34 cell oscillator???

[xander12505]

I modified the period 17 oscillator 54P17.1 to make it unstable, and then stabilized it with a beacon. When i put the beacon in its second fase, it takes the pattern 34 generations to turn back to it's original pattern. I'm wondering if this counts as a trivial example or not, because I modified 54P17.1 to depend on the beacon for stabilizing.

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x = 16, y = 15, rule = B3/S23
2o$2o$2b2ob2o$2b2obobo$5bobo3b2o$2b2obob2o3bo$3bobo6bob2o$bo2bobob3obo
2bo$b2obobo4bobo$4bobo2b2o2b2o$4bobo3bobo$5b2obobobo$7bobobo$7bobo$8b
2o!

If you look closely at the upper right part of the bottom square of the beacon, then go 2 cells to the right, you can see the cell I modified.

[p46beth]

Interesting. There can be multiple definitions of a "true" p34 oscillator. Because the p17 you give is unstable by itself, I suppose there could be a definition which would make this a true p34. The prevalent definition, however, requires that at least one cell must oscillate at the full period, which does not happen in the pattern you gave.

Either way, it is still an interesting idea.

[hkoenig]

It's possible for a single object to contain multiple oscillator rotors.

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x=36, y=33
2o14b2o3b2o$obo13bo4bo4bo$19bobo3bobo$2bobo13b2obob2obo$3b2o17bo$5b2o$5bob
o2$7bobo$8b2o7$2o22bo$o22bobo$2b2o19bobo4b2o$21b3ob2o4bo$3bobo14bo10bob2o$21b
3ob2o3b2obobo$5bobo15bobo7bobo$30bobobo$7bobo20bo2bo$9bo16b2o3b2o$11bo13b
ob4o$10b2o13bo4bo$12b2o12b3o$12bobo13b2o2$14bobo$15b2o!

On the top line at the left is a 16-bit object which appears to be the smallest case, but here both rotors are period 2, so there's no new period. On the right is an 18-bit object with a Period 2 and a Period 3 rotor, making the object itself Period 6.

Historically, talking about a Pn oscillator has implied that an object has a single rotor, which is why in the second row, both objects may be Period 10, the one on the right (found by Dean Hickerson) is the "smallest oscillator" since it has a single rotor.

In some ways this mirrors the difference between "objects" and "pseudo-objects", in that the latter can be subdivided.

(My definition above could conflict with the "at least one cell must oscillate at the full period" one, if it's possible to have a composite rotor in which two rotors with different periods overlap and support each other. For example, a Period 6 which is actually a composite of Period 2 and Period 3. But I don't even know if that's possible, or if an example has already been discovered.)