Templeting and self-assembly

Templeting and self-assembly represent the two extremes of the spectrum of determinate pattern-assembly processes. A templeted pattern can be defined as one that requires a prepattern or templet explicitly specifying the final topology of the pattern. Conversely, a self-assembling pattern can be defined as one for which the inherent constraints of the precursor elements alone are sufficient to specify the final pattern. Both concepts can be directly expressed in matrix notation, and a simple matrix measure, the templeting index, characterizes the relative amount of templeting or of self-assembly in any particular system. With this language, a fundamental principle of pattern-assembly becomes evident: in the determinate realm, some patterns can only be assembled using the same-sized templets--templets that are at least as large as the final pattern.