Tilings closed under translation in only one direction

Question

Background

A tiling or tessellation of the plane is periodic if it is closed under at least two non parallel translations. Three examples of periodic tilings, including their corresponding translation vectors, are shown below:

                                                 

Question

I wonder if tilings that are closed under only one translation also exist, and if so, what they are called. I am also curious what they look like.

Answer 1

I don't know what they are called, they might not even have a name. But I can come up with two simple examples on the spot: Take your two first examples (triangles and squares), take a single row from those, and push that row a little bit to the side. You have now broken the vertical symmetry, and have only the horizontal symmetry left.

If you have symmetry in only one direction (say horizontal), then the pattern consists not of repeated, finite-size tiles, but of repeated infinitely tall, finite-width columns. Make whatever column you like, copy it indefinitely, and put all those columns next to one another (at the same height). You now have yourself an example.