
 Alvy Ray Smith Cellular Automata Papers 
  The class of pattern sets accepted by cellular automata (CA, finite, connected subsets of cells in a 2dimensional cellular space) is shown to be precisely the class of languages generated by the monotonic array grammars, a generalization of contextsensitive grammars to the 2dimensional integer grid. 
  It was originally written as the introduction to the German edition of Theory of SelfReproducing Automata, by John von Neumann, edited (posthumously) by Arthur W Burks, University of Illinois Press, Urbana, 1968. 
  A collection of n finite, identical automata are considered, where each one, at each unit time step, takes a new state as a function of the state taken at the preceding step by itself and by certain other automata in the collection, called its neighbors, arbitrarily chosen, but limited in number. 
 alvyray.com /Papers/PapersCA.htm (1730 words) 
