[biggiemac42]

This is a really good and not at all easy to answer question. The most I can say is that folks earlier this year used some SAT solver equivalent to find notable patterns that cannot be constructed - including a still life and an oscillator https://conwaylife.com/wiki/Unsynthesizable_oscillator_1. This doesn't have much bearing on the probability of constructability for an arbitrary large pattern.

[JKCalhoun]

Yeah, I was wondering, with todays computing power, if it were possible to run outrageously large random Life universes and use some sort of software to look for "interesting patterns" (whatever that means).

Or are these "discoveries" being done by hand?

[OscarCunningham]

A lot of discoveries have come from 'soup search' where you start with a random 16 by 16 square and let it evolve. We've run over 156 trillion soups https://catagolue.hatsya.com/statistics. This tends not no produce complicated machines, but rather small components that can then be engineered into larger patterns.