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For W22, simply use B3/S23:T0,1. Of course, this does not allow you to compare multiple patterns side-by-side, so a rule table would still be helpful.
Actually, how hard would it be to write a script to generate a rule tree for 1d elementary CA?
One question is: if you start with a single cell in a circular world, what will the eventual period be?
For R110, in a circular universe of width n, we have period:
For W22 we have:
Then, there's the question of how long it takes to stabilize. In W22, the time taken for a single cell to stabilize in an n cell circular universe is: