  We give a construction of a self-similar tiling of the plane with any
prescribed expansion coefficient $\lambda\in\C$ (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 only if
either $\lambda$ or $\lambda e^{2\pi i/m}$ is a complex Perron number for which
$e^{2\pi i/m}$ is in $\Q[\lambda]$, respectively $Q[\lambda e^{2\pi i/m}]$.
