Sunday, October 6, 2013

Wallpaper Groups: p1

It's back to blogging after a week of vacation and catching up at work. A week ago I spoke with a friend about patterns and math, and he introduced me to the concept of Wallpaper Groups. This is a mathematical categorization of patterns that examines characteristics like translations, mirroring, rotation, and gliding after mirroring. An interesting fact is that mathematicians have found there only exist 17 Wallpaper Groups. If you're interested in blending Euclidean Geometry and art design, check out these resources:

Wikipedia article on Wallpaper Groups
U Science article on Wallpaper Group p1

This isn't easy math, and it's taken me a little while to work through these diagrams. I thought I could explore this subject over the next 17 posts, creating a new pattern for each of the groups. I've also been creating pinboards on Pinterest for each wallpaper group. The math sites I found are lacking beautiful patterns in their demonstration of the groups, so I thought I could add more material. It's also a fun way to look for the underlying structure in patterns.

Today's pattern is called p1. The name comes from crystallography, and the p indicates the cell (basic unit) type, and 1 means there is no rotation. The basic cell shape is a parallelogram. The cell is translated (shifted) about the plane, but is not mirrored or rotated. Here's my example.

primitive cell for p1 wallpaper design
Basic cell and lattice

p1 wallpaper with cell translated across plane
The cell repeated across the plane

coloring the p1 wallpaper

p1 floral wallpaper with repeating parallelogram cell
Colored p1 wallpaper design

detail of p1 wallpaper pattern

And thanks to my boyfriend for that sweet marker set for my birthday. If you'd like to see more examples, checkout my Pinterest board on the p1 wallpaper group.