[nennes]

I'd be curious to see code that generates an initial state that when running indefinitely can create a stable state which looks as much as possible like a given image.

That would basically be the "living" representation of the image, as far as game of life rules go.

Does this sound solvable by DP?

[Someone]

If you cheat, that’s trivial.

Start with the target stable state, and add something that, on its own, dies out, far enough from the target stable state to not interfere with it.

You could cheat a tiny bit less by removing a small stable part from the ‘edge’ of the target pattern, firing gliders at it that, just before hitting the smaller target, collide to complete the stable pattern.

I think you can generate many stable patterns by taking this to the extreme: start with an empty target area, and fire gliders at it that collide and add stable parts one by one.

You may need lots of gliders, but since the board is infinite, it’s easy to prevent the separate glider groups from interfering with each other.

[egypturnash]

Dense grid of traffic-light oscillators would work too, it wouldn't move across the board.

So could a bunch of beehives/loafs/etc.

[virgil_disgr4ce]

Not sure what you mean by DP, but this should in general be possible (granted enough memory & computing power). The problem for me is that stable states have to be fairly sparse, so I'm not sure how you'd get one to really look like anything at all ...

[nennes]

Yes, dynamic programming as mentioned. Good point about the stable states being sparse, meaning we wouldn't be able to get close enough to a good representation of the image.

[saagarjha]

Dynamic programming, presumably. The other abbreviations are much less appropriate in this context.