Statorless (100% volatility) p46 oscillator, by stabilizing twin bees shuttle on p46 glider streams:
Code: Select all
x = 148, y = 69, rule = B3/S23
18b2obo117b2obo$13b3o2b2o2bo3b2o8b3o64b3o14b2o12b3o2b2o2bo$14b2o6bo3b
2o8bo3bo62bo3bo12b2o13b2o6bo$15b3o3b2o13bo4bo61bo4bo27b3o3b2o$16bo3bo
16bo3bo20b2o9b2o14b2o13bo3bo28bo3bo$63b2o8b2o15b2o$16bo3bo16bo3bo17b5o
22b5o13bo3bo28bo3bo$15b3o3b2o13bo4bo17b4o23b4o13bo4bo27b3o3b2o$14b2o6b
o3b2o8bo3bo62bo3bo12b2o13b2o6bo$13b3o2b2o2bo3b2o8b3o7bo12b4o23b4o13b3o
14b2o12b3o2b2o2bo$18b2obo24bobo10b5o22b5o48b2obo$46b2o15b2o8b2o15b2o
54b2o$62b2o9b2o14b2o54bobo$147bo2$105bobo$106b2o$6b2o98bo$5b2o$7bo$35b
o$34bo$34b3o$134b3o$136bo$135bo$117bo$118b2o$18bo98b2o$17b2o$17bobo2$
23bo$23bobo$23b2o98b2o$122bobo$124bo2$128bobo$129b2o$29b2o98bo$28b2o$
30bo$12bo$11bo$11b3o$111b3o$113bo$112bo$140bo$141b2o$41bo98b2o$40b2o$
40bobo2$o$obo54b2o14b2o9b2o$2o54b2o15b2o8b2o15b2o$5bob2o48b5o22b5o10bo
bo24bob2o$4bo2b2o2b3o12b2o14b3o13b4o23b4o12bo7b3o8b2o3bo2b2o2b3o$4bo6b
2o13b2o12bo3bo62bo3bo8b2o3bo6b2o$4b2o3b3o27bo4bo13b4o23b4o17bo4bo13b2o
3b3o$6bo3bo28bo3bo13b5o22b5o17bo3bo16bo3bo$56b2o15b2o8b2o$6bo3bo28bo3b
o13b2o14b2o9b2o20bo3bo16bo3bo$4b2o3b3o27bo4bo61bo4bo13b2o3b3o$4bo6b2o
13b2o12bo3bo62bo3bo8b2o3bo6b2o$4bo2b2o2b3o12b2o14b3o64b3o8b2o3bo2b2o2b
3o$5bob2o117bob2o!
I was
almost going to say that this is the first known statorless p46. However, it turns out that
there was already one found by JP21 which I somehow missed when reviewing posts a few days ago. Too bad.
(Note that strict volatility p46 is not possible using twin bees shuttle. It flips halfway through its period over a cell-centered axis, making the central column p23.)
p46n
I also had a look at infinite families of statorless oscillators based on glider loops, given that there are p46 glider reflectors and all. Indeed, it is not hard to see that any p46n oscillator is possible as a statorless period:
Code: Select all
x = 234, y = 240, rule = LifeHistory
87.3A$87.3A$86.A3.A$86.A4.A$87.A3.2A9.2A.A117.2A.A$84.A4.A2.A4.3A2.2A
2.A3.2A8.3A64.3A14.2A12.3A2.2A2.A$83.A6.2A6.2A6.A3.2A8.A3.A62.A3.A12.
2A13.2A6.A$84.A14.3A3.2A13.A4.A61.A4.A27.3A3.2A$100.A3.A16.A3.A20.2A
9.2A14.2A13.A3.A28.A3.A$147.2A8.2A15.2A$100.A3.A16.A3.A17.5A22.5A13.A
3.A28.A3.A$99.3A3.2A13.A4.A17.4A23.4A13.A4.A27.3A3.2A$3.A94.2A6.A3.2A
8.A3.A62.A3.A12.2A13.2A6.A$2.2A93.3A2.2A2.A3.2A8.3A7.A12.4A23.4A13.3A
14.2A12.3A2.2A2.A$.A2.A50.A46.2A.A24.A.A10.5A22.5A48.2A.A$.A53.2A73.
2A15.2A8.2A15.2A54.2A$2A.2A49.A.A89.2A9.2A14.2A54.A.A$A3.A2.2A222.A$.
2A$.3A185.A.A$20.2A39.A5.A122.2A$20.A.A37.3A3.3A21.2A98.A$20.A38.A2.
