Friezes from Function Graphs

This Demonstration shows simple friezes from function graphs. Three unit cells are shown.
Example: For , the function plotted is


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Here means mirror, means half-turn, and means glide reflection [1].
For functions we use parts of shifted ordinary functions (to avoid accidental symmetry): , , …, , , , ….
The mirror about the axis is obtained using and , and about the half-turn by using and .
The mirror about the axis is obtained using both graphs and filled to the axis.
[1] F. A. Farris, Creating Symmetry: The Artful Mathematics of Wallpaper Patterns, Princeton: Princeton University Press, 2015 pp. 52–53.
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