Here is a cellular automaton that creates wave-like patterns using relatively simple rules, the Java code can be found here: https://gist.github.com/SeanBP/1c1baadcf064467629d9.
The idea is that each cell contains eight vectors (each pointing to a different neighbor) with a given value. That value is then passed on to its neighbors in a way that's described below.
Patterns usually propagate in diamond shapes, and are able to interfere with each other. This rule would probably be very difficult to put into Golly, since there is an infinite number of states a single cell can hold.