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The pictures below show the typical behavior of rule 73—first with completely random initial conditions, and then with initial conditions in which no run of an even number of black squares occurs.

In the second case rule 73 exhibits typical class 3 behavior—with the usual uncontrolled transmission of information. In the first case, however, the black walls that are present seem to prevent any long-range transmission of information at all.

So can one then achieve something intermediate in rule 73—in which information is transmitted, but only in a controlled way?

The pictures at the top of the next page give some indication of how this might be done. For they show that with an appropriate background rule 73 supports various localized structures, some of which move. And while these structures may at first seem more like those in rule 54 than rule 110, I strongly suspect that the complexity of the typical behavior of rule 73 will be reflected in more sophisticated interactions between the structures—and will eventually provide what is needed to allow universality to be demonstrated in much the same way as in rule 110.

Captions on this page:

Two examples of rule 73. The top example uses completely random initial conditions; the bottom example uses initial conditions in which no run of an even number of black squares ever occurs. The bottom example is actually part of the pattern obtained from a single black cell—just to the right of the center column, starting with step 1000.

Examples of localized structures in rule 73. Note that in the last case shown, the background patterns on either side are mirror images.

From Stephen Wolfram: A New Kind of Science [citation]