Spiroplots: a New Discrete-time Dynamical System to Generate Curve Patterns
Casper van Dommelen, Marc van Kreveld, and Jérôme Urhausen

Proceedings of Bridges 2020: Mathematics, Art, Music, Architecture, Education, Culture
Pages 353–360
Regular Papers

Abstract

We introduce a new procedural dynamic system that can generate a variety of shapes that often appear as curves, but technically, the figures are plots of many points. We name them spiroplots and show how this new system relates to other procedures or processes that generate figures. Spiroplots are an extremely simple process but with a surprising visual variety. We prove some fundamental properties and analyze some instances to see how the geometry or topology of the input determines the generated figures. We show that some spiroplots have a finite cycle and return to the initial situation, whereas others will produce new points infinitely often. This paper is accompanied by a JavaScript app that allows anyone to generate spiroplots.

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