2A.2A2.A19.2A$59.3A5.3A21.A$119.A$118.A$43.2A73.3A$44.2A172.3A$43.A
176.A$.3A5.3A207.A$.A2.2A.2A2.A189.A$2.3A3.3A191.2A$3.A5.A21.3A68.A
98.2A$31.A69.2A$32.A68.A.A2$107.A$32.A74.A.A$32.2A73.2A98.2A$2.2A5.2A
20.A.A26.2A5.2A137.A.A$2.2A5.2A48.A.A5.A.A138.A$58.3A7.3A$58.2A.3A.3A
.2A141.A.A$43.2A14.5A.5A143.2A$43.A.A15.A5.A45.2A98.A$43.A18.2A.2A45.
2A$114.A$96.A$95.A$20.2A39.A5.A27.3A$21.2A37.2A5.2A126.3A$20.A38.A.2A
3.2A.A127.A$2.3A3.3A48.A.2A3.2A.A126.A$2.3A3.3A49.3A3.3A155.A$.A.2A3.
2A.A48.3A3.3A156.2A$.A.2A3.2A.A42.3A68.A98.2A$2.2A5.2A43.A69.2A$3.A5.
A45.A68.A.A2$84.A$9.A74.A.A54.2A14.2A9.2A$9.2A73.2A54.2A15.2A8.2A15.
2A$8.A.A78.A.2A48.5A22.5A10.A.A24.A.2A$.A86.A2.2A2.3A12.2A14.3A13.4A
23.4A12.A7.3A8.2A3.A2.2A2.3A$2.2A84.A6.2A13.2A12.A3.A62.A3.A8.2A3.A6.
2A$88.2A3.3A27.A4.A13.4A23.4A17.A4.A13.2A3.3A$90.A3.A28.A3.A13.5A22.
5A17.A3.A16.A3.A$140.2A15.2A8.2A$90.A3.A28.A3.A13.2A14.2A9.2A20.A3.A
16.A3.A$88.2A3.3A27.A4.A61.A4.A13.2A3.3A14.A$5.3A3.3A74.A6.2A13.2A12.
A3.A62.A3.A8.2A3.A6.2A6.2A6.A$4.A9.A73.A2.2A2.3A12.2A14.3A64.3A8.2A3.
A2.2A2.3A4.A2.A4.A$4.A3.A.A3.A43.A5.A24.A.2A117.A.2A9.2A3.A$5.3A3.3A
43.3A3.3A158.A4.A$6.A5.A43.A3.A.A3.A158.A3.A$56.A9.A159.3A$57.3A3.3A
160.3A2$166.A$165.2A$164.A2.A50.A$59.2A.2A100.A53.2A$60.A.A100.2A.2A
49.A.A$56.2A.2A.2A.2A96.A3.A2.2A$56.A2.A3.A2.A97.2A$56.A9.A97.3A$5.2A
5.2A42.A2.A3.A2.A116.2A39.A5.A$4.A2.A3.A2.A42.2A5.2A117.A.A37.3A3.3A$
4.A9.A168.A38.A2.2A.2A2.A$4.A2.A3.A2.A207.3A5.3A$4.2A.2A.2A.2A$8.A.A$
7.2A.2A194.2A$207.2A$206.A$164.3A5.3A$164.A2.2A.2A2.A$5.3A3.3A151.3A
3.3A$4.A9.A151.A5.A21.3A$4.A3.A.A3.A43.A5.A129.A$5.3A3.3A43.3A3.3A
129.A$6.A5.A43.A3.A.A3.A$56.A9.A$57.3A3.3A129.A$195.2A$165.2A5.2A20.A
.A26.2A5.2A$165.2A5.2A48.A.A5.A.A$221.3A7.3A$221.2A.3A.3A.2A$67.2A
137.2A14.5A.5A$69.A136.A.A15.A5.A$60.A.A143.A18.2A.2A$60.2A$61.A2$
183.2A39.A5.A$15.A45.A5.A116.2A37.2A5.2A$16.A43.2A5.2A114.A38.A.2A3.
2A.A$14.3A42.A.2A3.2A.A95.3A3.3A48.A.2A3.2A.A$2.3A3.3A48.A.2A3.2A.A
95.3A3.3A49.3A3.3A$2.3A3.3A49.3A3.3A95.A.2A3.2A.A48.3A3.3A$.A.2A3.2A.
