Using a reaction I found involving three copies of
Jason's p33, I was able to construct a p33 statorless 90-degree glider reflector that can form glider loops. This allows for all statorless oscillators of period p33n (another infinite family).
p33 statorless 90-degree glider reflector:
Code: Select all
x = 268, y = 251, rule = LifeHistory
113.A.A$112.A10.A.A$111.A3.A10.A$111.A2.A8.A3.A$111.A12.A2.A$113.A13.
A$111.A.A11.A$110.A14.A.A$113.A14.A$111.3A11.A$125.3A4$108.3A$108.A
19.3A$111.A18.A$108.A.A16.A$108.A19.A.A$110.A19.A$107.A2.A17.A$110.A
17.A2.A$107.A.A18.A$129.A.A3$104.A.A$103.A28.A.A$97.2A.2A4.A28.A$97.A
7.A26.A4.2A.2A$90.A6.A2.A.3A28.A7.A$85.3A.A2.A6.A34.3A.A2.A6.A$84.A7.
A46.A6.A2.A.3A$88.2A.2A53.A7.A$84.A.A59.2A.2A$78.A.A71.A.A$77.A80.A.A
$76.A3.A80.A$76.A2.A78.A3.A$76.A82.A2.A$78.A83.A$76.A.A81.A$75.A84.A.
A$78.A84.A$76.3A81.A$160.3A4$73.3A$73.A89.3A$76.A88.A$73.A.A86.A$73.A
89.A.A$75.A89.A$72.A2.A87.A$71.A3.A87.A2.A$74.A88.A3.A$71.A.A90.A$65.
A.A97.A.A$59.2A.2A107.A.A$59.A7.A107.2A.2A$52.A6.A2.A.3A104.A7.A$47.
3A.A2.A6.A110.3A.A2.A6.A$46.A7.A122.A6.A2.A.3A$50.2A.2A129.A7.A$46.A.
A135.2A.2A$40.A.A147.A.A$39.A156.A.A$38.A3.A156.A$38.A2.A154.A3.A$38.
A158.A2.A$40.A159.A$38.A.A157.A$37.A160.A.A$40.A160.A$38.3A157.A$198.
3A4$35.3A$35.A165.3A$38.A164.A$35.A.A162.A$28.A6.A165.A.A12.2C$28.A8.
A165.A6.A5.C.C$28.A.A4.A.A163.A8.A5.C$35.A165.A.A4.A.A$203.A3$27.3A$
26.3A7.2A171.3A13.C$28.A7.A164.2A7.3A11.2C$35.3A164.A7.A13.C.C$28.A5.
A2.A163.3A$28.A5.A.A164.A2.A5.A$27.A.A5.A166.A.A5.A$28.2A13.2A158.A5.
A.A$28.A8.3A.2A.2A148.2A13.2A$37.2A4.A11.A137.2A.2A.3A8.A$38.A11.A4.
2A126.A11.A4.2A$25.A22.2A.2A.4A124.2A4.A11.A$24.2A23.2A130.4A.2A.2A
22.A$24.A.A30.A130.2A23.2A$25.A155.A30.A.A$25.A187.A$213.A$25.A$25.3A
185.A$24.3A184.3A$212.3A3$52.A$59.2A125.A$21.A30.4A.2A.2A116.2A$13.2A
38.2A4.A11.A105.2A.2A.4A30.A$12.2A.2A.4A32.A11.A4.2A94.A11.A4.2A38.2A
$2.A11.A4.2A43.2A.2A.4A92.2A4.A11.A32.4A.2A.2A$.2A4.A11.A45.2A98.4A.
2A.2A43.2A4.A11.A$4A.2A.2A63.A98.2A45.A11.A4.2A$7.2A156.A63.2A.2A.4A$
A229.2A$238.A$258.C$257.2C$257.C.C4$68.A$75.2A93.A$.A66.4A.2A.2A84.2A
$8.2A59.2A4.A11.A73.2A.2A.4A66.A27.3C$.4A.2A.2A59.A11.A4.2A62.A11.A4.
2A59.2A34.C$2.2A4.A11.A59.2A.2A.4A60.2A4.A11.A59.2A.2A.4A28.C$3.A11.A
4.2A59.2A66.4A.2A.2A59.A11.A4.2A$13.2A.2A.4A66.A66.2A59.2A4.A11.A$14.
2A133.A66.4A.2A.2A$22.A200.2A$216.A7$84.A$91.2A61.A$17.A66.4A.2A.2A
52.2A$24.2A59.2A4.A11.A41.2A.2A.4A66.A$17.4A.2A.2A59.A11.A4.2A30.A11.
A4.2A59.2A$18.2A4.A11.A59.2A.2A.4A28.2A4.A11.A59.2A.2A.4A$19.A11.A4.
2A59.2A34.4A.2A.2A59.A11.A4.2A$29.2A.2A.4A66.A34.2A59.2A4.A11.A$30.2A
101.A66.4A.2A.2A$38.A168.2A$200.A3$108.3A$109.3A16.3A$109.A17.3A$129.
