This appears to be a consequence of the delay before one driver responds to changes in speed of cars in front of them.

Note that if the rule for the finite automaton is represented for example as {{1, 2}, {2, 1}} where each sublist corresponds to a particular state, and the elements of the sublist give the successor states with inputs Range[0, k - 1] , then the n th element in the output sequence can be obtained from Fold[rule 〚 #1, #2 〛 &, 1, IntegerDigits[n - 1, k] + 1] - 1 while the first k m elements can be obtained from Nest[Flatten[rule 〚 # 〛 ] &, 1, m] - 1 To treat examples such as case (c) where elements can subdivide into blocks of several different lengths one must generalize the notion of digit sequences. … (As discussed on page 1070 , this representation is unique so long as one does not allow any pairs of adjacent 1's in the digit sequence.) It then turns out that if one expresses the position n as a generalized digit sequence of this kind, then the color of the corresponding element in substitution system (c) is just the last digit in this sequence.

Diophantine equations Any algebraic equation—such as x 3 + x + 1  0 —can readily be solved if one allows the variables to have any numerical value. But if one insists that the variables are whole numbers, then the problem is more analogous to the discrete constraints in the main text, and becomes much more difficult. … With four variables one has for example 3 3 + 4 3 + 5 3  6 3 , 1 3 + 6 3 + 8 3  9 3 —but with fourth powers the smallest result is 95800 4 + 217519 4 + 414560 4  422481 4 .

The rule in this case is that a cell should be black whenever one or the other, but not both, of its neighbors were black on the step before.

Each of these structures is seen in one type of plant growth or another, as illustrated on page 409 .

At an idealized level one might imagine trying to do this by inserting into the system some kind of paddle which would experience force as a result of impacts from particles.

Indeed, almost all of the detailed applications ever made of the full Second Law have been concerned with just one specific area: the behavior of gases.

Note that the cases shown are in a definite order reading down successive columns, with special cases given before more general ones.

So if two expressions are equivalent then by applying the rules of the appropriate axiom system it must be possible to get from one to the other—and in fact the picture on page 775 shows an example of how Values of expressions obtained by using operators of various forms.

Each gate performs a simple logic operation; for example, letting charge pass in one channel only if charge is present in the other channel. … One of the crucial ideas of a general-purpose computer is that sequences of such bits of data in memory can represent information of absolutely any kind. … A language provides a fixed set of constructs that allow one to specify computations.