ACTA issues

Intersecting two-dimensional fractals with lines

Shigeki Akiyama, Klaus Scheicher

Acta Sci. Math. (Szeged) 71:3-4(2005), 555-580

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

Keyword(s): Twin Dragon, Rauzy Fractal, Tiling

Received March 9, 2004, and in revised form July 14, 2005. (Registered under 5887/2009.)