Symmetry of a Mystery Curve
This Demonstration shows graphs of the function , where , , and are complex coefficients and the frequencies , , and are integers. In particular, for the frequencies 1, 6, and -14, the curve has five-fold symmetry.
The following theorem is shown [1, pp. 13]:
Suppose that and are integers and that all the frequency numbers in the finite sum
Then, for any choice of the coefficients , satisfies the symmetry condition
for all .
 F. A. Farris, Creating Symmetry: The Artful Mathematics of Wallpaper Patterns, Princeton: Princeton University Press, 2015.