Abstract. The Twin Dragon and Rauzy fractals are intersected with the real axis. In the Twin Dragon case, unexpectedly from its fractal nature, the intersection is an interval characterized by a finite automaton. For the case of the Rauzy fractal, it is proved that the intersection has infinitely many components.
AMS Subject Classification
(1991): 11K26, 11A63, 37B50, 52C23, 28A80
Received March 9, 2004, and in revised form July 14, 2005. (Registered under 5887/2009.)