Heh, I think I can find answers for "surprising" a lot more easily than for "useful". The main practical use for Conway's Life is as a teaching tool, giving a nice explorable example of layers upon layers of incredible complexity that can arise from very simple rules. So I suppose that people who can benefit from that kind of insight might find Conway's Life "useful", in a way -- engineers, mathematicians, and just anyone who is curious about the universe we live in and the physical laws that seem to underly its behavior.
The big surprise that I've been spending the most time on lately is the utterly strange result that if you can build something by colliding gliders together -- no matter now many gliders and no matter how big the final pattern is -- then you can also build it by starting with exactly fifteen gliders in an otherwise empty Life universe:
It's a mind-bending result -- partly just a mathematical trick, since you end up encoding a whole lot of information in the space between the gliders -- but it's just really amazing that all the details have actually been figured out to make the trick work, and that it's possible to simulate the whole process on a personal computer.
dvgrn|1 year ago
The big surprise that I've been spending the most time on lately is the utterly strange result that if you can build something by colliding gliders together -- no matter now many gliders and no matter how big the final pattern is -- then you can also build it by starting with exactly fifteen gliders in an otherwise empty Life universe:
It's a mind-bending result -- partly just a mathematical trick, since you end up encoding a whole lot of information in the space between the gliders -- but it's just really amazing that all the details have actually been figured out to make the trick work, and that it's possible to simulate the whole process on a personal computer.