Abstract :
There are many tilings of the plain, some of them are periodic, others are aperiodic. A chromatic number of a tiling is defined as the minimum number of colours needed to colour the tiles in such a way that every two adjacent tiles have different colours. Determining the chromatic number of a periodic tiling is mostly easy but this problem has not been investigated for aperiodic tilings yet. In this paper the problem is solved for one of the most known aperiodic tiling called Penrose kite-and-dart tiling. This tiling is often used as a planar model for so called quasicrystals.
