Yes, the rules of Conway's Game of Life is Turing Complete.

The glider shape (the thing moving diagonally out of the window in this meme) can be created non-destructively by a glider gun (another shape that creates gliders), which can be controlled using stored pixels in another configuration within the glider gun, including taking in input from other gliders, such that the whole thing can loop and do everything necessary to be a universal Turing machine. Not super efficiently, but it will still do the things that Turing machines can do, given enough cycles.