Simple systems can create beautiful patterns. Think of the simple mathematical definitions of fractals and the Mandelbrot set. 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. There is a tutorial in the app and a video about it. The formal description, mathematical aspects, and observations are in the paper.