  Markovian memory embedded in a binary system is shaping its evolution on the
basis of its current state and introduces either clustering or dispersion of
binary states. The consequence is directly observed in the lengthening or
shortening of the runs of the same binary state and also in the way the
proportion of a state within a sequence of state measurements scatters about
its true average, which is quantifiable through the Markovian self-transition
probabilities. It is shown that the Markovian memory can even imitate the
evolution of a random process, regarding the long-term behavior of the
frequencies of its binary states. This situation occurs when the associated
binary state self-transition probabilities are balanced. To exemplify the
behavior of Markovian memory, two natural processes are selected. The first
example is studying the preferences of nonhuman troglodytes regarding
handedness. The Markovian model in this case assesses the extent of influence
two contiguous individuals may have on each other. The other example studies
the hindering of the quantum state transitions that rapid state measurements
introduce, known as the Quantum Zeno effect (QZE). Based on the current
methodology, simulations of the experimentally observed clustering of states
allowed for the estimation of the two self-transition probabilities in this
quantum system. Through these, one can appreciate how the particular hindering
of the evolution of a quantum state may have originated. The aim of this work
is to illustrate as merits of the current mathematical approach, its wide range
applicability and its potential to provide a variety of information regarding
the dynamics of the studied process.
