Guam wrote "2 gliders (G0) to glider converter with repeat time 51"
Great find! This is very useful for building high-period, low-diameter oscillators like the ones described in my paper with Buckingham "Tight Bounds on Periodic Cell Configurations in Life":
http://projecteuclid.org/DPubS/Reposito ... 1047674205
This took me a few hours to put together and it's a lot more elegant than the one I used when writing the paper (some explanation follows the pattern). Here is a period-16966 glider gun that can be set to have any period 19110-536n for n=1,2, ..., 16 by sending a stream of n gliders.
Code: Select all
x = 305, y = 191, rule = B3/S23
The idea is to build a variable-period oscillator based on n-bit counters. The period grows exponentially with the number of counter bits, so it is more compact than an oscillator based on path distances. It uses a gun based on all still-life components that can be triggered by a glider, but this gun also has an n-bit counter and stops itself after producing 2^n gliders. In addition, it sends the output gliders into another n-bit counter with a preset state m (1<=m<=2^n) such that it absorbs all 2^n gliders but outputs a single glider after step m, and also restores the counter to its original state.
Putting these together, you get a reflector that outputs a glider after a+b*m steps for some constants a, b and has a something like a b*2^n recovery time. You can bounce a glider between two reflectors like this, as long as the second reflector gives the first reflector sufficient recovery time. This makes it possible to realize all oscillator periods c+b*(2^n + m) for some constants b and c.
After building this oscillator (for n=4) i realized that it could not only be triggered by a glider from outside, but its period could actually be adjusted just by sending a different number of gliders. In this example, it receives a series of 4 initial gliders and has period 16966. It can be triggered with n = 1 to 16 gliders, and will have period 19110-536n. The reason is that the gliders are sent through one of the 4-bit counters (base on semi-snarks). It is preset to all 1s so that the first glider causes the bits to reset and outputs a glider. Subsequent gliders will increment the state of the
counter, reducing the oscillator period.
More than 16 gliders introduces a second glider in the reflector shuttle, which eventually destroys the pattern. It is possible to stop the gun, restoring its initial state, using a synchronized glider/glider collision in a several different places. After that, it can be reset to any other oscillator period by sending the appropriate number of gliders.