The classic Faraday wave experiment consists of a horizontal layer of fluid that spontaneously develops a pattern of standing waves on its surface as it is driven by vertical oscillation with amplitude exceeding a critical value. Faraday wave experiments have consistently produced patterns with remarkably high degrees of symmetry. Quasipatterns, which are quasiperiodic in any spatial direction, are particularly interesting since there is, as yet, no satisfactory theoretical understanding of their formation. We use multi-frequency parametric forcing to investigate the formation of patterns and approximate quasipatterns in a model partial differential equation, which plays the same role for the Faraday wave experiment that the Swift--Hohenberg equation plays for convection. We exploit three-wave resonant interactions to design forcing functions that ought to produce complex patterns, and make quantitative comparisons between weakly nonlinear predictions and the solutions of the PDE. This comparison reveals the limitations of the theory, and we explore ways in which these limitations can be addressed. Based on: Design of parametrically forced patterns and quasipatterns, by A.M. Rucklidge and M. Silber. SIAM J. Applied Dynamical Systems 8 (2009) 298-347.