  A number-conserving cellular automaton is a cellular automaton whose states
are integers and whose transition function keeps the sum of all cells constant
throughout its evolution. It can be seen as a kind of modelization of the
physical conservation laws of mass or energy. In this paper, we first propose a
necessary condition for triangular and hexagonal cellular automata to be
number-conserving. The local transition function is expressed by the sum of
arity two functions which can be regarded as 'flows' of numbers. The
sufficiency is obtained through general results on number-conserving cellular
automata. Then, using the previous flow functions, we can construct effective
number-conserving simulations between hexagonal cellular automata and
triangular cellular automata.
