  Motility is characteristic of life, but a common basis for movement has
remained to be identified. Diverse systems in motion shift between two states
depending on interactions that turnover at the rate of an applied cycle of
force. Although one phase of the force cycle terminates the decay of the most
recent state, continuation of the cycle of force regenerates the original decay
process in a recursive cycle. By completing a cycle, kinetic energy is
transformed into probability of sustaining the most recent state and the system
gains a frame of reference for discrete transitions having static rather than
time-dependent probability. The probability of completing a recursive cycle is
computed with a Markov chain comprised of two equilibrium states and a kinetic
intermediate. Given rate constants for the reactions, a random walk reproduces
bias and recurrence times of walking motor molecules and bacterial flagellar
switching with unrivaled fidelity.
