This is turing complete

[CrispyPin]

The README states

We lose Turing completeness because our new procedure is not deterministic, but practice shows that this formalism still allows to describe a huge range of interesting random processes.

But you can create a deterministic system with strict enough patterns.

Example of conways game of life in an async CA https://www.youtube.com/watch?v=oXiqMGhn9rk&t=749s

Rule 110 (which is turing complete) implemented in MarkovJunior:

rule_110.mp4

rule_110.xml

[mxgmn]

That is an interesting question indeed! I'm a little swamped at the moment, but I'll answer as soon as I have time.