A48.3A3.3A95.A.2A3.2A.A42.3A$.A.2A3.2A.A38.A114.2A5.2A43.A$2.2A5.2A
37.2A116.A5.A45.A$3.A5.A39.2A2$172.A$172.2A$4.2A.2A18.A143.A.A$3.A5.A
15.A.A136.A$.5A.5A14.2A137.2A$2A.3A.3A.2A$3A7.3A$.A.A5.A.A48.2A5.2A$
2.2A5.2A26.A.A20.2A5.2A$37.2A$38.A129.3A3.3A$167.A9.A$167.A3.A.A3.A
43.A5.A$38.A129.3A3.3A43.3A3.3A$39.A129.A5.A43.A3.A.A3.A$37.3A21.A5.A
68.C82.A9.A$60.3A3.3A66.C84.3A3.3A$59.A2.2A.2A2.A65.3C$59.3A5.3A$27.A
$25.2A$26.2A194.2A.2A$223.A.A$219.2A.2A.2A.2A$.3A5.3A207.A2.A3.A2.A$.
A2.2A.2A2.A38.A168.A9.A$2.3A3.3A37.A.A117.2A5.2A42.A2.A3.A2.A$3.A5.A
39.2A73.C42.A2.A3.A2.A42.2A5.2A$67.3A54.C.C40.A9.A$68.2A54.2C41.A2.A
3.A2.A$62.2A2.A3.A96.2A.2A.2A.2A$14.A.A49.2A.2A100.A.A$14.2A53.A100.
2A.2A$15.A50.A2.A$67.2A$67.A2$5.3A160.3A3.3A$5.3A159.A9.A$4.A3.A158.A
3.A.A3.A43.A5.A$4.A4.A158.3A3.3A43.3A3.3A$5.A3.2A9.2A.A117.2A.A24.A5.
A43.A3.A.A3.A$2.A4.A2.A4.3A2.2A2.A3.2A8.3A64.3A14.2A12.3A2.2A2.A73.A
9.A$.A6.2A6.2A6.A3.2A8.A3.A62.A3.A12.2A13.2A6.A74.3A3.3A$2.A14.3A3.2A
13.A4.A61.A4.A27.3A3.2A$18.A3.A16.A3.A20.2A9.2A14.2A13.A3.A28.A3.A$
65.2A8.2A15.2A$18.A3.A16.A3.A17.5A22.5A13.A3.A28.A3.A$17.3A3.2A13.A4.
A17.4A23.4A13.A4.A27.3A3.2A$16.2A6.A3.2A8.A3.A62.A3.A12.2A13.2A6.A84.
2A$15.3A2.2A2.A3.2A8.3A7.A12.4A23.4A13.3A14.2A12.3A2.2A2.A86.A$20.2A.
A24.A.A10.5A22.5A48.2A.A78.A.A$48.2A15.2A8.2A15.2A54.2A73.2A$64.2A9.
2A14.2A54.A.A74.A$149.A2$107.A.A68.A45.A5.A$108.2A69.A43.2A5.2A$8.2A
98.A68.3A42.A.2A3.2A.A$7.2A156.3A3.3A48.A.2A3.2A.A$9.A155.3A3.3A49.3A
3.3A$37.A126.A.2A3.2A.A48.3A3.3A$36.A127.A.2A3.2A.A38.A$36.3A126.2A5.
2A37.2A$136.3A27.A5.A39.2A$138.A$137.A$119.A$120.2A45.2A.2A18.A$20.A
98.2A45.A5.A15.A.A$19.2A143.5A.5A14.2A$19.A.A141.2A.3A.3A.2A$163.3A7.
3A$25.A138.A.A5.A.A48.2A5.2A$25.A.A137.2A5.2A26.A.A20.2A5.2A$25.2A98.
2A73.2A$124.A.A74.A$126.A2$130.A.A68.A$131.2A69.A$31.2A98.A68.3A21.A
5.A$30.2A191.3A3.3A$32.A189.A2.2A.2A2.A$14.A207.3A5.3A$13.A176.A$13.
