Floating mandalas

Farcot, E.

Abstract

This article considers geometric patterns arising from infinite series of concentric circles, whose radii converge to zero. As an archetype of such design, the initial focus is on level curves of the surface given by z = sin (1/r) in cylindrical polar coordinates, before generalising to other periodic functions. Since any horizontal section of this surface comprises an infinite number of circles, there is no physical medium on which a complete visualisation can be achieved. As we explore different computer-based representations, the reader will be presented with a sample of surprisingly stunning patterns involving intricate arrangements of moir´e and related patterns. Especially when considering rectangular grid approximations, these patterns are reminiscent of mandala figures. We discuss how they arise due to the finite nature of any computing or display device, epitomised by floating-point approximations of real numbers. Code is provided as a means to generate an endless supply of artworks.

Citation

Farcot, E. (2025). Floating mandalas. Journal of Mathematics and the Arts, https://doi.org/10.1080/17513472.2025.2457917

• Journal Article Type: Article
• Acceptance Date: Jan 21, 2025
• Online Publication Date: Feb 1, 2025
• Publication Date: Feb 1, 2025
• Deposit Date: Jan 22, 2025
• Publicly Available Date: Feb 2, 2026
• Journal: Journal of Mathematics and the Arts
• Print ISSN: 1751-3472
• Electronic ISSN: 1751-3480
• Publisher: Taylor and Francis
• Peer Reviewed: Peer Reviewed
• DOI: https://doi.org/10.1080/17513472.2025.2457917
• Public URL: https://nottingham-repository.worktribe.com/output/44425122
• Publisher URL: https://www.tandfonline.com/doi/full/10.1080/17513472.2025.2457917#graphical-abstract