Sunday, October 13, 2013

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.

Wallpaper group diagram legend glide reflection.svgan axis of glide reflection.
Image and Key: Source: Wikipedia

pg cell wallpaper group
pg cell

pg wallpaper group example
pg wallpaper

Tuesday, October 8, 2013

Wallpaper Group pm

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

Wallpaper group diagram legend reflection.svgan axis of reflection.
Image and Key: Source: Wikipedia

Here's the cell I created quickly in Illustrator:

pm wallpaper group cell

And here's the resulting pattern:

example pattern from pm wallpaper group

Monday, October 7, 2013

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:

p2 wallpaper cell structure from Wikipedia

Wallpaper group diagram legend rotation2.svga centre of rotation of order two (180°).
Wallpaper group diagram legend rotation3.svga centre of rotation of order three (120°).
Wallpaper group diagram legend rotation4.svga centre of rotation of order four (90°).
Wallpaper group diagram legend rotation6.svga centre of rotation of order six (60°).
Wallpaper group diagram legend reflection.svgan axis of reflection.
Wallpaper group diagram legend glide reflection.svgan axis of glide reflection.
 Image and Key: Source: Wikipedia

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

example of p2 wallpaper cell with cat
The cell structure contains a 180 degree rotation
 Once we create our cell, we translate it both vertically and horizontally to cover the plane.

example of p2 wallpaper group with cat pattern
The cell is translated across the plane to create a pattern

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

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.

Tuesday, October 1, 2013

Spotted: Chicago

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

hexagon pattern mercat chicago