I started hunting around in parameter space trying to get my head around what makes the traveling pulse stable and predictable. I don't yet have a set of exact rules, but what I've learned is that the reactions need to be slow compared to the diffusion. This is achieved by simply lowering the concentration of the gates and resistors appropriately. Next, the pull down gates 1 & 2 are very small compared to the feedback and shutdown gates. Also, the "tired" charging gate is very small so that you can delay the onset of the shutdown.
The biggest point is obvious when you look at the phase diagram: you have to let the system get back into steady-state before another pulse hits it. Also interesting is how perfectly straight are the edges of the phase diagram. I think that this means that the gates are run way out of their linear regions and are running in steady-state most of the time. I'm going to try to make a graph to make sense of that.
I also found that it is easy to make complex patterns form when you push the system really hard as in the following class-3-like cellular automata. Note that the system was started with symmetric initial conditions and has full symmetric rules yet is symmetric only until it starts to interact with itself; once it reaches the boundaries, it becomes asymmetric. Fascinating. I suppose this is because the "periodicity" of the pattern is not related to the size of the container so the two periods start to alias in some weird sense.
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