Let the Numbers Do the Walking: Generating Turtle Dances on the Plane from Integer Sequences

Adam Colestock
Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture
Pages 139–146 Regular Papers


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.