Wallpaper Group pg

I've been pretty sick this week, so the updates have been scarce. Tonight I spent a little time working on wallpaper group pg, which features a glide reflection. Part of the cell is reflected and then translated.

an axis of glide reflection.

Image and Key: Source: Wikipedia

pg cell

pg wallpaper

Wallpaper Group pm

Tonight's wallpaper group is pm, which indicates a primitive cell that is mirrored:

Key:

an axis of reflection.

Image and Key: Source: Wikipedia

Here's the cell I created quickly in Illustrator:

And here's the resulting pattern:

Also check out my pinboard on Wallpaper Group pm.

Wallpaper Groups: p2

Tonight I'm continuing my exploration of Wallpaper Groups with an example from group p2. Cells in this group have the following structure:

Key

	a centre of rotation of order two (180°).
	a centre of rotation of order three (120°).
	a centre of rotation of order four (90°).
	a centre of rotation of order six (60°).
	an axis of reflection.
	an axis of glide reflection.

 Image and Key: Source: Wikipedia

Now applying cats. Note my example flips the parallelogram 90 degrees.

The cell structure contains a 180 degree rotation

 Once we create our cell, we translate it both vertically and horizontally to cover the plane.

The cell is translated across the plane to create a pattern

For more examples of p2 patterns, check out my pinboard.

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.

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.

Spotted: Chicago

 I've been away visiting Chicago for a friend's wedding. I spotted this hexagonal pattern at Mercat, at the Renaissance Hotel.