Possible P38?

[devinallen]

Hi there! I'm a new user, so i might get a lot of stuff wrong here. Anyway, I'l cut to the chase. I MAY have found a P38 oscillator. It might be a P30 though. I can't really tell.

x = 34, y = 31, rule = B3/S23
7$8b2o$9bo$4b3o2b2o$2b3obo3bo$2bo4bob2o$6bobo$4b2obo4bo$4bo3bob3o$4b2o
2b3o$5bo$5b2o2$11bo6bobo$13bo4bo2bo$14b2o5b2o$9b2o8bo3b2o$9b2o10b2o$
18bo2bo5b2o$18bobo6bobo$29bo$29b2o!

[Alexey_Nigin]

Hello, and welcome to the forums!

There exist a few tools that let you find the period of an oscillator. My favourite one is the oscillizer, which is very user-friendly. If you go to that page, enter your pattern and click Analyse, you will find out that your oscillator is p120.

I should probably explain why you ran into error. When you combine oscillators of two different periods, that periods don't add up. In particular, p8 and p30 don't give you p38, as 38 is not divisible by 8, and, as a result, p8 part will not return to the same phase after 38 ticks. It means that the period of your oscillator must be divisible by 8. But it also must be be divisible by 30 for the same reason. So, it's natural to conjecture that the period is the smallest number divisible by 8 and 30. This number, denoted by LCM(8,30), equals 120. Hey, we have figured out the period without oscillizer!

Everything is a bit more difficult than that, (un)fortunately. Consider this oscillator:

Code: Select all

x = 10, y = 20, rule = B3/S23
2bo4bo$2ob4ob2o$2bo4bo17$3o!

It consists of a p15 and a p2, so it's period is LCM(15,2)=30. But the cells on the top oscillate at period 15, while at the bottom there are cells oscillating at period 2. There is also a cell in the middle of the blinker which is always on, so we can say it oscillates at period 1. You see that no cell oscillates at whole period. Such oscillators are called trivial, because the halves don't really interact. On the contrary, your oscillator is non-trivial, as there is one cell right between the galaxy and the buckaroo which oscillates at p120. This cell is white in the oscillizer.

Frankly speaking, everything is not so simple, and pA plus pB doesn't necessarily give p(LCM(A,B)). But it's a much more more complicated thing called rephasing, and I don't want to write about it now.

If you have any questions,feel free to ask.

And I think a non-trivial oscillator is a pretty good achievement for a newcomer!

[codeholic]

Neither. It is a p120 oscillator. Oscillator periods do not simply add up, you need to take the least common multiple (lcm). lcm(8, 30) = 8 * 30 / gcd(8, 30) = 240 / 2 = 120.

Oscillators composed of known oscillators are found very easily with gencols. I highly recommend learn how to use it.

[devinallen]

Thanks!