  We consider Ising models defined on periodic approximants of aperiodic
graphs. The model contains only a single coupling constant and no magnetic
field, so the aperiodicity is entirely given by the different local
environments of neighbours in the aperiodic graph. In this case, the partition
function zeros in the temperature variable, also known as the Fisher zeros, can
be calculated by diagonalisation of finite matrices. We present the partition
function zero patterns for periodic approximants of the Penrose and the
Ammann-Beenker tiling, and derive precise estimates of the critical
temperatures.
