THE CONSTRUCTION OF SELF-SIMILAR TILINGS

We give a construction of a self-similar tiling of the plane with any prescribed expansion coefficient lambda is an element of C (satisfying : the necessary algebraic condition of being a complex Perron number). For any integer m > 1 we show that there exists a self-similar tiling with 2 pi/m-rotational symmetry group and expansion lambda if and onl y if either lambda or lambda e(2 pi i/m) is a complex Perron number fo r which e(2 pi i/m) is in Q[lambda], respectively Q[lambda(e2 pi i/m)] .