The Wrought Iron Beauty of Poncelet Loci

TL;DR

This paper presents a web-based interactive tool for exploring Poncelet triangle loci, highlighting their aesthetic qualities and potential applications in art and design, with a focus on generative art and visual exploration.

Contribution

The paper introduces an interactive online platform for real-time exploration of Poncelet loci, emphasizing their aesthetic appeal and potential for artistic and architectural use.

Findings

Collected hundreds of Poncelet loci into an online gallery

Enhanced some loci with graphic design for aesthetic appeal

Proposed potential applications in metalwork and architecture

Abstract

We've built a web-based tool for the real-time interaction with loci of Poncelet triangle families. Our initial goals were to facilitate exploratory detection of geometric properties of such families. During frequent walks in my neighborhood, it appeared to me Poncelet loci shared a palette of motifs with those found in wrought iron gates at the entrance of many a residential building. As a result, I started to look at Poncelet loci aesthetically, a kind of generative art. Features were gradually added to the tool with the sole purpose of beautifying the output. Hundreds of interesting loci were subsequently collected into an online "gallery", with some further enhanced by a graphic designer. We will tour some of these byproducts here. An interesting question is if Poncelet loci could serve as the basis for future metalwork and/or architectural designs.