We present a discrete, stochastic model for wind formed ripples in san
d, which are observed to increase in size through mergers and seemingl
y approach an asymptotic spatial scale. The model is shown to predict
(1) a logarithmic increase in pattern scale with time, (2) a proportio
nality between the microscopic discrete scale (sand grain diameter) an
d the macroscopic pattern scale (ripple height), and (3) a lack of sca
le separation. The implications are that growth and apparent stabiliza
tion of scale both can be explained by a single mechanism, and that th
e evolution of wind ripples and other physical systems of this type ca
nnot be modeled by either deterministic methods or spatial continuum m
ethods.