Just like building a real computer, you don't have to hold all of the concepts in your mind at once, just start with basic building blocks and work your way up the ladder of abstraction to parentheses or space invaders or whatever floats your boat. :)
That can fall down a little when it comes to debugging. You end up having to break everything back down to component parts more than if you could keep larger parts in your head at once.
I probably could do it, understanding all the parts implies that. Eventually. Just not in a reasonable amount of time, and perhaps not as neatly.
Oddly beautiful seeing it run too. And the gliders flowing around put me in mind a bit of the ants that run Pratchett's Hex.