Interesting question

[Rhombic]

Are other p4 oscillators known such that each phase of the oscillator is equivalent to a 90º rotation of the previous phase, with no intermediates, in a two-state rule?
https://catagolue.appspot.com/object/xp ... knr5ks2-i3

there are many p2 of this kind, e.g. blinker (it becomes the previous phase, rotated 180º)
Due to the constraints, only p2 and p4 can be considered.

Main question:
Is there a p4 in Life (CGoL) such that every phase is equivalent to the previous phase, rotated by 90º?

How would we prove that none exist?

[BlinkerSpawn]

I'm pretty sure Pinwheel and Clock 2 qualify, and possibly that one p4 in DRH-oscillators.rle where four mazings hassle another spark, but all that depends on your definition of "intermediates".
If you're specifically looking for statorless p4 oscillators that rotate, I don't believe (EDIT: wrong) there are any known yet but I feel like that wouldn't be terribly difficult to search for.
Also, the blinker doesn't rotate 180 degrees every phase, only 90.

[calcyman]

If you're specifically looking for statorless p4 oscillators that rotate, I don't believe there are any known yet...

...and possibly that one p4 in DRH-oscillators.rle where four mazings hassle another spark...

[BlinkerSpawn]

Heh, must've been under the impression that mazings had a stator.
The oscillator I was referring to, for reference:

Code: Select all

x = 21, y = 21, rule = B3/S23
10bo$10bo$10b3o$11b2o$6b3o2b2o$8b3o$8b3o$17b2o$15bobo$3b2o5b2o2bo5bo$b
obo6b3o2bo3b2o$o5bobo$bo3b2obo2b2o4bobo$18bo$3bobo6bo$4bo7bo$12b3o$13b
2o$8b3o2b2o$10b3o$10b3o!

[muzik]

And here they are, all three of them:

Code: Select all

x = 50, y = 21, rule = B3/S23
4b2o12b2o18bo$4b2o12b2o17bobo2$4b4o10b4o13bo3b2o$3bo2bobob2o5bo2bobob
2o8bo5bo$3bobo2bob2o5bobo2bob2o9bobo$2obo3b2o5b2obobo2bo14b2o6bo$2obo
4bo5b2obo4bo22bo$4b4o10b4o9bo5b2o4b3o$31bo11b2o$6b2o12b2o7b3o7b2o2b2o
2b3o$6b2o12b2o7b2o6bob2o4b3o$29b2o2b3obobo5b3o$31b3o$31b3o6bo$39bobo2$
37bo3b2o$36bo5bo$37bobo$39b2o!

So the question naturally arises: are there more of this type of oscillator? Also, should they be given a name?

[dvgrn]

So the question naturally arises: are there more of this type of oscillator?

Sure. There are lots more where this random sample comes from, assuming that the highly mysterious "no intermediates" requirement doesn't disqualify it somehow. Just weld four copies of your favorite P4 together:

Code: Select all

x = 23, y = 23, rule = LifeHistory
11.2A$10.B2AB$11.2B$10.2B$9.B3A$9.A.2B$10.A.2BA$7.3A2.2A.A$6.A8.A$.B
4.2A7.A.2A$2AB.4B8.A.2B.A$2AB2AB11.A4BA$.B.BA.A8.B3A.2BA$4.BA.A7.2A4.
A$7.A8.A$7.A.AB2.3A$8.2AB.A$10.BA.A$10.B2AB$11.2A$10.2A$9.B2AB$10.2A!

Even mirror-symmetric p4s will fit the bill, as far as I can see -- the final composite will look like it's mirror-symmetric at any given moment, but it won't be, quite:

Code: Select all

x = 13, y = 13, rule = LifeHistory
.2AB5.2BA$B3A5.2ABA$B2A.A3.A.3B$2B.A.A.A.A.BA$2.A2.A.A2.A$3.3A.3A2$3.
3A.3A$2.A2.A.A2.A$BA.A.A.A.A.AB$BAB.A3.A.3A$A3B5.B3A$.ABA5.3B!

Also, should they be given a name?

Please, no! Names are best invented when people have been saying "p4-oscillator-where-each-phase-is-a-90-degree-rotation-of-the-previous-phase" for a year or two, and collectively discover after careful reflection that they really really can't get along without a shorter way to say that.

So... sometime in 2019, just look back through the twenty-three pages of this thread and see what people have been calling these things for the past year -- and there's your official name. If this thread still has only one page and no postings since May 2017, well, then no neologism is needed.

For this kind of question it's possible I'm a little biased from trying to keep the Life Lexicon update from going wildly out of control, so don't let me spoil your fun -- but also don't be in a great hurry to make a new LifeWiki article about these things...!