Penrose gave a talk at the Royal Institution about his periodic filings. Well worth a watch: http://youtu.be/th3YMEamzmw
It's light on math and heavy on hand-drawn transparencies being lined up on an overhead projector. He has these inscrutable registration marks that he matches by hand -- reminds one of the alien code in the movie Contact.
One of my favorite parts concerns some mysterious scribblings by Kepler that seem to presage his work!