3A172.2A$113.3A73.2A$115.A$114.A$142.A21.3A5.3A$143.2A19.A2.2A.2A2.A
38.A$43.A98.2A21.3A3.3A37.A.A$42.2A122.A5.A39.2A$42.A.A185.3A$231.2A$
2.A222.2A2.A3.A$2.A.A54.2A14.2A9.2A89.A.A49.2A.2A$2.2A54.2A15.2A8.2A
15.2A73.2A53.A$7.A.2A48.5A22.5A10.A.A24.A.2A46.A50.A2.A$6.A2.2A2.3A
12.2A14.3A13.4A23.4A12.A7.3A8.2A3.A2.2A2.3A93.2A$6.A6.2A13.2A12.A3.A
62.A3.A8.2A3.A6.2A94.A$6.2A3.3A27.A4.A13.4A23.4A17.A4.A13.2A3.3A$8.A
3.A28.A3.A13.5A22.5A17.A3.A16.A3.A$58.2A15.2A8.2A$8.A3.A28.A3.A13.2A
14.2A9.2A20.A3.A16.A3.A$6.2A3.3A27.A4.A61.A4.A13.2A3.3A14.A$6.A6.2A
13.2A12.A3.A62.A3.A8.2A3.A6.2A6.2A6.A$6.A2.2A2.3A12.2A14.3A64.3A8.2A
3.A2.2A2.3A4.A2.A4.A$7.A.2A117.A.2A9.2A3.A$142.A4.A$143.A3.A$144.3A$
144.3A!
Since the p46 glider reflection used here has even-phase parity, four copies are sufficient to form a periodic glider loop with a cycle length (in terms of generations) that is a multiple of 8 (more specifically, LCM(8,46)=184). Pushing back the top-right half of the pattern every 23fd (distance of 23 full diagonals), we get all cycle lengths 736+184n = 46*4*(4+n). So by filling the glider loop, any period that is a multiple of 46, that is at least 46 (the repeat time) and that divides 46*4*(4+n) for some n can be achieved. Namely, any period that is a multiple of 46.
(It is worth noting that codeholic's statorless p92 was already known before.)
p64n
Just to verify previous statements made regarding certain families, I took
wwei23's statorless p64 glider reflector and turned it into a glider loop:
Code: Select all
x = 159, y = 129, rule = LifeHistory
111.3A$99.2A23.2A2$97.A3.A21.A3.A$97.A4.A19.A4.A$99.A.A.A8.A8.A.A.A$
80.A19.A.A.A5.2A.2A5.A.A.A$67.2A10.3A10.2A7.A4.A11.A4.A$67.2A.A7.A.A.
A7.A.2A8.A3.A2.A5.A2.A3.A$71.A6.A.A.A6.A19.A5.A$68.A10.3A10.A10.2A15.
2A$69.A.2A7.A7.2A.A16.A2.A.A2.A$71.2A7.A7.2A18.A.A3.A.A7.2A.2A.A$80.A
28.A5.A7.2A2.2A.2A$80.A50.A$92.4A15.3A9.2A$91.A4.A.2A23.2A5.2A$91.A4.
A3.A29.2A$94.2A4.A15.A6.A$79.3A9.2A4.A2.A14.A.A5.2A.2A2.2A$90.A2.A3.A
2.A14.A2.A5.A.2A.2A$90.A2.A4.2A16.2A$84.A5.A4.2A$83.A.A4.A3.A4.A53.A$
83.A2.A4.2A.A4.A52.3A$84.2A9.4A52.A.3A$150.A3.A$149.A3.A$148.3A.A$
149.3A$150.A3$148.A$146.A2.A$149.A$146.A2.A$141.2A3.A2.A6.3A$146.A2.A
$149.A$137.2A7.A2.A$136.A2.A8.A$98.2A36.A.A$97.A2.A4.2A.6A23.A$97.A.A
5.2A.6A36.A$98.A6.2A42.3A$105.2A5.2A34.3A.A$94.A10.2A5.2A28.2A5.A3.A$
94.A10.2A5.2A29.A6.A3.A$94.A17.2A24.3A2.2A6.A.3A$105.6A.2A22.3A.A3.A
7.3A$105.6A.2A22.A4.A.2A8.A$140.A.A$138.2A.A4.A$85.A7.3A7.A34.A3.A.3A
$138.2A2.3A$83.3A.A13.A.3A33.A$82.A.2A7.3A7.2A.A32.2A$82.2A.A6.A3.A6.
A.2A$80.A.3A7.A3.A7.3A.A$93.3A$82.A23.A3$64.A$64.A$64.A$52.A23.A2$50.
