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During the past decade interest in the formation of complex
disorderly patterns far from equilibrium has grown rapidly. This
interest has been stim ulated by the development of new approaches
(based primarily on fractal geometry) to the quantitative
description of complex structures, increased understanding of
non-linear phenomena and the introduction of a variety of models
(such as the diffusion-limited aggregation model) that provide
paradigms for non-equilibrium growth phenomena. Advances in
computer technology have played a crucial role in both the
experimental and theoret ical aspects of this enterprise.
Substantial progress has been made towards the development of
comprehensive understanding of non-equilibrium growth phenomena but
most of our current understanding is based on simple com puter
models. Pattern formation processes are important in almost all
areas of science and technology, and, clearly, pattern growth
pervades biology. Very often remarkably similar patterns are found
in quite diverse systems. In some case (dielectric breakdown,
electrodeposition, fluid-fluid displacement in porous media,
dissolution patterns and random dendritic growth for example) the
underlying causes of this similarity is quite well understood. In
other cases (vascular trees, nerve cells and river networks for
example) we do not yet know if a fundamental relationship exists
between the mechanisms leading the formation of these structures.
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