Patterns in 2 Dimensions

Patterns which are made up and used as fabric or wallpaper are also made up of repeating “chunks”. As with our 1D patterns, we could recreate them using a single unit of repeat (like a potato stamp) or could check their repeat by sliding the pattern over itself (this time in either direction). This type of sliding is mathematically known as a translation, and if a pattern can do this we say it has “transformation symmetry”. This isn’t so simple to check in 2D, but if you had a particular pattern printed onto acetate twice, you could slide one over the other to demonstrate the transformation symmetry. These make you wonder whether it would be possible to spin a pattern or flip it over and thus how it would exactly fit onto itself. These ideas can be combined to make 17 different basic repeating patterns that you can use to arrange as motifs onto fabric. These are offically known as the “17 wallpaper patterns”.

Block printing would be a relatively simple way to create a 2D repeating pattern. By creating a stamp, and replicating this across a piece of paper or fabric, a pattern with transformation symmetry would be born.

Repeating 2D patterns are plentiful in the world around us, for example in a brick wall, a parquet floor, a honeycomb, or on things like fabric, wallpaper and wrapping paper.