Consider a 3D function . Now evaluate it at each point of a integer lattice grid. Compute corresponding to each point and plot it as a color defined by some palette that suits your aesthetic. The consequence is a what we term the “modulo rug”.
For example, below is a plot of .
We get a pattern of circles around a central circular system reminiscent of ogdoadic arrangements in various Hindu maṇḍala-s. From the aesthetic viewpoint, the best modulo rugs are obtained with symmetric functions higher even powers — this translates into some pleasing symmetry in the rug. Several examples of such are shown below.
All the above are composite numbers. Accordingly, there is some repetitiveness in the structure. However, if is a prime then we have the greatest complexity in the rug. One example of such is plotted below.
See also: 1) Sine rugs; 2) Creating patterns through matrix expansion.