Planar and spherical hierarchical, multi-resolution cellular automata

We present a new generalized definition of spatial hierarchy and use it to create a data structure for spatial hierarchies on the plane and the sphere. The data structure is then used as the basis for hierarchical, multi-resolution cellular automata which are topology-independent so that many topologies may be studied. In these systems the dynamics of a focal cell is dependent on its neighbors and also the cell above and below it in the next coarser or finer resolution. Results from a multi-resolution version of the Game of Life show complex and unexpected behavior which is dependent on the topology chosen and initial conditions. These results and the software which produced them provide a proof of concept for the new data structure and algorithms. These may be especially useful for data analysis and simulation at the global scale.