In May and June 2021 David Raucci (hotdogPi) on the ConwayLife forums discovered some oscillators in Conway's Life at small populations, small periods or both, which provoked me to make a little stamp collection of the smallest known non-trivial oscillators by minimum population up to p106 where I opined "the rectifier becomes more efficient than the snark for building adjustable glider loops". This turned out to be not quite right – a rectifier loop's length is of the form 8n + 2 and hence cannot have a period that is a multiple of 4 – but that gap is filled by p4 bumper and p8 bouncer/bumper loops, providing a universal upper bound of 141 cells at p187 and above.

This repository started out as an independent script in my glider synthesis database Shinjuku as an automatic generator of the aforementioned glider loops and collector of other smallest known oscillators of periods n – hence the name Skopje, North Macedonia's capital. It still requires lifelib however.

To get the smallest known oscillator of period 109 in Conway's Life together with its minimum population:

from skopje import skop
skop109, minpop109, source109 = skop(109)[0]

skop() returns a list of triples (lifelib Pattern, minimum population, description) to allow ties as in the p4, p7 and p128 cases; to get the pattern's apgcode and RLE use skop109.apgcode and skop109.rle_string() respectively. The function compares several different constructions as well as a list of fixed oscillators, LCM or otherwise, to arrive at its final result.

SKOPs in other rules can be found by passing the rule= argument; the supplied string gets run through lifelib's sanirule() function before being mapped to a filename. The file itself should contain three objects:

• lt, the lifetree under which computations are performed.
• fixeds, a multiline string where each line gives the period of a fixed oscillator, its apgcode and its minimum population, all separated by spaces.
• cfuncs, a sequence of functions each accepting a period and returning None if its corresponding construction is not applicable to that period or (Pattern, minimum population) otherwise. The latter element can itself be None to indicate that the period is in a range where the population does not follow a defined formula.