This is an interesting question, but I think your hypothesis is wrong.
Any pattern of physics that eventually exerts control over a region much larger than its initial configuration does so by means of perception, cognition, and action that are recognizably AI-like.
In order to not include things like an exploding supernova as “controlling a region much larger than its initial configuration” we would want to require that such patterns be capable of arranging matter and energy into an arbitrary but low-complexity shape, such as a giant smiley face in Life.
If it is indeed possible to build some sort of simple and robust “area clearer” pattern as the other comments discuss (related post here), then nothing approaching the complexity of an AI is necessary. Simply initialize the small region with the area clearer pattern facing outwards and a smiley face constructer behind it.
It seems to me that the only reason you’d need an AI for this is if that sort of “area clearer” pattern is not possible. In that case, the only way to clear the large square would be to individually sense and interact with each piece of ash and tailor a response to its structure, and you’d need something somewhat “intelligent” to do that. Even in this case, I’m unconvinced that the amount of “intelligence” necessary to do this would put it on par with what we think of as a general intelligence.
This is an interesting question, but I think your hypothesis is wrong.
If it is indeed possible to build some sort of simple and robust “area clearer” pattern as the other comments discuss (related post here), then nothing approaching the complexity of an AI is necessary. Simply initialize the small region with the area clearer pattern facing outwards and a smiley face constructer behind it.
It seems to me that the only reason you’d need an AI for this is if that sort of “area clearer” pattern is not possible. In that case, the only way to clear the large square would be to individually sense and interact with each piece of ash and tailor a response to its structure, and you’d need something somewhat “intelligent” to do that. Even in this case, I’m unconvinced that the amount of “intelligence” necessary to do this would put it on par with what we think of as a general intelligence.