  In this article we discuss potential Markov partitions for three different
Wang tile protosets. The first partition is for the order-24 aperiodic Wang
tile protoset that was recently shown in the Ph.D. thesis of H. Jang to encode
all tilings by the Penrose rhombs. The second is a partition for an order-16
aperiodic Wang protoset that encodes all tilings by the Ammann A2 aperiodic
protoset. The third partition is for an order-11 Wang tile protoset identified
by Jeandel and Rao as a candidate order-11 aperiodic Wang tile protoset. The
emphasis is on some experimental methodology to generate potential Markov
partitions that encode tilings. We also apply some of the theory developed by
Labb\'{e} in analyzing such an experimentally discovered partition.
