自相似集和某些正则构形的扰动及分形的比较
Perturbation of self-similar sets and some regular configurations and comparison of fractals
摘要：
我们考虑两个点集之间的距离，这是修改的Hausdorff度量，并应用它们来描述一些分形，如$δ$ -拟自相似集，和其他一些几何概念，在欧几里得空间，如平铺与准原型和模式与准图案。对于满足开集条件的$δ$ -拟自相似集，我们得到了与P.A. P.莫兰。本文试图从分形的“形式”的角度来探讨分形，并提出一些相关的问题。最后，我们试图探讨一个问题--近似晶体的非晶态固体表现出什么性质和行为？
英文摘要：
We consider several distances between two sets of points, which are modifications of the Hausdorff metric, and apply them to describe some fractals such as $δ$-quasi-self-similar sets, and some other geometric notions in Euclidean space, such as tilings with quasi-prototiles and patterns with quasi-motifs. For the $δ$-quasi-self-similar sets satisfying the open set condition we obtain the same result as a classical theorem due to P. A. P. Moran. In this paper we try to gaze on fractals in an aspect of their "form" and suggest a few of related questions. Finally, we attempt to inquire an issue -- what nature and behavior do non-crystalline solids that approximate to crystals show?
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
