The Star of David neighbourhood is a isometric neighbourhood often used by those implementing twodimensional lattice gasses. The automata divides the plane into tesselating hexagons. On each iteration the six triangular subcells of domain are used to determine the range via a (usually reversible) map function. The "FHP" Lattice Gas (named after Frisch, Hasslacher and Pomeau) is one of the best known automata that use this neighbourhood. This automata was designed to obey the NavierStokes equations in the macroscopic limit. This is something which hexagonal neighbourhoods appear to be able to accomplish with ease, while for rectangular neighbourhoods, appears to be possible only with awkward constructions. Sometimes the domain is modified in such a manner that there are additional cells in the center of each hexagon. These may be used to simulate particles at rest and can assist with simulating other phenomena. A number of models which use lattice gasses have collision rules which are nondeterministic in the case of a headon collision between two particles. If it is necessary to retain true invertability, another "layer" is sometimes required to act as an invertible random number generator for the process. In the lattice gas literature, this automaton is often represented on a triangular lattice, with particles being represented as arrows pointing along the lines from the nodes. Whatever the virtues of this representation, this seems to disguise what constitutes a cell  and hides the hexagonal nature of the automaton  an aspect emphasised here. Despite apparent differences, the two forms of representation are equivalent. One positive aspect of the Star of David neighbourhood  when compared to the Margolus neighbourhood or the "Q*Bert" neighbourhood is that it performs the same operation on every time step. Many other automata with this property have gained it at the expense of dividing the cellular space into independent alternating sublattices  but use of the Star of David neighbourhood avoids this.
