The basic idea is to use the distance of the gliders to encode information, so when they hit each other allows for an embedding of a Turing machine.
I'm no expert here but some basic ideas are that some small number of gliders (two?) can hit each other and produce a "glider gun", allowing for just a few gliders to "upgrade" to producing a steady stream of gliders. There's a "Reverse Caber Tosser" (RCT) structure which has a stationary element that "tosses" a glider back and forth with a structure moving away (or towards?) it, emitting another glider in another direction after each toss, allowing for logarithmic glider/population growth. Another key idea looks to be the "glider producing switch engine" (GPSE) which incorporates the ideas of the RCT with a delay and some other logic?
The distances involved are astronomical because they're encoding everything in the distance but they still manage to make it Turing machine equivalent with only 15 gliders.
Anyway, I'm floored at the ingenuity of the GoL community. It's as close to programming with butterflies as I've ever seen [0].
I'm no expert here but some basic ideas are that some small number of gliders (two?) can hit each other and produce a "glider gun", allowing for just a few gliders to "upgrade" to producing a steady stream of gliders. There's a "Reverse Caber Tosser" (RCT) structure which has a stationary element that "tosses" a glider back and forth with a structure moving away (or towards?) it, emitting another glider in another direction after each toss, allowing for logarithmic glider/population growth. Another key idea looks to be the "glider producing switch engine" (GPSE) which incorporates the ideas of the RCT with a delay and some other logic?
The distances involved are astronomical because they're encoding everything in the distance but they still manage to make it Turing machine equivalent with only 15 gliders.
Anyway, I'm floored at the ingenuity of the GoL community. It's as close to programming with butterflies as I've ever seen [0].
[0] https://xkcd.com/378/