  We present a general method for the design of 2-dimensional nonlinear
photonic quasicrystals that can be utilized for the simultaneous phase-matching
of arbitrary optical frequency-conversion processes. The proposed scheme--based
on the generalized dual-grid method that is used for constructing tiling models
of quasicrystals--gives complete design flexibility, removing any constraints
imposed by previous approaches. As an example we demonstrate the design of a
color fan--a nonlinear photonic quasicrystal whose input is a single wave at
frequency $\omega$ and whose output consists of the second, third, and fourth
harmonics of $\omega$, each in a different spatial direction.
