A mathematical structure for analyzing maps

The growing use of computers in environmental management is profoundly changing data collection procedures, analytic processes, and even the decision-making environment itself. The emerging technology of geographic information systems (GIS) is expanding this revolution to integrate spatial information fully into research, planning, and management of land. In one sense, this technology is similar to conventional map processing involving traditional maps and drafting aids, such as pens, rub-on shading, rulers, planimeters, dot grids, and acetate sheets for light-table overlays. In another sense, these systems provide advanced analytic capabilities, enabling managers to address complex issues in entirely new ways. This report discusses a fundamental approach to computer-assisted map analysis that treats entire maps as variables. The set of analytic procedures for processing mapped data forms a mathematical structure analogous to traditional statistics and algebra. All of the procedures discussed are available for personal computer environments.