A class of tilings of Z^2 having mixed dynamical spectrum and visually dramatic self-correlations.
by
Natalie M. Priebe
Rensselaer Polytechnic Institute

A class M of self-similar tilings of the plane out of black and white unit squares will be introduced which has much in common with the sequence usually attributed to Morse. Tilings in this class have mixed dynamical spectrum. From such a tiling it is possible to construct ``correlation tilings'' which can be shown to be generalizations of Toeplitz sequences. These correlation tilings, while fascinating to view because of their dramatic beauty, will also provide information about the structure of the underlying tiling. Some tilings from M also have special correlation tilings called ``center shifts'' which can display far more delicate patterns; these will be discussed as well. Preliminary results and several questions about M, correlation tilings, and center shifts will be presented.

Date received: March 17, 1998