  We propose a probabilistic cellular automata model for the spread of
innovations, rumors, news, etc. in a social system. The local rule used in the
model is outertotalistic, and the range of interaction can vary. When the range
R of the rule increases, the takeover time for innovation increases and
converges toward its mean-field value, which is almost inversely proportional
to R when R is large. Exact solutions for R=1 and $R=\infty$ (mean-field) are
presented, as well as simulation results for other values of R. The average
local density is found to converge to a certain stationary value, which allows
us to obtain a semi-phenomenological solution valid in the vicinity of the
fixed point n=1 (for large t).
