In each case a string consisting of a single white element is eventually generated—but this takes respectively 12, 28 and 34 steps to happen.

Region (a) shows a block separator—corresponding to a dashed line in picture (d) on page 679 —hitting the single black element in the sequence that exists at the first step. Because the element hit is black, an object must be produced that allows information from the block at this step to pass through.

The second system generates all strings where the second-to-last element is white, or the string ends with a run of black elements delimited by white ones.

Deducing cellular automaton rules Given a complete cellular automaton pattern it is easy to deduce the rule which produced it just by identifying examples of places where each element in the rule was used, as in the picture below.

Note that with 3 and 4 elements, only forms inequivalent under interchange of element labels are shown.

Implementation [of network cellular automata] Given a network represented as a list in which element i is {a, i , b } , where a is the node reached by the above connection from node i , and b is the node reached by the below connection, each step corresponds to NetCAStep[{rule_, net_}, list_] := Map[Replace[#, rule] &, list 〚 net 〛 ]

(a) (Successive digits sequence) The sequence produced is repetitive, with the element at position n being black for n odd and white for n even. … (b) (Thue–Morse sequence) The color s[n] of the element at position n is given by 1 - Mod[DigitCount[n - 1, 2, 1], 2] . … The color of the element at position n is given by 2 - (Floor[(n + 1) GoldenRatio] - Floor[n GoldenRatio]) (see page 904 ), while the position of the k th white element is given by the so-called Beatty sequence Floor[k GoldenRatio] .

The particular initial condition shown can be obtained by applying the substitution system -> , -> , starting from a single black element (see page 83 ).

[Universal] tag systems Marvin Minsky showed in 1961 that one-element-dependence tag systems (see page 670 ) can be universal.

The importance of explicitness Looking through this book, one striking difference with most previous scientific accounts is the presence of so many explicit pictures that show how every element in a system behaves.