Simple Calculation of Moiré Patterns

The indicial equation is a simple but surprisingly powerful tool: assign an index to each line (or circle, or ray) in two overlapping grids, set their difference equal to a constant, and the moiré pattern falls out algebraically. This paper works through several cases, parallel lines, concentric circles, radial rays, concurrent lines, and shows that the resulting patterns are classical curves: hyperbolas, ellipses, parabolas, pencils of circles. The mathematics is elementary, mostly high-school level, but the results are not obvious.