A.3A19.3A.A$52.2A.A17.A.2A$18.2A32.A.2A7.3A7.2A.A$19.A33.3A.A13.A.3A$
14.3A2.2A$12.3A.A3.A34.A7.3A7.A$12.A4.A.2A41.A3.A33.E$16.A.A43.A3.A
31.2E$5.A8.2A.A4.A22.2A.6A9.3A33.2E$4.3A7.A3.A.3A22.2A.6A$3.3A.A6.2A
2.3A24.2A$4.A3.A6.A29.2A5.2A$5.A3.A5.2A28.2A5.2A$6.A.3A34.2A5.2A$7.3A
42.2A6.A$8.A36.6A.2A5.A.A$21.A23.6A.2A4.A2.A$20.A.A36.2A$7.A11.A2.A$
5.A2.A11.2A$8.A$5.A2.A$2A3.A2.A6.3A66.E$5.A2.A73.2E$8.A74.2E$5.A2.A$
7.A3$8.A$7.3A$6.A.3A$5.A3.A$4.A3.A$3.3A.A52.4A9.2A$4.3A52.A4.A.2A4.A
2.A$5.A53.A4.A3.A4.A.A$62.2A4.A5.A$41.2A16.2A4.A2.A$28.2A.2A.A5.A2.A
14.A2.A3.A2.A$27.2A2.2A.2A5.A.A14.A2.A4.2A$35.A6.A15.A4.2A$27.2A29.A
3.A4.A10.A$27.2A5.2A23.2A.A4.A9.3A$34.2A9.3A15.4A9.A.A.A$27.A48.A.A.A
$27.2A.2A2.2A41.3A$28.A.2A.2A34.2A7.A7.2A$67.A.2A7.A7.2A.A$37.2A7.A7.
2A10.A11.A11.A$44.2A.2A20.A8.A8.A$36.A3.A11.A3.A8.2A.A19.A.2A$35.A4.A
2.A5.A2.A4.A7.2A23.2A$34.A.A.A4.A5.A4.A.A.A$33.A.A.A17.A.A.A$31.A4.A
5.A2.A.A2.A5.A4.A15.3A$31.A3.A6.A.A3.A.A6.A3.A$43.A5.A$33.2A23.2A$45.
3A!
Here, this reflector is an odd-phased reflector, making eight copies necessary. (It is important that the loop's cycle length is a multiple of 8.) Pushing back the top-right half every 8fd gives cycle lengths 960+64n = 64*(15+n). So any period that is a multiple of 64, that is at least 64 (the repeat time) and that divides 64*(15+n) for some n can be achieved. Namely, any period that is a multiple of 64.
p45+15n
Finally, I noticed a rather cryptic statement somewhere on LifeWiki:
If anyone knows what "modified p15 bumper" means, do tell me, because I certainly am not qualified to tell you. However, it is entirely possible to construct a glider loop with just the PD-pair reflector as follows:
Code: Select all
x = 107, y = 89, rule = LifeHistory
76.3A$54.3A19.3A$55.A21.A$55.A21.A$54.3A20.A$76.A.A$54.3A$54.3A$76.A.
A$54.3A20.A$55.A21.A$55.A21.A$54.3A19.3A$76.3A$40.2A6.2A$38.A4.A2.A4.
A9.A2.A.2A.A2.A$38.A4.A2.A4.A9.4A.2A.4A$38.A4.A2.A4.A9.A2.A.2A.A2.A
18.3A$40.2A6.2A41.A.A$91.3A$91.3A$91.3A$91.3A$91.A.A$91.3A4$100.4A$
50.A2.A4.A2.A37.6A$48.3A2.6A2.3A34.8A$50.A2.A4.A2.A35.2A6.2A$98.8A$
66.A32.6A$65.3A32.4A3$65.3A2$65.A.A$65.A.A2$40.A24.3A$39.3A2$65.3A$
39.3A24.A2$39.A.A$39.A.A2$39.3A3$3.4A32.3A25.E$2.6A32.A24.2E$.8A57.2E
$2A6.2A35.A2.A4.A2.A$.8A34.3A2.6A2.3A$2.6A37.A2.A4.A2.A$3.4A4$13.3A$
13.A.A39.E$13.3A38.E$13.3A38.3E$13.3A$13.3A$13.A.A41.2A6.2A$13.3A18.A
2.A.2A.A2.A9.A4.A2.A4.A$34.4A.2A.4A9.A4.A2.A4.A$34.A2.A.2A.A2.A9.A4.A
2.A4.A$57.2A6.2A$28.3A$28.3A19.3A$29.A21.A$29.A21.A$29.A20.3A$28.A.A$
50.3A$50.3A$28.A.A$29.A20.3A$29.A21.A$29.A21.A$28.3A19.3A$28.3A!
As in the p64n case, this reflector is an odd-phased reflector, making eight copies necessary. Pushing back the top-right half every 15fd gives cycle lengths 720+120n = 15*8*(6+n). So any period that is a multiple of 15, that is at least 45 (the repeat time) and that divides 15*8*(6+n) for some n can be achieved. Namely, any period 45+15n.
Other infinite families?
These are the infinite families based on glider loops that I'm aware of. If there are any others I missed, do let me know.