As well as showing that there are substitution rules with any Perron
inflation factor, in [Ken96]
, R. Kenyon
gives an explicit construction for the Perron numbers that satsify:
$xn - a xn-1 + b x + c$, where
$a, b$, and
$c$ are natural numbers.
This is an example of that method given in that paper.
A locally isomorphic version with polygonal tiles is Kenyon (1,2,1) Polygon.
The construction of self-similar tilings
Geom. Funct. Anal. 1996, 6, 3, pp. 471--488, MR1392326