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a ''self-similar structure''. The homeomorphisms may be [[iterated function|iterated]], resulting in an [[iterated function system]]. The composition of functions creates the algebraic structure of a [[monoid]]. When the set ''S'' has only two elements, the monoid is known as the [[dyadic monoid]]. The dyadic monoid can be visualized as an infinite [[binary tree]]; more generally, if the set ''S'' has ''p'' elements, then the monoid may be represented as a [[p-adic number|p-adic]] tree.
a ''self-similar structure''. The homeomorphisms may be [[iterated function|iterated]], resulting in an [[iterated function system]]. The composition of functions creates the algebraic structure of a [[monoid]]. When the set ''S'' has only two elements, the monoid is known as the [[dyadic monoid]]. The dyadic monoid can be visualized as an infinite [[binary tree]]; more generally, if the set ''S'' has ''p'' elements, then the monoid may be represented as a [[p-adic number|p-adic]] tree.
一个自相似的结构。同胚可以迭代，产生迭代函数系统。函数的组合产生了幺半群的代数结构。当集合S只有两个元素时，幺半群此时称为二元幺半群。二元幺半群可以表示为无限二叉树；更一般地说，如果集合S有p个元素，则一元类可以表示为p进树。
The [[automorphism]]s of the dyadic monoid is the [[modular group]]; the automorphisms can be pictured as [[Hyperbolic coordinates|hyperbolic rotation]]s of the binary tree.
The [[automorphism]]s of the dyadic monoid is the [[modular group]]; the automorphisms can be pictured as [[Hyperbolic coordinates|hyperbolic rotation]]s of the binary tree.
A more general notion than self-similarity is [[Self-affinity]].
A more general notion than self-similarity is [[Self-affinity]].
比自相似性更一般的概念是自仿射性。
==Examples==
==Examples==