Fractal geometry is a mathematical theory devoted to the study of complex shapes called fractals. Although an exact definition of fractals has not been established, fractals commonly exhibit the property of self-similarity: the reiteration of irregular details or patterns at progressively smaller scales so that each part, when magnified, looks basically like and then the process is repeated indefinitely on the segments at each stage of the construction.
Self-similarity is built into the construction process by treating segments at each stage the same way as the original segment was treated. Since the rules for getting from one stage to another are fully explicit and always the same, images of successive stages of the process can be generated by computer. Theoretically, illustrates a major attraction of fractal geometry: simple processes can be responsible for incredibly complex patterns.
A worldwide public has become captivated by fractal geometry after viewing astonishing computer-generated images of fractals; enthusiastic practitioners in the field of fractal geometry consider it a new language for describing complex natural and mathematical forms. They anticipate that fractal geometry's significance will rival that of calculus and expect that proficiency in in mathematics only if it becomes a precise language supporting a system of theorems and proofs.
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