Complexity and Redundancy in Binary Maps

The complexity of binary maps that is provided by the areal arrangement of colors is considered, and measured using information theory. In addition, information theory provides other measures that have an interpretation in a map context. One of these, redundancy, is examined and found to bear a striking empirical relationship to a spatial autocorrelation statistic. It is argued that spatial autocorrelation is, conceptually as well as empirically, the two-dimensional equivalent of redundancy. It too measures the extent to which the occurrence of an event (color) in an areal unit constrains, or makes more probable, the occurrence of an event in a neighboring areal unit.