After stumbling on a picture where growing and undulating circles create an Archimedean spiral, I recreated this to played with different parameters in this scheme.
The basic idea is to draw circles of growing sizes, offsetting its center along an (invisible) circle. By this, the circles are more dense in different places, forming ‘optically’ a spiral of denser color. [This effect is essentially the same as the shockwave an airplane creates at supersonic speeds - see soundbarrier - just that here the source of the waves travels in a circle].
The effect of varying some of the parameters, like the growth of circles and the size of offsetting circle, together with adding alternating colors, is shown in the following video - resulting in some nice Moire-like patterns depending on the ratio of the parameters.
Just playing with parameters and colors generates a wide variety of patterns (click to enlarge):
More systematically, in the next figure the size of the offset circle grows to the right while the increase of the angle along the offsetting circle decreases from top to bottom (click to enlarge):