11552

Morphing Wallpaper Functions

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].
We use functions such as , where .
Since producing these graphics might be slow, start with a low resolution using RGB colors, fix the lattice parameters and , then use a photograph.

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

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.