  We treat a turbulent velocity field as a message in the same way as a book or
a picture. All messages can be described by their entropy per symbol $h$,
defined as in Shannon's theory of communication. In a turbulent flow, as the
Reynolds number $Re$ increases, more correlated degrees of freedom are excited
and participate in the turbulent cascade. Experiments in a turbulent soap film
suggest that the spatial entropy density $h$ is a decreasing function of $Re$,
namely $h \propto -\log Re$ + const. In the logistic map, also analyzed here,
increasing the control parameter $r$ increases $h$. A modified logistic map
with additional coupling to past iterations suggests the significance of
correlations.
