I tell a story of a dancing turtle and introduce a mathematical form based in turtle geometry and modular arithmetic. Sequences of integers generated from a discrete parametric function determine the turn angles for a single meandering point and produce symmetric and varied designs on the plane. I also analyze the mathematical properties of the form, highlight emergent features within the form set and show designed objects incorporating these patterns. Finally, I propose several variations of the initial algorithm that hold promise for future inquiry and mathematics-driven making.