Again, in order to prevent large-scale patterns (such as false contours), an intentionally applied form of noise is used to randomize the quantization error. This process is known as dithering. The Floyd-Steinberg algorithm implements dithering using the error diffusion technique—in other words, it pushes (adds) the residual quantization error of a pixel onto its neighboring pixels, to be dealt with later. It spreads the quantization error out according to the distribution shown in the following screenshot, as a map of the neighboring pixels:

In the previous screenshot, the current pixel is represented with a star (*) and the blank pixels represent the previously-scanned pixels. The algorithm scans the image from left to right and top to bottom. It sequentially quantizes the pixel values one by one, each time the quantization error is distributed among the neighboring pixels (yet to be scanned), while not affecting the pixels that already got quantized. Hence, if a number of pixels have been rounded downward, it becomes more likely that the following pixel will be rounded upward by the algorithm so that the average quantization error is close to zero.

The following screenshot shows the algorithm pseudocode:

The following screenshot shows the output binary image obtained with a Python implementation of the previous pseudocode; it shows a drastic improvement over the previous half-toning method in the quality of the binary image obtained:

The code is left as an exercise.