Wolfram spent a great deal of time studying the simplest form of Cellular Automaton - the 1-Dimension 2-State CA. In these, the set of cells is an infinitely long line of one unit thickness, and the state of a cell is dependent on itself and its two neighbours. The two states are generally referred to simply as "black" and "white".

1-Dimension Cellular Automata are usually represented as a horizontal line, with the successor state immediately below, and so on. The vertical axis therefore represents time. In this way, patterns and repeating sequences may be readily detected.

In the above example, the rules are simple:

• If the left and right neighbours are different, the cell becomes black.
• If the left and right neighbours are the same, the cell becomes white.

The initial state of the cell itself has no bearing on the outcome.

While Life had a single set of rules, what makes the 1-Dimension Cellular Automata interesting is when different rule sets are considered. Since the result state for a particular cell is dependent on only three cells (left, self and right), each of which can have two states, there are 2 to the power 3, that is 8, rules. Each rule can have two outcomes, so there are 2 to the power 8, that is 256, rule sets.

Take the rule set which produced the above example: Each column is a rule, specifying the result state for a given set of inputs (left, self and right respectively). If we always lay out the rules in the same sequence, and we then substitute 0 for white and 1 for black in the bottom row we can form an 8-digit binary number, in this case 01011010. Converting this binary number to decimal we get 90, and this rule set can be uniquely identified as rule set 90.

(Confusingly, Wolfram refers to an entire rule set as a rule, so he would call this rule 90. Other writers use the term rule set and that seems to make more sense to me.)

The results of rule set 90 show a fairly simple pattern. There is a small amount of complexity in the increasing size of the triangles and the nested patterns which fill the gaps between them, but none of this is particularly surprising.

Some rule sets of course are totally uninteresting. Rule set 0 (all rules result in white) and rule set 255 (all rules result in black) are particularly boring. And rule 250 (see below) produces a pattern of alternating black and white which is only marginally more interesting.

But then Wolfram tried rule set 30...