  We analyze certain eigenstates of the quantum baker's map and demonstrate,
using the Walsh-Hadamard transform, the emergence of the ubiquitous Thue-Morse
sequence, a simple sequence that is at the border between quasi-periodicity and
chaos, and hence is a good paradigm for quantum chaotic states. We show a
family of states that are also simply related to Thue-Morse sequence, and are
strongly scarred by short periodic orbits and their homoclinic excursions. We
give approximate expressions for these states and provide evidence that these
and other generic states are multifractal.
