The focus of this book is a mathematical structure modeling a physical or biological system that can be in any of a number of ‘states.’ Each state is
characterized by a set of binary features, and differs from some other neighbor state or states by just one of those features.
In some situations, what distinguishes a state S from a neighbor state T is that S has a particular feature that T does not have. A familiar example is a partial solution of a jigsaw puzzle, with adjoining pieces. Such a state can be transformed into another state, that is, another partial solution or the final solution, just by adding a single adjoining piece. This is the first example discussed in Chapter 1. In other situations, the difference between a state S and a neighbor state T may reside in their location in a space, as in our second example, in which in which S and T are regions located on different sides of some common border.m
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