Contains implementations of alternative geometries for spaces which can be used in clustering algorithms. Using the spaces based on optimal sphere packing should result in slightly better affinity heuristics with only minor extra computational requirements. Comparison is here:

This metric is a good measure of how much unnecessary noise is added to distances and how easily points can slide past each other when being annealed.

The lattice implementation benchmarks look a little bumpy because of strangeness in sphere packing in different numbers of dimensions. It is likely optimal in dimensions 2 through 8 and close to it in 15 but there may be significant improvements possible in the other numbers of dimensions.

For visualization 2d lattice should be used. It 'crystallizes' nicely as shown here:

For applications which need antipodes (opposite points) Torus is best.