A mind stretching experience.
Managed to get Professor Penrose to sign my copy of The Emperor's New Mind.
Some notes and key words jotted down during the lecture :
- icosahedral symmetry
- crystalline patterns can have rotational symmetry as well as translational symmetry
- n-fold symmetry
- Penrose tiles are surrounded by rings of 10 pentagons
- only 3 kinds of polygons are used to create Penrose tiles : star, jester's cap and pentagon
- Penrose tiles exhibit a "non-repeating quasi 5-fold symmetric pattern"
- Robert Ammann solids (3-D tiling)
- J Kepler (1619) in his book Harmonice Mundi shows tiling patterns that anticipate Penrose tiles
- Penrose tiles exhibit a "hierarchical structure"(?)
- Penrose tiles have a connection with fractals
- there seem to be analogies between the formation of quasi crystals and the superposition principle in quantum mechanics ("non-local choice" is present in both)
- Penrose tiling uses only two structures : kites and darts