Dithering is a technique to reduce the color space of a picture, to prevent horrible artifacts. For example, when only (pure) black and white are available, naive rounding leads to this monstrosity, which you surely recognize as Caravaggio's Saint Jerome Writing (original image from Wikimedia Commons).

The grey-level values could be imitated by the density of white pixels. This can be done if rounding error is recorded and distributed. Here are two standard, simple methods, and their hybrid.

Caravaggio's Saint Jerome Writing

Caravaggio's Saint Jerome Writing, Floyd-Steinberg dithering Caravaggio's Saint Jerome Writing, Froginson-Toadberg dithering Caravaggio's Saint Jerome Writing, Atkinson dithering

Floyd-Steinberg Dithering (left) diffuses the error to nearby pixels, so that gray areas are realizied as sprinkled with white pixels. But that makes very dark (and very white) areas look unnatural, because we don't really distinguish them from pure black. See the usual place (also here, and here) for details and conventions used below.

Atkinson's dithering (right) distributes only part of the error (7/8), which means that low deviations from black accumulate slower, and don't reach the threshold to be displayed as white. This enlarges the uniform black areas. But they encroach too much: parts of the table or the book are gone, and the half-shadow on the right shrinks.

By construction, it's perfectly alright to take the mean of the parameters. Only 1/16 of the error is lost then, and the effect is very pleasing. With this method we can better appreciate Frogs and Toads, which is why I call it the Froginson‑Toadberg dithering. Its “matrix” is

0X9/322/32
5/327/323/320
02/3200
 .