Feasible models of computation: three- dimensionality and energy consumption

Using cellular automata as models of parallel machines we investigate the relation between (r-1)- and r-dimensional machines and constraints for the energy consumption of r-dimensional machines which are motivated by fundamental physical limitations for the case r=3. Depending on the operations which must be considered to dissipate energy (state changes, communication over unit-length wires, ...), some relations between the relative performance of 2-dimensional and 3-dimensional machines are derived. In the light of these results it seems imperative that for feasible models of computation energy consumption has to be considered as an additional complexity measure