Bit analysis of 2D-Spiroplots and the generation of 3D-Spiroplots

Abstract

This study investigates the effect of varying bit precisions on the accuracy and computational efficiency of generating Spiroplots, which are a procedural dynamical system used to generate beautiful figures created by Casper van Dommelen, Marc van Kreveld and Jérôme Urhausen in the 2020 paper: ”Spiroplots: a new discrete-time dynamical system to generate curve patterns”. Our research determines that while higher bit precision can marginally enhance the accuracy of a Spiroplot, it does so at a notable computational cost. Additionally, enhancements to the original Spiroplot application are proposed, introducing new point-drawing order methods for situations where points overlap on identical pixel locations. Furthermore, the second half of the paper introduces an extension to the original 2D-Spiroplot concept, paving the way for the creation of 3D-Spiroplots. By overcoming the challenges of defining a rotation axis in three-dimensional space, we have crafted methods that maintain desirable properties like retaining the center of gravity. Our proposed techniques result in intricate and symmetrical 3D patterns that are both mathematically consistent and visually appealing. This paper is accompanied by an application that allows for the running of 2D and 3D-Spiroplots.