For me the easiest of these guns to comprehend is the p57 one, so let’s work our way up to that.
Start by considering the heptomino that has acquired the somewhat erroneous name of herschel. It arises, along with some debris, early in the evolution of the r pentomino and spits out a glider, which is how the glider was discovered back in 1970. Without the r pentomino’s debris, the herschel stabilizes in 128 generations leaving two blocks, two glders, and a ship. But a notable thing about the herschel is that its evolution isn’t centered around its original position; most of the action happens to one side. Here’s a herschel (in red) and its stable state (in green), with the cells that otherwise were live in blue:Notice how, aside from the gliders, most of the action happened off to the left of the initial state.
So you can use a hershel over here to make something happen over there. In particular, you can imagine setting up some still lifes that will interact with the herschel in such a way as to make another herschel happen over there — while preserving the still lifes. Like this. Start with this state: and 117 generations later you have this state:plus a glider off to the southwest, which can be disposed of with another eater if you want. The eaters and snake perturb the herschel without getting injured; the block gets destroyed but is then remade in the same place.
So that’s very cool. It’s called a conduit. You could put a second conduit to the right of the first, positioned so the herschel output by the first conduit is in just the right place to be input to the second one, and at generation 234 the herschel will appear to the right of the second conduit. And of course you could put a third conduit, and a fourth, and a fifth, and so on, and transport that herschel as far as you like in a straight line, popping up every 117 generations.
What’s a little less obvious is that if you can contrive a way to feed such a track of conduits a periodic series of herschels, they’ll get transported just fine even if they turn up more often than every 117 generations. In fact, this conduit is ready to accept its next herschel as frequently as every 63 generations.
Furthermore, you’re not limited to straight lines. There are other conduits that will transport a herschel around a corner. Some conduits do a mirror flip of the herschel, some don’t. Some even manage to send a herschel backwards.
So with some ingenuity, you can set up a track of conduits that goes around four corners and connects back on itself in a loop! All of this was pioneered by David Buckingham in the 1990s, and his period 61 loop was the first period 61 Life oscillator discovered.
Since then there’s been lots of herschel conduit exploration going on, involving discovery of both new conduits and new ways to make use of them. And that’s what’s going on in the p57 gun; you have a loop, built of conduits that can accept herschels every 57 generations. Unfortunately you can’t just leave out one of the tub-with-tail still lifes that eats the gliders emitted by the herschels without breaking the conduit, but hanging off the bottom of the loop is a crazy lump of a period 3 oscillator. It hassles the nearby conduit into spitting out a glider while preserving the conduit action, and, boom, p57 gun.