Penrose and Aperiodic Tiling

The tiling shown in the lectures was in fact one of three forms of Penrose tiling, and was not in fact the original form. The original created by Penrose used 5 different tile styles, shown here.

http://en.wikipedia.org/wiki/File:Penrose_Tiling_(P1).svg

The symmetry and other properties are completely equivalent between the three styles, and is an example of of substitution. This is where one can break the original shapes into smaller variations, and use these to reconstruct the the tiling.

Due to this possible substitution the tiling shares some features with fractals, in that it may be inflated or deflated, yet present the same image and symmetry.

A list of other forms of aperiodic tiling in various geometries can be found here:
http://en.wikipedia.org/wiki/List_of_aperiodic_sets_of_tiles