Categorizing Celtic Knot Designs

Roger Antonsen, Laura Taalman
Proceedings of Bridges 2021: Mathematics, Art, Music, Architecture, Education, Culture
@inproceedings{bridges2021:87,
  author      = {Roger Antonsen and Laura Taalman},
  title       = {Categorizing Celtic Knot Designs},
  pages       = {87--94},
  booktitle   = {Proceedings of Bridges 2021: Mathematics, Art, Music, Architecture, Culture},
  year        = {2021},
  editor      = {Swart, David and Farris, Frank and Torrence, Eve},
  isbn        = {978-1-938664-39-7},
  issn        = {1099-6702},
  publisher   = {Tessellations Publishing},
  address     = {Phoenix, Arizona},
  url         = {https://archive.bridgesmathart.org/2021/bridges2021-87.html}
}

Abstract

In this paper we investigate and enumerate classes of rectangular Celtic knot designs. We introduce criteria for reducing, filtering, and categorizing such designs in order to obtain pleasing, Celtic-looking patterns. We use Hamming graphs to manage large collections of related designs, begin to uncover relationships between Celtic designs, and attempt to identify mathematically and aesthetically significant characteristics of designs.