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Not completely absolute oscillator, but family of oscillators which has similar properties. Here you can see 7 basic blocks.

x = 26, y = 15, rule = Langtons-Ant
25.H2$21.H2.F2$17.H2.F2$13.H2.F2$9.H2.F2$5.H2.F2$.H2.F2$F!
Each time when we add symmetrically 2n blocks, it always oscillates with p(n ...

Small and not very interesting addenum.

Oscillators which produce and use still life for their working.
Specific one (look at it with slow speed).

English not my native.

There exist another thread about LA, but I more appreciate this one. I have noticed some (maybe) interesting things, here they are:

1) If we place 2 ants with same direction and coordinats (x1,y1) and (x2,y2) on infinite grid (all cells one-colored), so they:

1.1) may meet ...

danny wrote:Ah, so something like this:

You are absolutely right, thank you twice! It works only for n>1 (but I don't think that this small detail has some sense).

I don't quite understand, are you looking for something like this pattern due to David Greene?:
First of all, thank you for answer! I also have problems with understanding (exactly how this pattern works). But, yes, it include something like what I am looking for. Let me show:

x = 23, y = 47 ...

Not sure where to put this question. Also english is not my native.

Take any oscillator. Choose any generation (we need at least one). Clone it n times on infinite grid with two conditions: 1) each copy shifted by the same distance from previous (we need at least one way); 2) for any natural n ...