Boundary of the rauzy fractal sets in R x C generated by P(x)=x(4)-x(3)-x(2)-x-1

Abstract

We study the boundary of the 3-dimensional Rauzy fractal epsilon subset of R x C generated by the polynomial P(x) = x(4)-x(3)-x(2)-x-1. The finite automaton characterizing the boundary of epsilon is given explicitly. As a consequence we prove that the set epsilon has 18 neighboors where 6 of them intersect the central tile epsilon in a point. Our construction shows that the boundary is generated by an iterated function system starting with 2 compact sets.