Table 5: Patterns from Single Site Seeds

Patterns generated by evolution from configurations containing a single nonzero site.

The first part of the table shows pictures for all distinct rules. Since the initial configuration is not invariant under complementation, rules which differ by complementation can produce different patterns, and are shown separately. Only the minimal representative is shown for rules related by reflection. In all cases, the patterns correspond to evolution for 38 time steps.

Many rules are seen to yield equivalent patterns. The results of table 7 can often be used to deduce these equivalences.

Some rules (such as 122) yield asymptotically homogeneous patterns. Others (such as 90 and 150) yield asymptotically self similar or fractal patterns. (The fractal dimensions of the patterns obtained from rules 90 and 150 are respectively and .) But some rules (such as 30 and 73) yield irregular patterns which show no periodic or almost periodic behaviour. The second part of the table gives some of the distinct patterns obtained by evolution for 360 time steps. Note that the structure on the right of the pattern generated by rule 110 eventually dies out, leaving an essentially periodic structure.

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