Quasipatterns in parametrically forced systems

We examine two mechanisms that have been put forward to explain the selection of quasipatterns in single- and multifrequency forced Faraday wave experiments. Both mechanisms can be used to generate stable quasipatterns in a parametrically forced partial differential equation that shares some characteristics of the Faraday wave experiment. One mechanism, which is robust and works with single-frequency forcing, does not select a specific quasipattern: we find, for two different forcing strengths, 12-fold and 14-fold quasipatterns. The second mechanism, which requires more delicate tuning, can be used to select particular angles between wavevectors in the quasipattern.