Frieze Functions

This Demonstration makes use of the following table of recipes to create frieze functions, represented by series of the form , with complex coefficients . Let represent a half-turn, and perpendicular mirror symmetries, and a glide reflection along the axis.
The functions used here are truncated to
according to the rules. For example, gives
and there would be four interior terms in the functions for and .
Only two copies of a unit cell are shown.


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The recipes are taken from [1, p. 59].
[1] F. A. Farris, Creating Symmetry, The Artful Mathematics of Wallpaper Patterns, Princeton: Princeton University Press, 2015.
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