Effect of Boundary Conditions on Cellular Automata that Classify Density
Abstract
The properties of twostate nearestneighbour cellular automata (CA) that are capable of density classification are discussed. It is shown that these CA actually conserve the total density, rather than merely classifying it. This is also the criterion for any CA simulation of DFT. The effect of boundary and periodicity conditions upon the evolution of such CA are elaborated by considering linear and cyclic lattices and boundary conditions consistent with the conservation criterion. In a bounded linear lattice, it is possible to achieve a configuration with a single 01 and no 10 domain wall, or vice versa, but this is not possible in a cyclic lattice, where these two domain walls have to appear in pairs. This determines the final stable state of the automaton.
 Publication:

arXiv eprints
 Pub Date:
 April 1998
 DOI:
 10.48550/arXiv.compgas/9804001
 arXiv:
 arXiv:compgas/9804001
 Bibcode:
 1998comp.gas..4001S
 Keywords:

 Cellular Automata and Lattice Gases
 EPrint:
 8 pages