The finite number of interior component shapes of the Levy dragon (Q972604)

The Levy dragon is a connected self-similar tile with disconnected interior. It was previously known that there are at least 16 different shapes of its interior components. This paper gives us a deeper insight into the Levy dragon. Using simple properties of an infinite sequence of curves which converge into the Levy dragon, the author proves that the number of different shapes of the interior components is finite. A detailed description of the buildup of those shapes as unions of various contractions of three convex polygonal shapes is given, and the number of shapes is determined.