Quasicrystals in driven systems

Quasicrystalline patterns can form on surfaces of liquids subjected to vibrational motion.

This can happen both with single tone and two tone drive.

• attached paper by Vinals;

• Lifshitz, R. & Petrich, D. M. Theoretical model for Faraday waves with multiple-frequency forcing.
  Phys. Rev. Lett. 79, 1261–1264 (http://dx.doi.org/10.1103/PhysRevLett.79.1261)

Questions:

• can such states be also generated in 3D?
• is there a connection between Vinals interacting mode theory and the electronic theory of quasicrustals?