In lattice gas automata Head-on collisions conserve, in addition to total particle number, the difference of particle numbers in any pair of opposite directions. Thus, head-on collisions on a triangular lattice conserve a total of four scalar quantities. This means that in ad dition to mass and momentum conservation, there is a spurious conservation law.
Ref: page no: 7, Lattice Gas Hydrodynamics in Two and Three Dimensions".risch, U. ; d'Humieres, D. ; Hasslacher, B. ; Lallemand, P. ; Pomeau, Y. ; Rivet, J.P.