Construction of topological representation of geometric patterns using Cantor self-similar set
Mathematical Physics
2023-06-21 v1 Disordered Systems and Neural Networks
General Topology
math.MP
Abstract
Universal representation of geometric patterns of disordered matters is investigated with the aid of general topology. By utilizing the result obtained in the previous study (S. Ohmori, et.al., Phys. Scr. 94, 105213 (2019)) that any patterns can be represented by a specific topological space, a construction of topological representation of patterns using Cantor set is shown. The obtained topological representations are then demonstrated by the contractions that characterize the self-similarity of Cantor set. For some practical geometric patterns, e.g., network, dendritic, and clusterized patterns, their topological representations are focused on.
Keywords
Cite
@article{arxiv.2306.10237,
title = {Construction of topological representation of geometric patterns using Cantor self-similar set},
author = {Shousuke Ohmori and Yoshihiro Yamazaki and Tomoyuki Yamamoto and Akihiko Kitada},
journal= {arXiv preprint arXiv:2306.10237},
year = {2023}
}