I’ve dabbled intermittently with Conway’s Game of Life — strong emphasis on both “dabbled” and “intermittently” — for more than 45 years now. In fact I think I read Martin Gardner’s classic article on the subject in the October 1970 Scientific American when it was hot off the press (in my high school library), a month or so before William Gosper found the first glider gun. That gun bounces two queen bee shuttles off one another; the mechanism repeats itself every 30 generations, producing a glider each time, so it’s a period 30 gun. The following year Gosper found another glider gun, with period 46.
You can perhaps imagine a gun like one of these, which emits a glider, for instance, every 50 generations, but whose mechanism repeats itself at a multiple of that period — every 100 generations, say. In that case one says the gun has a true period of 100 and a pseudo period of 50. (Despite the pejorative connotations of “pseudo”, though, if you’re using a gun to build something, it’s probably the pseudo period that’s of more interest to you.)
The shortest (pseudo) period a glider gun can have is 14. If you try to make a glider stream with shorter period, it doesn’t work: the gliders interact with each other and die. There are guns known with all pseudo periods from 14 on up.
For the true periods, though, there are holes. All periods from 62 up exist, but the smallest true period known is 20, and there are quite a few periods in between with no known gun.
But fewer such holes than there were a couple days ago.
On Wednesday, “AbhpzTa”, a newcomer to the conwaylife.com forums, posted a p61 gun:
and “AbhpzTa” compactified it this morning:
Just an hour later, Matthias posted a p57 gun:
Three new true periods found in less than 48 hours!
How do these things work? Like I said, I dabble, and there’s a lot of arcane Life knowledge out there I’m not up on. But I think I get at least some of the ideas at work here, and I’ll write them up for my own benefit if no one else’s soon.