!Converted with LaTeX2HTML 95.1 (Fri Jan 20 1995) by Nikos Drakos (firstname.lastname@example.org), CBLU, University of Leeds >
More subtle than Wolfram's Class IV automata are another class which seem to exhibit natural barriers, not just the quiescent regions which characterize Class IV. Areas of independent evolution are observed, which seem to go about their business independently of what is happening in other regions .
Nor are the barriers always invariable; they may go through their own relatively simple cycle of evolution while still separating regions of more complex activity. Let us call such regions macrocells to distinguish them from the individual cells of which the automaton is composed. When their width is short their behaviour must be periodic of relatively short duration. There is the slight difference that their evolution will be subject to different boundary conditions than if the macrocells were cyclic or part of an infinite cyclic pattern. Wider macrocells have a correspondingly longer -- exponentially longer -- period for repetition.
An explanation can be found by consulting the de Bruijn diagram; it is found that there are certain nodes, for which all incoming or outgoing links survive in the period diagram, even if they do not continue on to form closed loops. It is only necessary that there is an unbroken chain from a node with complete incoming links to another (possibly the same) with complete outgoing links. These chains form the prospective cell membrane; the environment of the terminal cells ensures that the membrane will evolve properly, no matter the content of the macrocells which they enclose.
Slight perturbations are possible; a membrane may be stable in most environments and attacked by configurations in others. Once it starts to dissolve, the membrane will diminish by two cells each generation, and no long term declarations can be made about the evolution. Membranes may form spontaneously when conditions are right; it is also possible to have periodic membranes or shifting membranes. With moving boundaries, the de Bruijn diagram need only be adjusted so that all the pertinent links correspond to a consistent translation. However, the positioning of the guard strings must be changed; instead of flanking the boundary membrane they must run ahead of it ensuring an adequate anticipation of the glider which they are protecting.
A final variation, which is also often encountered, is to find that not all the links beyond the terminal nodes in the de Bruijn diagram are guard links, but that the macrocell will only place cells near the membrane whose links are guarding. As an extreme case, a wall of one color could confine cells of different colors, but still dissolve when confronted with cells of its own color.
Since the critical requirement for a membrane is the presence of guard links at its extremes, its internal structure can be simple or complex as the occasion demands. Thus, there could be loops in the chain defining the membrane, allowing macrocells to be separated by membranes of varying structure.