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.

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. … On each line going down the page, the black dot on the left indicates which instruction in the program is being executed at the corresponding step.

Cyclic addition After t steps, the dot will be at position Mod[m t, n] where n is the total number of positions, and m is the number of positions moved at each step. … An alternative interpretation of the system discussed here involves arranging the possible positions in a circle, so that at each step the dot goes a fraction m/n of the way around the circle.

The cells marked by dots have colors that are taken as given, and then the colors of other cells are filled in according to the average that is obtained by starting from all possible initial conditions. … What happens is that the function that determines the color of a particular cell from the colors of cells in a nearby column rapidly becomes extremely Patterns generated by rule 30 after averaging over all possible initial conditions that reproduce the arrangements of colors in the cells indicated by dots.

The active cell is indicated by a black dot. … But unlike a cellular automaton, a mobile automaton has only one "active cell" (indicated here by a black dot) at any particular step.

Divisors The picture below shows as black squares the divisors of each successive number (which correspond to the gray dots in the picture in the main text).

Note that for rules outside of a distorted semicircle centered on the dot at the left-hand side of the page, and touching the three other sides of the page, the patterns generated grow at each step, rather than tending to a limit of fixed size.

But dotted around the picture one sees many definite white triangles and other small structures that indicate at least a certain degree of organization.

Notations [for logical primitives] Among those in current use are (highlighted ones are supported directly in Mathematica): The grouping of terms is normally inferred from precedence of operators (typically ordered  , ¬ , ⊼ , ∧ , ⊻ , ⊽ , ∨ ,  ), or explicitly indicated by parentheses, function brackets, or sometimes nested underbars or dots.

A dot signifies that the rule does not change the color of the center cell in the neighborhood.