Threefold Color-Turning Wallpaper Functions
This Demonstration illustrates threefold color-turning wallpaper functions using complex functions in Fourier series of the form , where are color-turning waves, and are called lattice waves.[more]
The hexagonal lattice has basis vectors , , and the lattice coordinates are , .
The Fourier series are actually truncated to two terms: .[less]
The term "color-turning" refers to an -fold rotational symmetry of a figure, in which each successive image is colored differently .
We use the following recipes [1, pp. 131–140].
 F. A. Farris, Creating Symmetry: The Artful Mathematics of Wallpaper Patterns, Princeton: Princeton University Press, 2015.