Aperiodic tilings and quasicrystals
The aim is to understand the relationship between substitution and
projection properties of aperiodic tilings such as the Penrose tiling.
The following issues are of interest
Work in progress with Edmund Harriss (Queen Mary).
- Classification of substitution rules for classes tilings with
special projection properties. (In the Penrose case: substitution rules
for canonical projection tilings)
- Understanding the relationship between the set of substitution rules
(often a countable infinity) for substitution tilings.
- Generalized continued fractions and tilings.
- Substitution tilings with non-uniform scaling.
For an impression of the topic, see Andrew Lewis's short
introduction , inspired by a 3rd year course I taught at Warwick in
1998 and 1999.