File:Radial Interleaving of Lightness and Saturation.png

The key problem is that the colour space is a 3D space and an image can only support a 2D space.

An HSL format (with hue, saturation and lightness dimensions) is adopted for the colour space and a polar coordinate system is adopted for the pixels.

Hue is then matched to angles and both lightness and saturation are matched to distances from the centre of the image.

Under this setup, a way to characterise the relative contribution of lightness and saturation to distance also needs to be chosen. The three images correspond to three different choices, out of all the possible ones.

The left image shows a case where lightness and saturation are compounded in some way (like addition, multiplication, etc.) into a single parameter, and that parameter is matched to distance at a pixel by pixel level. With some appropriate compounding, the image may appear to be seamless from a distance, but closer inspection will show the dithering that emerges with this approach.

The central image shows a case where square bands of similar lightness are first formed and ordered based on decreasing lightness, from the centre to the border of the image, and then ripples of saturation are used to order pixels within those bands so that saturation may also change seamlessly. Dithering is significantly reduced, but lines of greyness (lack of saturation) appear, which are finely interleaved with colours.

The right image shows a case where both lightness and saturation are treated in a more balanced way: they are both partitioned in bands and made to ripple in alternate series of waves at different frequencies. Aside from the rippling's peaks and troughs, lightness still generally decreases with the distance from the centre, and saturation generally increases when moving away from the centre or the borders, towards a middle. From a distance the image looks neater and more varied in its colouring, but also shows a more intense and heterogeneous rippling.