A version of this pattern was used by my father as the basis for the creation of a light diffraction pattern, correctly predicting the aperiodic structure of Quasicrystals, discovered in 1982 by Dan Shechtman.
See Wikipedia for a full description of Quasicrystals and their discovery. Also see details of the Nobel Prize account (PDF).
Here is a High Resolution version. The original was kindly autographed by Roger Penrose in 2005.
Also, here is the original paper describing the Penrose Impossible Triangle and the Impossible Staircase.
Sir Roger Penrose
