The Art of Knot Data
Paweł Dłotko, Davide Gurnari, and Radmila Sazdanovic

Proceedings of Bridges 2024: Mathematics, Art, Music, Architecture, Culture
Pages 443–446
Short Papers

Abstract

Ernst and Sumners’ theorem, affirming that knots constitute a form of big data, coupled with the comprehensive knot tabulation by Burton, Hoste, Thistlethwaite, and Weeks, along with numerous computations of knot invariants, establishes the groundwork for employing big data methodologies in knot theory. Utilizing dimension reduction and machine learning methods, such as Ball Mapper, not only yields valuable insights into the statistical characteristics of knots but also offers compelling means to visually represent the intricate space of knots. The appeal of generative art obtained is multifaceted, encompassing both aesthetic appeal and the complexity of mathematical statements.

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