VISUALIZATION OF POLYNOMIALS

Effects of quantization (aliasing) of polynomials in two variables on rectangular lattices (computer monitors) are considered. We treat thes e effects as measures on the plane and consider the weak closure of th e class of all such measures generated by polynomials of a given degre e k (as the density of the supporting lattice increases). This closure describes the totality of the images visible on the screen from a lar ge distance (with respect to the distance between the pixels). An expl icit description of these images is given. We demonstrate that the ''c olors'' (values of the local densities of limit measures) range over t he countable ''spectrum'' S-k with the unique limit point 1/2 and that the union of the sets S-k for all natural k is dense in [0,1].