Abstract
This paper presents a family of two-dimensional parametric curves that produce frieze patterns with a range of symmetries, organic variations and spatial rhythms. The curves are described by Whewell equations that relate the tangential angle of the curve to its arc length through a series of sine terms. When the low-order harmonics of two sine components are comparable, the pattern develops rhythmic variations (i.e., beats) that may be thought of as a spatial analogue of combination tones in music theory. Inclusion of multiple sine components creates complex, polyphonic patterns with looping forms on a range of spatial scales. The family of curves is based on a historical description of meander bends and rivers, and extends that model to include multiple frequency components.