Functional Curves and Surfaces: Algebraic Geometry Inspired Visuals in Hydra

We present FCS (Functional Curves and Surfaces), a framework for synthesizing visual patterns by composing functions for curves and surfaces, implemented as an extension to Hydra, a popular tool for live coding visuals. The extension consists of functions for dozens of implicit and parametric curves and surfaces, which can be chained together in numerous ways to create striking visuals. FCS can also serve as a tool for students and practitioners of math, art, and computer science to learn algebraic geometry in a fun, creative way.