Border patterns … revisited

Border patterns, also known as freeze patterns, have been known to humanity for thousands of years, typically decorating the frame of a painting, mosaic, or some other two-dimensional design/pattern. They are straight symmetrical strips, of length finite by necessity but infinite in principle, and of constant, finite width. There exist seven types of them, discussed in several books, including my own ISOMETRICA (Chapter 2): p111, pm11, p1m1, p1a1, p112, pmm2, pma2. Below I am briefly discussing them from another point of view … with something else in mind (that may materialize in the future) 🙂

Border patterns are often considered to be one dimensional: this is quite imprecise, as there exist only two truly one-dimensional patterns, one with translation only (p) and one with reflection or rotation (m); below I show how these two patterns, appropriately placed at an upper and a lower level, can create six of the seven border patterns (the sad exception being pm11 — the only type besides p111 that has no level-swapping isometries).

border-one-two-ConvertImage

 

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s


%d bloggers like this: