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An Algebraic Description of Painted Digital Pictures

An algebraic system for binary digital pictures has already been described, along with the definition of the four arithmetic rules. In this paper, an extension of the binary algebraic system to a 2n-valued one is first proposed. It then becomes evident that this extended algebraic system satisfies several properties including those of a ring. An example of a 2n-valued model, an eight-valued algebraic system, is introduced and applied to painted digital pictures. Pictorial operations such as multiple arrangement, enlargement, differentiation, integration, and color changes are then dealt with by the combinations of the four arithmetic rules.