Morphing Wallpaper Functions

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This Demonstration morphs two wallpaper functions and
using interpolation, such that
on 25% of the domain on the left,
on 25% on the right, and in the middle is a linear interpolation of the two functions [1, pp. 201–202].
Contributed by: Izidor Hafner (March 2016)
(Based on work by Frank A. Farris)
Open content licensed under CC BY-NC-SA
Snapshots
Details
Recipes for the wallpaper functions are given below [1, pp. 211–213]. Symmetries are designated for a reflection,
for a rotation, and
for a glide reflection.
general lattice
rhombic (centered) lattice
rectangular lattice
Here means a vertical quarter-glide [1, pp. 117].
square lattice
Wave packets to create fourfold symmetry are:
,
.
Using for a central mirror,
swaps
and
. The symmetry is
[1, pp. 99–101].
hexagonal lattice
Wave packets to create threefold symmetry are:
,
.
Reference
[1] Frank A. Farris, Creating Symmetry: The Artful Mathematics of Wallpaper Patterns, Princeton: Princeton University Press, 2015.
Permanent Citation