Decomposable maps in general tessellation structures

摘要

For an arbitrary template T in an m-state d-dimensional tessellation structure, it is shown that there exists local maps on T which cannot be composed from a minmum number of applications of local maps on a simpler template. Further, it is shown that structures with local maps which have this property are in the minority. In particular, for a fixed template T, the fraction of local maps with minimal decompositions approaches O as m, the number of states, increases arbitrarily.