A
15.2A2.A$12.5A2.2A13.A2.12A2.A15.2A2.A.A$7.5A6.A15.A4.A.A3.6A15.A4.A
2.A$3.4A11.A15.A4.A.A6.5A11.2A5.A2.A$3A16.A15.A2.A3.A4.A4.2A8.2A7.A3.
A$19.2A14.A2.A3.A3.A6.3A5.A10.A2.A$21.4A11.A.A4.A.A9.2A2.2A11.A3.A$
25.3A8.2A5.2A12.2A13.A4.A$28.4A4.2A4.A.A11.4A12.A4.A$32.6A.3A2.A10.A
4.2A10.A5.A$36.7A2.A7.2A6.2A10.A4.A$36.A6.7A.2A10.2A8.A5.A$36.A10.2A.
6A8.2A7.A6.A$36.A11.2A6.6A4.2A5.A6.A$35.A11.A2.A11.8A3.A7.A$35.A9.2A
4.2A14.4A3.A7.A$35.A7.2A8.A17.4A7.A$35.A6.A11.A17.6A5.A$34.A5.2A13.2A
17.2A2.4A.A$34.A4.A17.A17.2A5.2A$34.A3.A19.A16.4A$34.A2.A21.2A14.A.3A
$33.A2.A24.A13.A3.3A$33.A.A26.A12.A4.A.A$33.A.A27.2A10.A5.A.2A$33.2A
30.A9.A6.A2.A$32.2A32.2A7.A7.A2.2A$32.A35.2A5.A8.2A2.A$32.A37.2A3.A
10.A.A$72.2A.A11.A.A$74.2A12.A!
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Re: 3456/278/5 (multiple state rule)

Postby Extrementhusiast » November 11th, 2010, 2:58 am

Because of the recent activity in the Star Wars rule, my interest in this rule has been revitalized. Here is a breeder:
x = 31, y = 120, rule = 3456/278/5
27.BC$25.B.A.D$25.C2AC.C$26.A3.D$24.C2BCD$23.BD4.C$24.CBABD$24.A.CA$
25.B3A$26.2A$25.4A$26.2A$18.ABDA$19.2AB$16.DC3A$19.A.D$18.ABC8$18.D.B
D$17.C.2A$16.B4AC$17.C.A.B$18.D.A8$18.BC.B$17.A.2AC$17.D4A$17.A.A$18.
BCD2$2.D$2.C$2DB$2CA$2B$2A$19.AC$17.D.3A$16.CB3AD$17.D.A.C$4.2A13.AB$
4.2B$4.2C$4.2D5$18.CDAC$17.B.2AD$16.A.3AB$17.B.A.A$18.CD2$3.D$3.C$3.B
D$2.2AC2D$3.BABC9.B$4.CA.B7.CDCA$3.D.B.C4.BC.B.B.B.A$4.2ACBA4.2AB.AC
2AB$3.A.3AC3.CA.C.B3A$4.BC2.B3.BDBD.D.A2.D$16.C5.C$14.D7.BD$21.A.C$4.
CDAC11.DCB.B2D$4.A2BDB10.DCB.A2C$5.AD.CA14.2B$5.2ADB15.2A$2.D.2A.C7.D
CBA$2.BA5.A5.DCBA$.ACD7A$2.BA.6A$3.BC2.A.A.DCBA$2.2AD.A4.DCBA$3.BC2A$
2.BA2DA.D$2.DCBCB.CBA$D3.A2.DCBA$2.2DC3AD$.CB2.2AC$2.D3A.A$3.AC.B$2.
5A$3.2A.3A$2.4A.2B$3.2A2.2C$7.2D5$7.2A$7.2B$7.2C$7.2D2$6.C2.C$6.4D$6.
B2.B$5.DB2ABD$5.C.2C.C$5.B4AB$5.A.2A.A$6.4A$7.2A!


Set memory:
x = 63, y = 35, rule = 3456/278/5
6$17.2D18.2D$17.2C18.2C$17.2B18.2B$17.2A18.2A$13.A19.A$12.3A17.3A$13.
A19.A3$13.CD$12.B.A19.A$12.4A17.3A$14.A19.A!


Read memory:
x = 20, y = 33, rule = 3456/278/5
17.A$16.3A$17.A3$7.CD$16.B.A$16.4A$DCBA14.A$DCBA14$17.A$16.3A$17.A4$18.A$17.3A$DCBA14.A$DCBA!


(Note: This memory actually functions as a NOT gate. To get what the memory actually has, just stick it through another NOT gate again.)


And to solve the question of the p6 gun, here are three dinky ones:
x = 13, y = 12, rule = 3456/278/5
6.2A$6.2B$6.2C$6.2D2$2.A2.C2.C2.A$.6A.5A$5A.A.4A$.A3.A.2A$4.5A.A$5.A
3.3A$10.A!


x = 8, y = 9, rule = 3456/278/5
.B2A$C.A.B$D3AC$.2A.D$.B2.2C$2.D2.A.C$2.CD3AD$2.BC.A$3.ABA!


x = 12, y = 6, rule = 3456/278/5
2.BA2.C3.A$C2ADA.6A$.2A.B3A2.A$.2A2.2A$6A$.A2.A!


The first one has a small rotor, the second one fits in less than a 10x10 box, and the third one has length (not width) 6.
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