A$109.A$109.A19.A$33.A74.A.A18.A$40.2A66.2A18.A.A74.A$33.4A.2A.2A66.A
19.2A66.2A$34.2A4.A11.A76.A66.2A.2A.4A$35.A11.A4.2A132.A11.A4.2A$45.
2A.2A.4A57.A72.2A4.A11.A$46.2A64.2A12.A57.4A.2A.2A$54.A56.A.A11.2A64.
2A$112.A12.A.A56.A$112.A13.A$126.A$112.A$110.3A13.A$111.2A13.3A$112.A
.A11.2A$124.A.A2$49.A$56.2A131.A$49.4A.2A.2A122.2A$50.2A4.A11.A111.2A
.2A.4A$51.A11.A4.2A100.A11.A4.2A$61.2A.2A.4A98.2A4.A11.A$62.2A104.4A.
2A.2A$70.A104.2A$168.A9$65.A$72.2A99.A$65.4A.2A.2A90.2A$66.2A4.A11.A
79.2A.2A.4A$67.A11.A4.2A68.A11.A4.2A$77.2A.2A.4A66.2A4.A11.A$78.2A72.
4A.2A.2A$86.A72.2A$152.A9$81.A$88.2A67.A$81.4A.2A.2A58.2A$82.2A4.A11.
A47.2A.2A.4A$83.A11.A4.2A36.A11.A4.2A$93.2A.2A.3A35.2A4.A11.A$94.2A5.
A35.3A.2A.2A$137.A5.2A2$107.A.A$109.2A18.A.A$109.3A16.2A$109.A17.3A$
129.A$109.A$109.A19.A$108.A.A18.A$108.2A18.A.A$109.A19.2A$129.A2$112.
A$112.2A12.A$111.A.A11.2A$112.A12.A.A$112.A13.A$126.A$112.A$110.3A13.
A$111.2A13.3A$112.A.A11.2A$124.A.A!
Background
I had a look to see if there was anything regarding p33n, after finding out there is a
known statorless (and strictly volatile) p33 oscillator based on eight copies of Jason's p33 interacting with each other. I ran a search for glider collisions on this oscillator, but was not able to get any reaction that could form a glider loop (although I found some 180-degree reactions that can form glider relays).
Conversely, Golly's patterns folder has the following 90-degree glider reflectors (they are not statorless, however):
Code: Select all
x = 128, y = 63, rule = B3/S23
83bo$82bobo$81bo2bo2$31bo49bobo$30bobo47b2o$29bo2bo47b2o8bobo$81bobo8b
2o$29bobo60b3o$2obo4b2obo16b2o51bo10bo$ob2o4bob2o16b2o8bobo40bob2o$4b
2o6b2o15bobo8b2o50bo$4bo7bo27b3o36bobo10bo$5bo7bo15bo10bo37bo2bo9bobo$
4b2o6b2o15bob2o58b2o$2obo4b2obo28bo38bobo10bo$ob2o4bob2o15bobo10bo40b
2o$4b2o6b2o12bo2bo9bobo39b2o$4bo7bo26b2o38bobo13bo$5bo7bo13bobo10bo54b
2o$4b2o6b2o15b2o47bo2bo12bobo$2obo4b2obo17b2o48bobo13bo$ob2o4bob2o15bo
bo13bo36bo14bo$43b2o$26bo2bo12bobo58b2o$27bobo13bo58bo6b2o$28bo14bo13b
2o36bo12b2o$56b2o52bo$43bo8b2o4bo$41b3o8b2o49bo$42b2o58bo2bo$105bo$47b
2o44b2o8bo$93b2o22b2o$44b2o19b2o50bobo$65bobo34b3o12bo$49b2o14bo36bobo
$39b2o8b3o50bobo$39b2o8bo52b2o11bo$114bobo$49bo14bo50bo$49bo13bobo40b
2o8bo9bo$48bobo12bo2bo7bo30bobo8b3o6b2o$48b2o23b2o30bobo17bobo$49bo13b
obo7bobo29b3o$62b2o52b3o$62b2o52bo$52bo10bobo40bo9bo$52b2o50bo2bo8bo$
51bobo9bo2bo37bo11bobo$52bo10bobo39b3o10bo$52bo65bo$60b2obo54bo$52bo
10bo52b3o$50b3o$51b2o8bobo$52bobo8b2o51b3o$63b2o53bo$61bobo54bo$117bob
o$60bo2bo54bo$60bobo$61bo!
Finding stabilizations
Two separate stabilizations of two copies of Jason's p33 (here I am talking about two copies, each having one end cancel the other out without needing anything else) are known already; they are both in the statorless p33 above. I ran a search for more of these but only found two others. The four of them (not including reflections and rotations) are given below (note we are ignoring the
odd keys which are intended to be temporary and are only here to make the pattern stable):
Code: Select all
x = 52, y = 226, rule = B3/S23
8bo$7bobo$6bo2bo2$6bobo$5b2o$5b2o8bobo$6bobo8b2o$17b3o$6bo10bo$6bob2o$
17bo$4bobo10bo$3bo2bo9bobo$16b2o$4bobo10bo$6b2o$6b2o$4bobo13bo$20b2o$
3bo2bo12bobo$4bobo13bo$5bo14bo2$20bo$18b3o$19b3o6$24bo$31b2o$24b4ob2ob
2o$25b2o4bo11bo$26bo11bo4b2o$36b2ob2ob4o$37b2o$45bo6$41bo7b2o$41bo2bo
2bo3bo$34b2o14bo$30b2ob4ob2ob2ob4obo$29bo15b2o$30bo2bo2bo2bo$31bo6bo
22$44bo$6bo36bobo$5bobo35bo2bo$4bo2bo$44bobo$4bobo39b2o$3b2o30bobo8b2o
$3b2o8bobo18b2o8bobo$4bobo8b2o16b3o$15b3o17bo10bo$4bo10bo27b2obo$4bob
2o27bo$15bo19bo10bobo$2bobo10bo18bobo9bo2bo$bo2bo9bobo18b2o$14b2o19bo
10bobo$2bobo10bo29b2o$4b2o39b2o$4b2o26bo13bobo$2bobo13bo12b2o$18b2o11b
obo12bo2bo$bo2bo12bobo12bo13bobo$2bobo13bo13bo14bo$3bo14bo$32bo$18bo
13b3o$16b3o13b2o$17b2o11bobo$18bobo22$5bo$4bobo$3bo2bo2$3bobo$2b2o$2b
2o8bobo$3bobo8b2o$14b3o$3bo10bo$3bob2o$14bo$bobo10bo$o2bo9bobo$13b2o$b
obo10bo$3b2o$3b2o$bobo13bo$17b2o$o2bo12bobo10bobo$bobo13bo13b2o$2bo14b
o13b3o$31bo$17bo$15b3o13bo14bo$16b2o13bo13bobo$17bobo10bobo12bo2bo$30b
2o$31bo13bobo$44b2o$44b2o$34bo10bobo$34b2o$33bobo9bo2bo$34bo10bobo$34b
o$42b2obo$34bo10bo$32b3o$33b2o8bobo$34bobo8b2o$45b2o$43bobo2$42bo2bo$
42bobo$43bo6$5bo$4bobo$3bo2bo2$3bobo$2b2o$2b2o8bobo$3bobo8b2o$14b3o$3b
o10bo$3bob2o$14bo$bobo10bo$o2bo9bobo$13b2o$bobo10bo$3b2o$3b2o$bobo13bo
$17b2o$o2bo12bobo$bobo13bo$2bo14bo11bobo$31b2o$17bo13b3o$15b3o13bo$16b
2o$17bobo11bo14bo$31bo13bobo$30bobo12bo2bo$30b2o$31bo13bobo$44b2o$44b
2o$34bo10bobo$34b2o$33bobo9bo2bo$34bo10bobo$34bo$42b2obo$34bo10bo$32b
3o$33b2o8bobo$34bobo8b2o$45b2o$43bobo2$42bo2bo$42bobo$43bo!
Unfortunately none of these allow for the 90-degree glider reflection(s) above without the glider passing through the oscillator.
So I went ahead and searched for a stabilization using three copies of Jason's p33. I found a number of them and decided to use this one, which is flat enough on its right side to allow for a 90-degree glider reflection without the glider passing through the oscillator:
Code: Select all
x = 60, y = 56, rule = B3/S23
15bo$14bobo$14b2o$14b2o$13b2o$13bo7bobo$13bo10bo$13b2o6bo3bo$14b2o6bo
2bo$13b3o9bo$14b2obo5bo$18bo4bobo$11b2o13bo$11b3o9bo$11b2o10b3o$12b2o$
13bo$13bo$12b2o$11b2o13b3o$11b3o14bo$11bobo11bo$12bo13bobo12b2o$28bo6b
o5bobo$26bo8bo5bo$26bobo4bobo$28bo4$34b3o13bo$26b2o7b3o11b2o$27bo7bo
13bobo$26b3o$26bo2bo5bo$27bobo5bo$28bo5bobo$19b2o13b2o$18b2ob2ob3o8bo$
8bo11bo4b2o30b3o$7b2o4bo11bo31bo$6b4ob2ob2o22bo19bo$13b2o23b2o$6bo30bo
bo$38bo$38bo4b2o$43b2o$38bo8b2o$36b3o7bobo$b2o7bo26b2o6b3o$o3bo2bo2bo
27bobo4bo$bo14b2o$2bob4ob2ob2ob4ob2o23bo2bo$5b2o15bo23bobo$12bo2bo2bo
2bo25bo$13bo6bo!
Then it is just a matter of using chains of the known two-copy forms to close the pattern. I elected to have all three ends line up on the same column and then just pasted in a glide reflection. This gives the result at the top of this post.