Fast flow-based algorithm for creating density-equalizing map projections.

Cartograms are maps that rescale geographic regions (e.g., countries,districts) such that their areas are proportional to quantitative demographicdata (e.g., population size, gross domestic product). Unlike conventional baror pie charts, cartograms can represent correctly which regions share commonborders, resulting in insightful visualizations that can be the basis forfurther spatial statistical analysis. Computer programs can assist datascientists in preparing cartograms, but developing an algorithm that canquickly transform every coordinate on the map (including points that are notexactly on a border) while generating recognizable images has remained achallenge. Methods that translate the cartographic deformations intophysics-inspired equations of motion have become popular, but solving theseequations with sufficient accuracy can still take several minutes on currenthardware. Here we introduce a flow-based algorithm whose equations of motionare numerically easier to solve compared with previous methods. The equationsallow straightforward parallelization so that the calculation takes only a fewseconds even for complex and detailed input. Despite the speedup, the proposedalgorithm still keeps the advantages of previous techniques: with comparablequantitative measures of shape distortion, it accurately scales all areas,correctly fits the regions together and generates a map projection for everypoint. We demonstrate the use of our algorithm with applications to the 2016 USelection results, the gross domestic products of Indian states and Chineseprovinces, and the spatial distribution of deaths in the London borough ofKensington and Chelsea between 2011 and 2014.