A class of 3-D distributed modular computing nets

Abstract

The class of flat triangular and layered nets of simple computing units, which gives rise to Newton and Hermite filters in two dimensions are extended to 3-D by means of two natural discrete ways. First, by means of the so called Pascal Pyramids; and second, by introducing a rectangular grilled “retina”, which leads to a kind of Newton quadrangular pyramids and to 3-D Newton Filters and Nets. Both cases can be extended to the continuous in the form of 2-D Hermite functions and filters of different orders (degree of derivatives). Preliminary results and examples are presented.