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arXiv · 1211.4968

Self-Similarity in Geometry, Algebra and Arithmetic

Arash Rastegar
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Abstract

We define the concept of self-similarity of an object by considering endomorphisms of the object as `similarity' maps. A variety of interesting examples of self-similar objects in geometry, algebra and arithmetic are introduced. Self-similar objects provide a framework in which, one can unite some results and conjectures in different mathematical frameworks. In some general situations, one can define a well-behaved notion of dimension for self-similar objects. Morphisms between self-similar objects are also defined and a categorical treatment of this concept is provided. We conclude by some philosophical remarks.

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Arash Rastegar. 2012-11-21. Self-Similarity in Geometry, Algebra and Arithmetic. https://arxiv.org/abs/1211.4968

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