Abstract: Dot diffusion has been proposed as a way of combining the strengths of ordered dithering and error diffusion to create a parallelizable halftoning technique. However, dot diffusion pays a price in image quality in order to achieve parallelizability. Space-filling curves have been used to improve error diffusion. We show that by combining dot diffusion with a space-filling curve traversal technique, a parallelizable halftoning technique results that does not pay a cost in image quality. This new technique we call space diffusion.