Examples of parametric curves, created by single pairs of non-piecewise parametric equations. I came up with the method for creating such curves (or at least if someone else beat me to it, I'm unaware of it). My method utilizes and reinforces high school level Math skills (domain/range, function transformations, function addition, function composition, writing sinusoid equations, parametric equations). Inspired by the "Batman Equation" of 2011 and Wolfram Alpha's "person curves."
Instructional how-to video here: https://youtu.be/oaIsCJw0QG8