Diffusion-based cartogram on spheres

A planar cartogram is a two-dimensional map, on which the area of each closed region is in direct proportion to a chosen extensive property. To date, various algorithms have been proposed to construct planar cartograms. This work extends the two-dimensional, diffusion-based, topologically invariant cartogram algorithm proposed by Gastner and Newman onto spheres. Unlike its planar counterpart, the spherical formulation does not require boundary conditions and is invariant to the rotation of input data on the sphere. An implementation of this spherical cartogram transformation is designed to generate readable topology-preserving cartograms on spheres. Lastly, the method is illustrated with applications to global data such as worldwide human population, gross domestic product (purchasing power parity), carbon dioxide emissions and regional data such as the Electoral College of the United States presidential election of 2016.