Dithering vs Ordered Dithering vs Error Diffusion

Random dithering could be termed the "bubblesort" of digital halftoning algorithms. It was the first attempt (documented as far back as 1951) to correct the contouring produced by fixed thresholding, and it has traditionally been referenced for comparison in most studies of digital halftoning. In fact, the name "ordered dither" (which will be discussed later) was chosen to contrast random dither.

While patterning was an important step toward the digital reproduction of the classic halftone, its main shortcoming was the spatial enlargement (and corresponding reduction in resolution) of the image. Ordered dither represents a major improvement in digital halftoning where this spatial distortion was eliminated and the image could then be rendered in its original size

structure

With this method, the average quatization error is reduced
by propagating the error from each pixel to some of its neighbors in
the scan order.