Implementation [of substitution systems] The rule for a neighbor-independent substitution system such as the first one on page 82 can conveniently be given as {1  {1, 0}, 0  {0, 1}} . … In this case, the evolution can be obtained using SSEvolveList[rule_, init_String, t_Integer] := NestList[StringReplace[#, rule]&, init, t] For a neighbor-dependent substitution system such as the first one on page 85 the rule can be given as {{1, 1}  {0, 1}, {1, 0}  {1, 0}, {0, 1}  {0}, {0, 0}  {0, 1}} And with this representation, the evolution for t steps is given by SS2EvolveList[rule_, init_List, t_Integer] := NestList[Flatten[Partition[#, 2, 1] /. rule]&, init, t] where the initial condition for the first example on page 85 is {0, 1, 1, 0} .

On a 2D square grid, one can use overlapping 2×2 square blocks. But on a 2D hexagonal grid, one must instead alternate on successive steps between hexagons and their dual triangles.

In most plants—at least after the embryonic stage—cells typically divide only in localized regions known as meristems, and each division yields one cell that can divide again, and one that cannot.

The number of turns or whorls varies widely, from less than one in a typical bivalve, to more than thirty in a highly pointed univalve such as a screw shell. Usually the coiled structure is obvious from looking at the apex on the outside of the shell, but in cowries, for example, it is made less obvious by the fact that later whorls completely cover earlier ones, and at the opening of the shell some dissolving and resculpting of material occurs.

But as soon as one tries to construct more explicit models of space and time one is immediately led to consider the possibility that they may be quite different.

For even if one takes these processes to be pure quantum ones, what I believe is that in almost all cases appropriate idealized limits of them will reproduce what are in effect the usual rules for observations in quantum theory. … But with a sufficiently large number of particles—and appropriate interactions—one expects that there can be. … But any sequence of bits one extracts must be deduced from a corresponding sequence of measurements.

But one of the reasons I created the Mathematica language was precisely to provide a much more general notation. … One point is that it is completely uniform and standardized: there can never be any hidden assumptions or ambiguity about what a particular piece of notation means, since ultimately it is defined by the actual Mathematica software system and its documentation (see below ). … And the final and very critical advantage of Mathematica notation is that one can not only read it, but also actually execute it on a computer, and interact with it.

For any wavelength distribution it turns out that if one scales these numbers to add up to one, then the chromaticity values obtained must lie within a certain region. Mixing n specific colors in different proportions allows one to reach any point in an n -cornered polytope.

Yet of the limited set of people exposed to higher mathematics, different ones often seem to think in bizarrely different ways. … And sometimes these are ones that people still find hard to grasp. … In designing Mathematica one of my challenges was to use constructs that are at least ultimately easy for people to understand.

The left-hand side of each rule must consist of one non-terminal symbol, and the right-hand side can contain only one non-terminal symbol. … The left-hand side of each rule must consist of one non-terminal symbol, but the right-hand side can contain several non-terminal symbols.