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Note (a) for How Do Simple Programs Behave?

Note that 2n has the same digits as n , but shifted one position to the left.

The number which appears at position i is given by BitXor[i, Floor[i/2]] .

[State networks for] shift rules The pictures below show networks obtained with rule 170, which just shifts every configuration one position to the left at each step.

Note (g) for Evolution of Networks

Network mobile automata The analog of a mobile automaton can be defined for networks by setting up a single active node, then having rules which replace clusters of nodes around this active node, and move its position.

Note (b) for Irreversibility and the Second Law of Thermodynamics

In a rectangular region, the position is given by Mod[a t, {w, h}] and every point will be visited if the parameters have irrational ratios.

Origins of Simple Behavior

A rather straightforward one, illustrated in the first set of pictures A sequence of elementary cellular automata whose rules differ from one to the next only at one position (a Gray code sequence).

Turing Machines

The black dot represents the position of the head at each step, and the three possible orientations of the arrow on this dot correspond to the three possible states of the head.

Time and Causal Networks

Picture (a) is a version of the standard representation that I have used for mobile automaton evolution elsewhere in the book—in which successive lines give the colors of cells on successive steps, and the position of the active cell is indicated at each step by a gray dot.

Emulating Other Systems with Cellular Automata

In the cellular automaton, the cells have eight possible colors, with the lightest two colors being used for cells not at the position of the head.

The instruction being executed is indicated at each step by the position of the dot on the left, while the numbers in each of the two registers are indicated by the gray blocks on the right.