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doi:10.1016/0097-8493(95)00068-2 
Copyright © 1996 Published by Elsevier Science Ltd.
Visualization of polynomials
Available online 12 February 1999.
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Abstract
Effects of quantization (aliasing) of polynomials in two variables on rectangular lattices (computer monitors) are considered. We treat these effects as measures on the plane and consider the weak closure of the class of all such measures generated by polynomials of a given degree k (as the density of the supporting lattice increases). This closure describes the totality of the images visible on the screen from a large distance (with respect to the distance between the pixels). An explicit description of these images is given. We demonstrate that the “colors” (values of the local densities of limit measures) range over the countable “spectrum” Sk with the unique limit point 1/2 and that the union of the sets Sk for all natural k is dense in [0, 1].
