Three Quarters (From the Pillowbook VIII)

Today we will talk about a single, very neglected pillow, which I will call 3/4. To make things look pretty, we will color it depending on its orientation, as follows.

Single 01

Discriminated for centuries by the other, more curvy pillows, 3/4 only likes to hang out with other 3/4s and hide its straight edges as much as possible. Like so:

Right1 p

These two examples are portions of periodic tilings of the entire plane. This way, all straight edges are hidden, and we have periodically placed holes. This quickly becomes more interesting. Here, for instance, is the only tiling that has just circular holes (up to symmetries, of course):

Right2 p

The holes can be more complicated, like these double holes in subtly different periodic tilings.

Right5 p

Next month, we will analyze these patterns a bit. For today, we end with an example that indicates that the holes can become really big (as we will learn).

Right6 p

For today it’s enough to have learned that also the seemingly uninteresting can do pretty things.

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