Threefold Color-Turning Wallpaper Functions

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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.


The hexagonal lattice has basis vectors , , and the lattice coordinates are , .

The Fourier series are actually truncated to two terms: .


Contributed by: Izidor Hafner (April 2016)
Based on work by: Frank A. Farris
Open content licensed under CC BY-NC-SA



The term "color-turning" refers to an -fold rotational symmetry of a figure, in which each successive image is colored differently [1].

We use the following recipes [1, pp. 131–140].


[1] F. A. Farris, Creating Symmetry: The Artful Mathematics of Wallpaper Patterns, Princeton: Princeton University Press, 2015.

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