Make a Conway's game of life simulator which can be run backward any amount up to the initial state, probably implemented by periodically storing state while running forward. This has probably already been done.
But what we really want to do is to be able to point to any object at the end and ask, "where did this spaceship come from?", "how was this formed?", "when was the last time this object interacted with something?", "when was the last time this pentadecathlon interacted with something that was not an ordinary glider reflection?"
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I am sorry, could you explain this one a bit more, i don't quite get it...
Hypothetically, you start a Methuselah-type pattern, and thousands of generations later, you happen to notice a heavyweight spaceship flying away to the side. The pattern left a lot of other debris, so you didn't notice the spaceship until now. Heavyweight spaceships are interesting, so you would like to watch the exact reaction that formed it: have the computer automatically rewind backward and isolate the moment in time that the spaceship formed.
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