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.
|Basic cell and lattice|
|The cell repeated across the plane|
|Colored p1 wallpaper design|
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.