The Coordinate Digit Density function and Map Information Content Analysis

There are many systematic methods for encoding spatial coordinates, but there do not seem to be equivalent analytic methods for quantifying the difference in information content of these encoded data. We propose the analysis of map information content using the Coordinate Digit Density Function as a useful device for examining and comparing information quantity between spatial data in different coordinate systems (including those with non-overlapping and interwoven eastings and northings). The Coordinate Digit Density Function benefits from the fact that the coordinates used can be in any number system (decimal, alphanumeric, hexadecimal, binary, etc.), and can be used to analyze various sets of atomic data—from pairs or sets of points, to features and entire maps. Using this function and Shannon’s (1948) formulae, total information content of a coordinate set can be calculated and thus compared to that of other systems or within a system. This paper presents and examines the Coordinate Digit Density Function for calculation and visual display of the degree of non-randomness in a system, and demonstrates its application in the cartographic problem of map information comparison. Specifically, we compare test data to illustrate the function’s use in analysis of information reduction by map projection, reduction of precision, coordinate translation, and map generalization.