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This research had three major themes: Fractal growth, pattern formation and the analysis of complexity; that is, the effects of random processes in creating hidden order in statistical system, the interplay between this hidden order and macroscopic order, and the analysis of these complex systems. For example, a dendritic crystal such as a snowflake has a complicated and beautiful pattern with much evidence of the underlying six-fold symmetry of ice. It is a pattern forming system. However, in a disordered environment (such as growth on a rough or dirty surface) this order is replaced by a new order, the fractal or scaling symmetry of a disordered crystal. In this case every part of the crystal is similar on the average to the whole (up to a change in scale). The description of these new kinds of order may require the introduction of new analytic and numerical methods

Growth and nonlinearity. Final project report, April 1, 1985--January 1, 1996