FANTOM PLANET

Dot maps show the geographic distribution of features in an area by placing dots representing a certain quantity of features where the features are most likely to occur. The fundamental steps in dot mapping are to select the dot size, determine the dot unit value, and place the correct number of dots in a random manner that correctly reflects the geographic distribution of features.

Selecting the dot size is a subjective decision, but the dot unit value has long been determined with the aid of the Mackay nomograph. Close examination of the nomograph finds it not appropriate for determining the dot unit value when dot placement is based on computer-generated random numbers that result in overlapping dots. A new graphical aid for dot unit value determination was created by modeling aggregate area of dots and amount of dot overlap using a truncated form of the unification equation from probability theory. Aggregate dot areas predicted by this equation were tested against actual random dots created for several common dot sizes, and high agreement was found between measured and predicted aggregate area. The new ESRI Dot Value Estimator was created by Aileen Buckley based on these results.

Pseudo-random dot placement with a maximum overlap constraint for dot pairs appears to better mimic how cartographers have traditionally placed dots. Pseudo-random dot placement can be thought of as similar to rigid random placement of circles in a square with maximum circle overlap limits from 0% (mutually exclusive dots) to 100% (totally random dots). Thinking of dot placement in this manner allowed a general equation for aggregate dot area to be devised as a linear combination of the mutually exclusive and totally random dot endpoint equations. Aggregate areas predicted by this general equation were found to closely match actual assemblages of pseudo-random dots with differing maximum dot pair overlaps.

The second part of this research focused on improving the guidance given for the placement of dots when mapping human population from U.S. Census data. MS GIS students [...] created a series of maps for San Bernardino county that illustrate the improvements in dot placement that result from using progressively smaller Census data collection units, and then using land use information to exclude areas unlikely to contain people. The final refinement was using road buffers as inclusion areas in rural areas.