Aperiodic Tiling with a Single Shape

(tongue in cheek) Joseph J. Sullivan knew this would happen this back in 1888, and was curious about how they come up with the idea, so wrote the song "Where Did You Get That Hat?"

I kid you not, the lyrics include "Where did you get that hat, Where did you get that tile?" https://youtu.be/0ueF74F26Q4?t=52 . Surprisingly apropos, no?

I first heard a snippet of the song from Dr. Who. I think Romana (as played by Lalla Ward) sang it? But I can't recall the episode.