Image dithering: a very simple error diffusion matrix

We have seen a number of different error diffusion matrices (and there are others we haven't discussed); the simplest of our matrices has been "Sierra Lite"

\[\frac{1}{4}\begin{bmatrix} 0& *& 2\\ 1& 1& 0 \end{bmatrix}\]

However, there is an even simpler one which seems to give very good results.

The simplest dither matrix usually given is

$$\frac{1}{2}\begin{bmatrix} *&1\\ 1&0 \end{bmatrix}$$

However, this tends to lead to undesirable artefacts, especially if there are large areas of a single grey scale. Here it is applied to the well known cameraman image, at 2 and 3 gray levels of output: