Rotary oscillators?

[Keiji]

So I was thinking about the way gliders flip and flip back and wondered about a pattern which became a copy of itself rotated 90 degrees after a number of generations.

Obviously, this would generate a period 4n oscillator, but I don't remember seeing any (other than glider/Herschel/queen bee/etc loops which have been specifically engineered to do this). Do any "natural" oscillators of this form exist?

[Extrementhusiast]

Nothing natural in Life, but there are two closely related engineered oscillators with period 4:

Code: Select all

....XX...
....XX.....
...........
....XXXX...
...X.X..X.XX
...X..X.X.XX
XX.X..X.X...
XX.X....X...
....XXXX.
.........
......XX.
......XX.

Code: Select all

....XX...
....XX.....
...........
....XXXX...
...X.X..X.XX
...X..X.X.XX
XX.XX...X...
XX.X....X...
....XXXX.
.........
......XX.
......XX.

In Morley (or Move), there is this simple, natural oscillator:

Code: Select all

.XX.
X..X
.XXX
.X..

[Sokwe]

There are several patterns with this property in Life:

Code: Select all

x = 595, y = 89, rule = B3/S23
545b2o5b2o$87b2o10b2o444b2o5b2o$86bo2bo8bo2bo$86b3o10b3o251bo4bo$89b
10o252b2ob4ob2o$88bo2b6o2bo253bo4bo$88b2o2b4o2b2o2$93bo$91b2o2bo$90bo
2bo$90bo5bo$90bo5bo241bo16b3o$338bo16bobo$78b2o12b3o12b2o228bobo15b3o$
79bo27bo230bo$79bobo23bobo230bo$80b2o23b2o231bo29bo175b2obo3bob2o$92b
3o243bo16b3o10bo175bo2bo3bo2bo$91bo3bo202b2o4b2o31bobo15bobo9bobo175b
3o3b3o$90bo5bo69bo131bobo2bobo32bo16b3o10bo$78b2o27b2o55b3o133b4o34bo
29bo$79bo9bo7bo9bo44b2o9bo86b2o46bo2b2o2bo62bo$79bobo7bo7bo7bobo45bo9b
2o78b2o5b2o46bo2b2o2bo62bo$65bo6bo7b2o23b2o46bobo87bobo54bo2bo63bobo$
65b3o4b3o15bo5bo57b2o87bobo62b2o58bo$68bo6bo15bo3bo143b2o2b2o63b3o57bo
92b3o3b2o$67b2o5b2o16b3o16bo6bo40bo80bob3o63b2obo106b2o47bobo10b2o63b
2o$109b3o4b3o40bobo148bobo98bo6b2o35b2o12bo10b2o63b2o$108bo6bo42bo143b
3o4bo2bo98b2o41bo2bo11bob2o$33b2o73b2o5b2o42bo82b3obo63b2o95bo4b2o40b
3o2b7obobob2o$33bo19b2o37b3o65b2o3b2o28b2o3b2o40b2o2b2o38b2o12bo5bo
100bob3o45b2o8bobo$bo23bob2ob2obo5b2o11bobo56b2o52bobo26bo7bo38bobo41b
o2bo11bo5bo101b3o45bo10bobo20b2o$b3o8b2o11b2obobobo6bo12bobob2o35bo13b
2o47b2o9bo29bobo41bobo39bo2bobo11bo5bo41bo4bo102b2obo4bo3bo21bobo$4bo
7bo18bo8bo12bobobo49bob2obo44bo9b2o26b2o3b2o21b2o10b2o5b2o6b2o35bo58b
2ob4ob2o105bo25b2obobo$3bo6bobo26b2o14bo51bob2obo16b2o23b3o66b2o10b2o
13b2o31bob2o15b3o43bo4bo58b3o72bobobo91b2o$3bo3bo2b2o41bo2bo72bobo22bo
129bo5bo120b3obo73bo76b2o15bobo7b2o$8bo30b2o15bo13b2o4b2o26bo10bo10b2o
bobo158bo8bo109b2o4bo72bo2bo74b2o17bo7b2o$5bo2bo14bo9b3o2bobo11bo3bo
12bobo4bobo25bo10bo10bobobo54b3o89b2ob2o8bo8bo110b2o76bo94b3o$6b3o14b
3o7bobo3bo12bo3bo12bo8bo49bo57b3o32b2o13bo11b2o13bo13bo21bo91b2o10b2o
6bo6b2o29b2o11bo25bo5bo38bo$26bo6bobo4b3o13bo12bobo4bobo14bo6b2o2bo10b
o2b2o6bo2bo64b3o24bob3o8b4o10bob3o8b4o13b2o2bo3b3o3b3o25b2ob2o66b2o10b
2o13b2o29b2o10bobo24bo5bo24b2o9b2o3bo34bo$2b2o21bobo14bo10bo2bo13b2o4b
2o21bo3b3o8b3o3bo8bo33b2o29bobo9b3o12bo3b2o6b2o2bo10bo3b2o6b2o2bo14b3o
13b3o3b3o7bo12bo135bo3bo23bo5bo14b2o7bobo9b2obob2o31bo3b2o$bobo5b2o14b
2o28bo36b3o3b2o6bo6bo6b2o3bo3bo32bo2bo28b3o8b3o14bobo2bo4bo2bobo11bobo
2bo4bo2bobo14b3o8bo20bo7bo2b2o136bo3bo24bobo17b2o7bo10bo6b2o29b2obob2o
9b3o$bo7bo43bobobo41bo3b3o8b3o3bo4bo3bo31bobobo20b3o33bo2b2o6b2o3bo2b
3o5bo2b2o6b2o3bo12b2o2bo7bo8bo11bo8b3o77b2o25b2o31b2ob2o24bobo26b3o9b
2obob2o12b3o14b2o6bo10bo7b2o$2o8b3o12b2o25bobob2o42b2o2bo10bo2b2o9bo
30b3obo20b3o34b4o8b3obo10b4o8b3obo11bo12bo8bo20b3o76bo2bo23bo2bo59bo
40b2o3bo12bo18b2obob2o9bobo7b2o$12bo12bo8bo17bobo71bo2bo30b3o60bo13b2o
11bo13b2o11b2ob2o17bo7b3o3b3o3bo2b2o75b2o25b2o60b2o3b2o38bo14b2o3bo14b
o3b2o9b2o$26bo6bobobob2o12b2o49bo10bo12bo23bobo39b3o8b3o116bo68b3o4bob
o17b3o4bobo57bo3bo2bo55bo19bo$25b2o5bob2ob2obo63bo10bo10bobobo24bo38bo
bo9b3o102bo8b2ob2o35bo32bo8bo17bo8bo58b6o24b3o30b3o$32bo93b2obobo19bo
2bo39b3o114bo46b2obo3b2o26bobo4b3o6b3o8bobo4b3o21b2o56b2o7bo17b2o$31b
2o56b3o15bob2obo16bobo18bobobo3b2o2bobob2o67b2o13b2o10b2o47bo3bobo43bo
3b2o28b2o25b2o27b2o37b2o17b2o7bobo15b2o16b2o$107bob2obo16b2o19bo2bo4b
2o2bobob2o67b2o6b2o5b2o10b2o54bo40bobo31bo2bo23bo2bo66b2o27b2o33b2o$
67b2o5b2o12bo3bo14b2o42b2o10bo28b2o3b2o44bobo68bo2bo42bo33b2o25b2o26b
6o$68bo6bo12bo3bo18b2o45b2o34bobo46bobo52bo14bobobo38bo2bo88bo2bo3bo$
65b3o4b3o11bo7bo63b2o31bo7bo39b2o2b2o53bo14bo2bo41bobo87b2o3b2o$65bo6b
o11b2o4bo4b2o11b2o5b2o49b2o24b2o3b2o41bob3o52bobo14b2o44bo42b2o13b2o
10b2o21bo$84bo4bobo4bo11bo6bo50b2o122b2o64bo46b2o6bo6b2o10b2o19bobo$
84bo3bo3bo3bo12b3o4b3o54b2o114bo2bo63bobo52b2o38bobo$77b2o6b2obo3bob2o
6b2o7bo6bo39b2ob2o3b2o4bo2bo66b3obo42bobobo63bo2bo46bo4b2o34bo5bo102b
2o$76bobo8bo5bo8bobo53b2ob2o3b2o2bo2bobo66b2o2b2o42bob3o61bo50bob3o36b
o5bo37b2o63b2o$76bo10bo5bo10bo69bo66bobo48b3o60bobo50b3o37bo5bo37b2o$
75b2o8b2obo3bob2o8b2o64bob2o67bobo94b2o10b2o3bo9b2o87bo$84bo3bo3bo3bo
59b2o13bo63b2o5b2o54bo2bo36b2o10b2o3bob2o6b2o84bo2bo$84bo4bobo4bo59b3o
76b2o59bo2b2o2bo52bo55b3o38bo$84b2o4bo4b2o59b2obo136bo2b2o2bo107b3obo
35bobobo$77b2o7bo7bo7b2o54bobo137b4o71b2o34b2o4bo34bobob2o25bo$76bobo
9bo3bo9bobo52bo2bo135bobo2bobo32b2o13bo21b2o35b2o38bobo21bo3bo4bob2o$
76bo11bo3bo11bo53b2o136b2o4b2o32bob3o8b4o14b3o3b2o28b2o6bo39b2o20bobo
10bo63b3o3b3o$75b2o27b2o230bo3b2o6b2o2bo3b3o7bo3bo2bob2o26b2o68bobo8b
2o63bo2bo3bo2bo$89b3o245bobo2bo4bo2bobo13b3o2b2o2b3o92b2obobob7o2b3o
60b2obo3bob2o$337bo2b2o6b2o3bo13b2obo2bo3bo92b2obo11bo2bo$337b4o8b3obo
15b2o3b3o84b2o10bo12b2o$338bo13b2o15b2o90b2o10bobo$369b2o103b2o3b3o3$
84b2o8b2o254b2o3b2o8b2o10b2o$84bo10bo254b2o3b2o8b2o10b2o$85b10o261b3o$
82b3o2b6o2b3o258bo2bo$82bo2bo2b4o2bo2bo258bo2bo$83b2o10b2o259b3o3$358b
3o$357bo2bo189b2o5b2o$357bo2bo189b2o5b2o$358b3o$350b2o8b2o$350b2o8b2o!

Only one of these (the p168 pi orbital, shown here with reduction by Scot Ellison) can be reduced in period by adding a second signal. Other than glider and Herschel loops, this is the closest thing we have to a reflectorless rotating oscillator (obviously it doesn't meet the 'reflectorless' criterion).

[Lewis]

Are there any oscillators known that reverse direction (like the queen bee shuttle or p46) except without any stabilisation at each end?

[Keiji]

Thank you for the examples Sokwe, they are all quite fascinating. :)

[Lewis]

Does this p32 in B37/S23 count as a reflectorless rotating oscillator?

Code: Select all

x = 5, y = 5, rule = B37/S23
2bo$2obo$2ob2o$2o$4bo!

[Sokwe]

Does this p32 in B37/S23 count as a reflectorless rotating oscillator?

Generally, the definition requires that two copies can be placed on the same track to reduce the period by half.

The period-272 oscillator alluded to in the LifeWiki article is this pattern:

Code: Select all

x = 73, y = 9, rule = B02348/S0123
69bo2bo3$b3o47b3o15b3o$bobo47bobo15bobo$b3o47b3o15b3o3$o2bo46bo2bo!

Even this is somewhat trivial, as the two halves interact slightly.

[Lewis]

I've found a spaceship in the ruloe with the p272 (the ship is probably already known):

Code: Select all

x = 4, y = 4, rule = B02348/S0123
b3o$3bo$3bo$o!

[knightlife]

Are there any oscillators known that reverse direction (like the queen bee shuttle or p46) except without any stabilisation at each end?

In seven generations this well known p14 oscillator does what you ask:

Code: Select all

x = 6, y = 7, rule = B3/S23
3b3o$2o3bo$5o2$5o$2o3bo$3b3o!

[ebcube]

+3-6-8:3 has a oscillator like this of period 32 (8*4):

Code: Select all

x = 3, y = 2, rule = +3-6-8c3
2BA$A!