Chaos from linear systems: Implications for communicating with chaos, and the nature of determinism and randomness

A method is developed for producing deterministic chaotic motion from the linear superposition of a bi-infinite sequence of randomly polarized basis functions. The resultant waveform is also formally a random process in the usual sense. In the example given, a three-dimensional embedding produces an idealized version of Lorenz motion. The one-dimensional approximate return map is piecewise linear; a tent or shift, depending on the Poincare section. The results are presented in an informal style so that they are accessible to a wide audience interested in both theory and applications of symbolic dynamics communication.