We have never discovered a self-replicating pattern in a random life-field. I once saw a calculation that showed you would need a computer with the volume within a few orders of magnitude of the solar system to do so (not mass, volume). All the ones we have are intentionally constructed.

Most theoretical work done on self-replicators in life works by assuming ultra-low density fields, maybe one live cell per billion at the start (a proportion which immediately plummets much lower owing to the fact that cells need 2 neighbours to survive) so the empty space rule will probably be similar. Even if you use a higher density, most of the space will end up filled with the same mixture of small scale still-lifes, oscillators and high entropy regions, busy but not interesting. Much like most of the empty space in our universe still mostly contains background radiations (I think).

As for the fields I looked at, in general it was quite easy to prove mathematically that they were uninteresting. Interestingness requires a mixture of stability and complexity which even the ones where I couldn't manage a proof lack.