Quantisation Error

At every pixel the difference between its value and the quantised value can be calculated

error(x, y) = original(x, y) - quantized(x, y)

For an 8 bit channel quantised to 1 bit, the error ranges from +/- 127. The Dithering algorithms try to preserve this lost data as best they can.

An image quantised to three stages

The error between the stage and the pixel value. As the pixels deviate further from the original value, the brighter they become. Once they reach the next bucket in the quantised image, the error resets to zero.

This image looks washed out because it is a red gradient, so the green and blue values are always zero and are always correct.

The point of a dithering algorithm is to spread out this error so it looks less obvious, and appears more like a gradual increase.