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Well, there are programs like Logic Life Search that can solve reasonably small instances of backwards search. This problem is quite hard in general. Part of the reason is that you have to consider sparks in the search. The pattern in question could have evolved from small predecessor pattern, but the reaction could have moved from the starting point and a several dying sparks could have been emitted all around. So you have to somehow figure the exact location, timing and nature of these sparks to successfully evolve the pattern backwards. Otherwise, it quite quickly devolves into bigger and bigger blob of seemingly random dust. In practice, backwards search is regularly applied to find smaller predecessors in terms of bounding box and/or population. See, for example, Max page. And the number of ticks backwards is quite small, we are talking about a single-digit number here.
I've got a very good intuition about foo-vectors from Let's remove Quaternions from every 3D Engine post.