UC-based polyomino oscillators and spaceships

[Bullet51]

According to LifeWiki, all known polyomino oscillators have period ≤ 15 and the only known polyomino spaceships are LWSS, MWSS and HWSS. Is it possible to build polyomino oscillators and spaceships of arbitrarily high periods?

It's conceivable that the answer is "yes". This polyomino is clearly synthesizable and generates gliders controllably:

Code: Select all

x = 711, y = 117, rule = B3/S23
526bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo$525b
3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o
6b3o6b3o6b3o$524b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b
5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o$518bo4b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b
2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o
2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o$517b
3o2b3o3b6o3b6o3b6o3b6o3b6o3b6o3b6o3b6o3b6o3b6o3b6o3b6o3b6o3b6o3b6o3b6o
3b6o3b6o3b6o3b6o3b3o$516b5ob3o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o
3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b
2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o$510bo4b2o3b3ob
5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o
4b5o4b5o4b5o$509b3o2b3o3b3o2b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b
3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o$508b5ob3o3b2o4bo8bo8bo8bo8b
o8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo$502bo4b2o3b3ob5o$
501b3o2b3o3b3o2b3o$500b5ob3o3b2o4bo$494bo4b2o3b3ob5o$493b3o2b3o3b3o2b
3o$492b5ob3o3b2o4bo$486bo4b2o3b3ob5o$485b3o2b3o3b3o2b3o$484b5ob3o3b2o
4bo$478bo4b2o3b3ob5o$477b3o2b3o3b3o2b3o$476b5ob3o3b2o4bo$470bo4b2o3b3o
b5o$469b3o2b3o3b3o2b3o$468b5ob3o3b2o4bo$462bo4b2o3b3ob5o$461b3o2b3o3b
3o2b3o$460b5ob3o3b2o4bo$454bo4b2o3b3ob5o$453b3o2b3o3b3o2b3o$452b5ob3o
3b2o4bo$446bo4b2o3b3ob5o$445b3o2b3o3b3o2b3o$444b5ob3o3b2o4bo$438bo4b2o
3b3ob5o$437b3o2b3o3b3o2b3o$436b5ob3o3b2o4bo$430bo4b2o3b3ob5o$429b3o2b
3o3b3o2b3o$428b5ob3o3b2o4bo$422bo4b2o3b3ob5o$421b3o2b3o3b3o2b3o$420b5o
b3o3b2o4bo$414bo4b2o3b3ob5o$413b3o2b3o3b3o2b3o$412b5ob3o3b2o4bo$406bo
4b2o3b3ob5o$405b3o2b3o3b3o2b3o$404b5ob3o3b2o4bo$398bo4b2o3b3ob5o$397b
3o2b3o3b3o2b3o$396b5ob3o3b2o4bo$390bo4b2o3b3ob5o$366b2o21b3o2b3o3b3o2b
3o$366b2o20b5ob3o3b2o4bo$148bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo
8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8b3o6bo8bo4b2o3b3ob5o$147b3o6b3o6b3o6b3o
6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b
3o6b3o6b3o6b3o6b3o6b3o2b3o3b3o2b3o$146b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o
4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b
5o4b5ob3o3b2o4bo$140bo4b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o
2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b
2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o
3b2o2b2o3b2o2b2o3b2o2b2o3b3ob5o$139b3o2b3o3b6o3b6o3b6o3b6o3b6o3b6o3b6o
3b6o3b6o3b6o3b6o3b6o3b6o3b6o3b6o3b6o3b6o3b6o3b6o3b6o3b6o3b6o3b6o3b6o3b
6o3b6o3b3o2b3o$138b5ob3o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b
2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o
2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b
2o2b2o3b2o2b2o3b2o2b2o3b2o4bo$132bo4b2o3b3ob5o4b5o4b5o4b5o4b5o4b5o4b5o
4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b5o4b
5o4b5o4b5o$131b3o2b3o3b3o2b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o
6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o6b3o$130b
5ob3o3b2o4bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo
8bo8bo8bo8bo8bo8bo8bo$124bo4b2o3b3ob5o$123b3o2b3o3b3o2b3o$122b5ob3o3b
2o4bo$116bo4b2o3b3ob5o$115b3o2b3o3b3o2b3o$114b5ob3o3b2o4bo$108bo4b2o3b
3ob5o$107b3o2b3o3b3o2b3o$106b5ob3o3b2o4bo$100bo4b2o3b3ob5o$99b3o2b3o3b
3o2b3o$98b5ob3o3b2o4bo$92bo4b2o3b3ob5o$91b3o2b3o3b3o2b3o$90b5ob3o3b2o
4bo$84bo4b2o3b3ob5o$83b3o2b3o3b3o2b3o$82b5ob3o3b2o4bo$76bo4b2o3b3ob5o$
75b3o2b3o3b3o2b3o$74b5ob3o3b2o4bo$68bo4b2o3b3ob5o$67b3o2b3o3b3o2b3o$
66b5ob3o3b2o4bo$60bo4b2o3b3ob5o$59b3o2b3o3b3o2b3o$58b5ob3o3b2o4bo$52bo
4b2o3b3ob5o$51b3o2b3o3b3o2b3o$50b5ob3o3b2o4bo$44bo4b2o3b3ob5o$43b3o2b
3o3b3o2b3o$42b5ob3o3b2o4bo$36bo4b2o3b3ob5o$35b3o2b3o3b3o2b3o$34b5ob3o
3b2o4bo$28bo4b2o3b3ob5o$27b3o2b3o3b3o2b3o$26b5ob3o3b2o4bo$20bo4b2o3b3o
b5o$19b3o2b3o3b3o2b3o$18b5ob3o3b2o4bo$12bo4b2o3b3ob5o$11b3o2b3o3b3o2b
3o$10b5ob3o3b2o4bo$4bo4b2o3b3ob5o$3b3o2b3o3b3o2b3o$2b5ob3o3b2o4bo$b2o
3b3ob5o$3o3b3o2b3o$b2o3b2o4bo$2b5o$3b3o$4bo!

A much larger version of the pattern may produce a RCT15 and regenerate itself.

But, to really see the pattern going over a full period, it would be better to encode information by bits in the pattern instead of encoding information via distance. The design of such a pattern may be copied from the unidimensional spaceship, except that there is no analogue of the blinker fuse, so all parts of the whole pattern need to be rebuilded simutaneously.

[squareroot12621]

A similar polyomino theme: it is possible to get infinitely large still lives/oscillators from polyominoes.

Code: Select all

x = 71, y = 19, rule = LifeHistory
3.2C.3A.3A.3A.3A.3A.3A.3A.3A.3A.3A.3A.3A.3A.3A.3A.2C$3.C.CA.3A.3A.3A.
3A.3A.3A.3A.3A.3A.3A.3A.3A.3A.3A.AC.C5$.C.2C.3A.3A.3A.3A.3A.3A.3A.3A.
3A.3A.3A.3A.3A.3A.3A.2C.C$.2C.C.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A
.A.A.A.A.A.A.A.A.A.A.A.C.2C$4.C.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A
.A.A.A.A.A.A.A.A.A.A.A.C$4.C.A.3A.3A.3A.3A.3A.3A.3A.3A.3A.3A.3A.3A.3A
.3A.A.C$5.C59.C3$4.2C59.2C$.C2.C61.C2.C$C.C.C61.C.C.C$.C2.C.4A.4A.4A.
4A.4A.4A.4A.4A.4A.4A.4A.4A.C2.C$4.C.A2.3A2.3A2.3A2.3A2.3A2.3A2.3A2.3A
2.3A2.3A2.3A2.A.C$5.C59.C!