1. The rule must not be biased.
2. The rule must be a Class 3 rule from elementary 1D cellular automata.
3. The initial generation must be "random".
Upon initial inspection, if the initial generation has a pattern, the pattern will exist in each generation. However, it's unclear if a pattern can be determined in any given column. Stephen Wolfram claims that the center column of Rule 30 is as random as true random events found in nature. That needs to be tested, and it remains to be seen if the other rules can also be random.
Rules shown: 30, 45, 75, 90, 105, & 150. Mirrors, complements, and complemented mirrors are not shown.