My immediate impulse is to say that it ought to be possible to create the smiley face, and that it wouldn’t be that hard for a good Life hacker to devise it.
I’d imagine it to go something like this. Starting from a Turing machine or simpler, you could program it to place arbitrary ‘pixels’: either by finding a glider-like construct which terminates at specific distances into a still, so the constructor can crawl along an x/y axis, shooting off the terminating-glider to create stable pixels in a pre-programmed pattern. (If that doesn’t exist, then one could use two constructors crawling along the x/y axises, shooting off gliders intended to collide, with the delays properly pre-programmed.) The constructor then terminates in a stable still life; this guarantees perpetual stability of the finished smiley face. If one wants to specify a more dynamic environment for realism, then the constructor can also ‘wall off’ the face using still blocks. Once that’s done, nothing from the outside can possibly affect it, and it’s internally stable, so the pattern is then eternal.
OP said I can initialize a large chunk as I like (which I initialize to be empty aside from my constructors to avoid interfering with placing the pixels), and then the rest might be randomly or arbitrarily initialized, which is why I brought up the wall of still-life eaters to seal yourself off from anything that might then disrupt it. If his specific values don’t give me enough space, but larger values do, then that’s an answer to the general question as nothing hinges on the specific values.
I was imagining that the goal configuration would be defined over the whole grid, so that it wouldn’t be possible to satisfy the objective within the initial region, since that seems most analogous to constructing an AI in, say, a single room on Earth and having it eventually influence the overall arrangement of matter and energy in the Milky Way.
My immediate impulse is to say that it ought to be possible to create the smiley face, and that it wouldn’t be that hard for a good Life hacker to devise it.
I’d imagine it to go something like this. Starting from a Turing machine or simpler, you could program it to place arbitrary ‘pixels’: either by finding a glider-like construct which terminates at specific distances into a still, so the constructor can crawl along an x/y axis, shooting off the terminating-glider to create stable pixels in a pre-programmed pattern. (If that doesn’t exist, then one could use two constructors crawling along the x/y axises, shooting off gliders intended to collide, with the delays properly pre-programmed.) The constructor then terminates in a stable still life; this guarantees perpetual stability of the finished smiley face. If one wants to specify a more dynamic environment for realism, then the constructor can also ‘wall off’ the face using still blocks. Once that’s done, nothing from the outside can possibly affect it, and it’s internally stable, so the pattern is then eternal.
This sounds like you’re treating the area as empty space, whereas the OP specifies that it’s filled randomly outside the area where our AI starts.
OP said I can initialize a large chunk as I like (which I initialize to be empty aside from my constructors to avoid interfering with placing the pixels), and then the rest might be randomly or arbitrarily initialized, which is why I brought up the wall of still-life eaters to seal yourself off from anything that might then disrupt it. If his specific values don’t give me enough space, but larger values do, then that’s an answer to the general question as nothing hinges on the specific values.
I was imagining that the goal configuration would be defined over the whole grid, so that it wouldn’t be possible to satisfy the objective within the initial region, since that seems most analogous to constructing an AI in, say, a single room on Earth and having it eventually influence the overall arrangement of matter and energy in the Milky Way.