The moirés of circles

When we draw on a screen of computer or when we print the family of all the concentric circles of integer radius less or equal to R with R large enough (see the figure 1), we can observe “moiré effects” that is to say regular white patterns. The goal of this paper is to give an explanation for such phenomena. In fact, the moiré effects that are generally dealt in the literature ([1],[2] for example) are made by two (or more) periodic structures, which contain black regions (like lines or points) and transparent ones, that overlap. For example, two figures which contains parallel black lines and which made a small angle, or two figures that contain concentric circles. Contrary to these studies, in this paper, we just consider one figure which contains concentric circles. So, our goal is to explain the moiré effects that we can observe on the figure made by the following sequence of instructions: