Omniperiodic Rules

[drc]

I'm interested in what rules are omniperiodic. Rule tables are allowed, and I need an example of every period up until the arbitrarily high period oscillators, then I just need one.

[BlinkerSpawn]

Can Generations rules be omniperiodicin the sense that every period allowable by the rule is achievable? If so, guns exist for every period in Star Wars, Free Star, and many variants.

Code: Select all

x = 65, y = 66, rule = 0345/2/10
7.2A8.A$7.2B7.3A$7.2C8.A$7.2D8.A$6.F2EFGHI4.2A$5.G.A2.A2.A.A.A36.GFED
CB$5.H9AB.A35.H.A2.A.A$5.I.A5.A.C.2A33.I.6A$7.A5.A.D.A35.2A3.A$6.2A5.
2AE.A34.2A4.A.A$5.A.2A4.A.F.2A31.3A5.2AB$6.B.2A3.A.G.A32.B.A5.A.C$7.C
.6AH.A32.C.A5.A.D$8.D.A2.A.I.2A31.D9AE$9.EFGHI3.A32.E.A2.A2.A.F$17.A
17.IHGFEDCBA2.IHGF.DCBA2.IHG$15.3A6.IHGFE7.A2.A2.A2.A2.A14.A$15.B.A6.
A2.A.DCBA.I30A$15.C.A3.A.6ADCBA.H.A14.A2.A2.A2.A2.A$15.D2A2.B.2A3.A.E
5.GFE.CBA2.I$15.E.A.C.2A4.A.F8.D.A2.A.H$15.F.A.D2A5.2AG8.C6A.G$15.G2A
.E.A5.A.H8.B.A3.2A.F$15.H.A.F.A5.A.I8.A.A4.2A.E$15.I.A.G9A10.2A5.2AD$
16.2A.H.A2.A2.A12.A5.A.C$17.A2.IHGFEDCBA9.I.A5.A.B$15.A.A20.H10A$15.B
3A19.G.A2.A2.A$15.C.A.A19.FEDCBA$16.DCB27.2I$17.2E27.2H$17.2F27.2G$
17.2G27.2F$17.2H27.2E$17.2I27.BCD$20.ABCDEF19.A.A.C$18.A2.A2.A.G19.3A
B$16.10AH20.A.A$16.B.A5.A.I9.ABCDEFGHI2.A$16.C.A5.A12.A2.A2.A.H.2A$
16.D2A5.2A10.9AG.A.I$16.E.2A4.A.A8.I.A5.A.F.A.H$17.F.2A3.A.B8.H.A5.A.
E.2AG$18.G.6AC8.G2A5.2AD.A.F$19.H.A2.A.D8.F.A4.2A.C.A.E$20.I2.ABC.EFG
5.E.A3.2A.B2.2AD$.A2.A2.A2.A2.A14.A.H.ABCD6A.A3.A.C$30AI.ABCD.A2.A6.A
.B$.A14.A2.A2.A2.A2.A7.EFGHI6.3A$5.GHI2.ABCD.FGHI2.ABCDEFGHI17.A$4.F.
A2.A2.A.E32.A3.IHGFE$4.E9AD31.2A.I.A2.A.D$4.D.A5.A.C32.A.H6A.C$4.C.A
5.A.B32.A.G.A3.2A.B$4.B2A5.3A31.2A.F.A4.2A.A$4.A.A4.2A34.A.E2A5.2A$6.
A3.2A35.A.D.A5.A$5.6A.I33.2A.C.A5.A.I$4.A.A2.A.H35.A.B9AH$5.BCDEFG36.
A.A.A2.A2.A.G$46.2A4.IHGF2EF$47.A8.2D$47.A8.2C$46.3A7.2B$47.A8.2A!

[drc]

Can Generations rules be omniperiodicin the sense that every period allowable by the rule is achievable? If so, guns exist for every period in Star Wars, Free Star, and many variants.

