Technically speaking, halftone screens are "tessallations" - patterns that cover a surface by the repeated use of a single shape, without gaps or overlapping. And since tessallations are popular decorative items - I end up seeing halftone screens everywhere. Here are a few from a recent trip to Seattle.
A classic Diamond halftone dot
An example of a high lpi traditional Square dot halftone
In contrast to a very low lpi Square dot
Waiting to cross the street I spot a mix of two halftone patterns
At first it appears to be a classic Round dot mixed with a more subtle Square dot halftone
But on closer examination it seems to be an exotic version of Esko's Concentric screening. Interestingly the pixels that make up this sidewalk halftone are round instead of the traditional square shape.
Walking past this building reveals a fine example of
Second order FM/stochastic screening.
Sometimes the final halftone screen is not visible, but instead, you can see the foundation for the halftone. Halftone screen dots are formed by a "threshold" array - basically a pattern made up of 256 shades of gray which determines which pixels are turned on to form the actual dot.
The tones of the granite pillar on this building
Make a great threshold array to create a
Mezzotint halftone (the right half of the photo below - click to enlarge)