Fun fact - the computiles piece is an uncredited rediscovery of Wang's work from the 1960's on computable tilings. Specifically, he went as far to show that the halting problem is equivalent to the 'domino problem' - can we tile the plane using a given finite set of dominoes (aka tiles) where we have infinitely many copies of each and the tiling must preserve edge-meet criteria. Every tiling is a computer program, every computer program is a tiling.