I don't know too much about it, but there is an offhand comment on the Langton's Ant wikia that if you take a pair of ants (n,n+1) apart (of the same colour, facing the same direction) then you will get an oscillating pattern - your block seems to be of this type if I understand correctly. Any set of such blocks whose oscillations do not intersect will oscillate, presumably. langtons-ant.wikia.com/wiki/Oscillator

I'm not sure if this is worthy of a full answer, but there is a similar question about expressing a graph in terms of the symmetric difference of complete bipartite graphs here: mathoverflow.net/questions/76043/…