Curving Spirolaterals

Robert J. Krawczyk
Bridges: Mathematical Connections in Art, Music, and Science (2001)
Pages 29–36


Spirolaterals are square spirals constructed of straight lines of increasing length. This paper investigates methods that can be used to transform their straight line turns into curves. From the tens of thousands of possible spirolaterals which have been found, that are all closed, with and without reversed turns, a series of artworks is developed showing possible curving methods: curve fitting, splines, inversion, antiMercator and circular transformations, along with hypocycloid and epicycloid curves. These transformations are implemented using CAD methods and custom software. A series of parameters are discussed which generate a variety of artwork.