Code: Select all

x = 65, y = 66, rule = 0345/2/10
7.2A8.A$7.2B7.3A$7.2C8.A$7.2D8.A$6.F2EFGHI4.2A$5.G.A2.A2.A.A.A36.GFED
CB$5.H9AB.A35.H.A2.A.A$5.I.A5.A.C.2A33.I.6A$7.A5.A.D.A35.2A3.A$6.2A5.
2AE.A34.2A4.A.A$5.A.2A4.A.F.2A31.3A5.2AB$6.B.2A3.A.G.A32.B.A5.A.C$7.C
.6AH.A32.C.A5.A.D$8.D.A2.A.I.2A31.D9AE$9.EFGHI3.A32.E.A2.A2.A.F$17.A
17.IHGFEDCBA2.IHGF.DCBA2.IHG$15.3A6.IHGFE7.A2.A2.A2.A2.A14.A$15.B.A6.
A2.A.DCBA.I30A$15.C.A3.A.6ADCBA.H.A14.A2.A2.A2.A2.A$15.D2A2.B.2A3.A.E
5.GFE.CBA2.I$15.E.A.C.2A4.A.F8.D.A2.A.H$15.F.A.D2A5.2AG8.C6A.G$15.G2A
.E.A5.A.H8.B.A3.2A.F$15.H.A.F.A5.A.I8.A.A4.2A.E$15.I.A.G9A10.2A5.2AD$
16.2A.H.A2.A2.A12.A5.A.C$17.A2.IHGFEDCBA9.I.A5.A.B$15.A.A20.H10A$15.B
3A19.G.A2.A2.A$15.C.A.A19.FEDCBA$16.DCB27.2I$17.2E27.2H$17.2F27.2G$
17.2G27.2F$17.2H27.2E$17.2I27.BCD$20.ABCDEF19.A.A.C$18.A2.A2.A.G19.3A
B$16.10AH20.A.A$16.B.A5.A.I9.ABCDEFGHI2.A$16.C.A5.A12.A2.A2.A.H.2A$
16.D2A5.2A10.9AG.A.I$16.E.2A4.A.A8.I.A5.A.F.A.H$17.F.2A3.A.B8.H.A5.A.
E.2AG$18.G.6AC8.G2A5.2AD.A.F$19.H.A2.A.D8.F.A4.2A.C.A.E$20.I2.ABC.EFG
5.E.A3.2A.B2.2AD$.A2.A2.A2.A2.A14.A.H.ABCD6A.A3.A.C$30AI.ABCD.A2.A6.A
.B$.A14.A2.A2.A2.A2.A7.EFGHI6.3A$5.GHI2.ABCD.FGHI2.ABCDEFGHI17.A$4.F.
A2.A2.A.E32.A3.IHGFE$4.E9AD31.2A.I.A2.A.D$4.D.A5.A.C32.A.H6A.C$4.C.A
5.A.B32.A.G.A3.2A.B$4.B2A5.3A31.2A.F.A4.2A.A$4.A.A4.2A34.A.E2A5.2A$6.
A3.2A35.A.D.A5.A$5.6A.I33.2A.C.A5.A.I$4.A.A2.A.H35.A.B9AH$5.BCDEFG36.
A.A.A2.A2.A.G$46.2A4.IHGF2EF$47.A8.2D$47.A8.2C$46.3A7.2B$47.A8.2A!

I meant in the sense of oscillators, but the guns can be stabilized.:

Code: Select all

x = 87, y = 88, rule = 0345/2/10
18.A$17.3A$18.A9$18.2A8.A$18.2B7.3A$18.2C8.A$18.2D8.A$17.F2EFGHI4.2A$
16.G.A2.A2.A.A.A36.GFEDCB$16.H9AB.A35.H.A2.A.A13.A$16.I.A5.A.C.2A33.I
.6A13.3A$18.A5.A.D.A35.2A3.A15.A$17.2A5.2AE.A34.2A4.A.A$16.A.2A4.A.F.
2A31.3A5.2AB$17.B.2A3.A.G.A32.B.A5.A.C$18.C.6AH.A32.C.A5.A.D$19.D.A2.
A.I.2A31.D9AE$20.EFGHI3.A32.E.A2.A2.A.F$28.A17.IHGFEDCBA2.IHGF.DCBA2.
IHG$26.3A6.IHGFE7.A2.A2.A2.A2.A14.A$26.B.A6.A2.A.DCBA.I30A$26.C.A3.A.
6ADCBA.H.A14.A2.A2.A2.A2.A$26.D2A2.B.2A3.A.E5.GFE.CBA2.I$26.E.A.C.2A
4.A.F8.D.A2.A.H$26.F.A.D2A5.2AG8.C6A.G$26.G2A.E.A5.A.H8.B.A3.2A.F$26.
H.A.F.A5.A.I8.A.A4.2A.E$26.I.A.G9A10.2A5.2AD$27.2A.H.A2.A2.A12.A5.A.C
$28.A2.IHGFEDCBA9.I.A5.A.B$26.A.A20.H10A$26.B3A19.G.A2.A2.A$26.C.A.A
19.FEDCBA$27.DCB27.2I$28.2E27.2H$28.2F27.2G$28.2G27.2F$28.2H27.2E$28.
2I27.BCD$31.ABCDEF19.A.A.C$29.A2.A2.A.G19.3AB$27.10AH20.A.A$27.B.A5.A
.I9.ABCDEFGHI2.A$27.C.A5.A12.A2.A2.A.H.2A$27.D2A5.2A10.9AG.A.I$27.E.
2A4.A.A8.I.A5.A.F.A.H$28.F.2A3.A.B8.H.A5.A.E.2AG$29.G.6AC8.G2A5.2AD.A
.F$30.H.A2.A.D8.F.A4.2A.C.A.E$31.I2.ABC.EFG5.E.A3.2A.B2.2AD$12.A2.A2.
A2.A2.A14.A.H.ABCD6A.A3.A.C$11.30AI.ABCD.A2.A6.A.B$12.A14.A2.A2.A2.A
2.A7.EFGHI6.3A$16.GHI2.ABCD.FGHI2.ABCDEFGHI17.A$15.F.A2.A2.A.E32.A3.I
HGFE$15.E9AD31.2A.I.A2.A.D$15.D.A5.A.C32.A.H6A.C$15.C.A5.A.B32.A.G.A
3.2A.B$15.B2A5.3A31.2A.F.A4.2A.A$15.A.A4.2A34.A.E2A5.2A$.A15.A3.2A35.
A.D.A5.A$3A13.6A.I33.2A.C.A5.A.I$.A13.A.A2.A.H35.A.B9AH$16.BCDEFG36.A
.A.A2.A2.A.G$57.2A4.IHGF2EF$58.A8.2D$58.A8.2C$57.3A7.2B$58.A8.2A9$68.
A$67.3A$68.A!