On Making Better Map Projections

Map projections. Aren't they something? Have you ever wondered what would happen if the Earth were modeled as a poly-nodal spring mesh and constrained to a plane? We wondered the exact same thing. So we did that. We took a geodesic grid, made each vertex a mass, and let it go. We got some neat map projections. We also did gradient descent to minimize the spring energy, and got slightly different map projections.