Cellular Logic Operations in N-Space

Abstract

The first studies in cellular logic in spaces having a dimensionality greater than two were undertaken by Ulam (1962) at the Los Alamos Scientific Laboratory in the early 1960’s. Much of this work was inspired by von Neumann (1951) who was studying cellular automata for the purpose of determining how computers could be made to reproduce themselves. Ulam and later Schrandt and Ulam (1960) concentrated on developing certain recursive relationships which, when operating upon a starting pattern or residue, would produce interesting patterns of growth (Chapter 12). As stated by Ulam (1962),

“The objects found in this way seem to be, so to say, intermediate in complexity between inorganic patterns like those of crystals and the more varied intricacies of organic molecules and structures. In fact one of the aims of the present note is to show, by admittedly somewhat artificial examples, an enormous variety of objects which may be obtained by means of rather simple inductive definitions and to throw a sidelight on the question of how much ‘information’ is necessary to describe the seemingly enormously elaborate structures of living objects.”