  For substitution satisfying Pisot, irreducible, unimodular condition, a
tiling substitution plays a key role in construction of a stepped surface and
Rauzy fractal. In this paper we will extend the method to hyperbolic
automorphisms on the free group of rank 2 in some class, and obtain set
equations of Rauzy fractals by virtue of a tiling substitution. We will also
see that the domain exchange transformation on Rauzy fractal is just a two
interval exchange transformation.
