Floating mandalas

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 generalizing 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 visualization 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 moiré 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, epitomized by floating-point approximations of real numbers. Code is provided as a means to generate an endless supply of artworks.