A conservation law in a Cellular Automaton is related to the invariance of some local additive quantity attached to the cells. Energy, momentum and mass are simulated as real values associated to local patterns of cell states.  A quantity is conserved if the total sum of its values in every configuration remains constant in time during CA evolution. Number conserving automata keep total cells count unchanged, having a binary special case, where number conservation refers to the invariance of total amount of 1s and 0s during the evolution of the automata.

Consideration of conservative properties in cellular automata may be useful in several ways. When modeling a physical system, conservation laws imply a significant number of design restrictions that should be included in the model. In physically realistic models of computation, conservation laws should naturally be taken into account. Additionally, conservation laws in a cellular automaton provide a kind of “physical” understanding about its dynamics that may be valuable to improve the comprehension of the underlying principles of the real physical phenomena.

Energy interchange rules cause EDCA to be an essentially conservative model. Roughly speaking, the positive energy requirement to increase cell state, being this energy generated only if another cell decreases by the same quantity, implies that a cell can increment its value only if other cells drop by the same value. Consequently, in EDCA behavior are expected orbits of configurations where total sum of cell values remains near to constant, or oscillating around a fixed value.       

More on conservative quantities in Energy Driven Cellular Automata can be found here.

Other works related to conservation laws in CA: Taati, Siamak. (2009). Conservation Laws in Cellular Automata. Department of Mathematics, University of Turku, FI-20014 Turku, Finland. 2009.