Anyone here read Berman and Moody's "The algebraic theory of quasicrystals with five-fold symmetries"? They study an operation called quasiaddition: x⊢y = Φ²x - Φy where Φ = (1+√5)/2. Doing that repeatedly to all the points in the pentagon shown here generates a quasicrystal, they claim!
(1/2)