Residue Patterns and Their Application to Graphic Design

Munekazu Sakamoto and Mikio Takagi

Center for Function-Oriented Electronics, Institute of Industrial Science, University of Tokyo, 7-22-1, Roppongi, Minato-ku, Tokyo 106, Japan

(Received November 26, 1990; Accepted January 28, 1991)

Keywords: Residue, Modulus Operation, Period, Symmetry, Polynomial with Rational Coefficients

Abstract. Residue patterns can have exact periodicity if polynomials with rational coefficients are used as generating functions. On this basis the authors have developed some techniques to make patterns on tetragonal or hexagonal lattice and to compose them from elementary patterns. Theorems on the condition of non-blank generation and on the number of these conditions of the same period are given.