Self-similarity in Math, Nature and Art
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Self-similarity- the recursive repetition of a structure at different scales or places in a larger form- is ubiquitous in the natural and built environments. It is an emergent phenomenon, generating complexity from a simple initial pattern and a set of transformations on that pattern. Trees, clouds, and coastlines as well as skyscrapers, Hindu temples, and quilts all exhibit prominent self-similarity in repetition, branching patterns, curves, or substructures. Artists have long been fascinated with self-similarity as a means to generate intricate forms, as catharsis for obsessive compulsions, and as an organizing principle for their work.