Toward a theory of patterns

Abstract

The purpose of this paper is to present a mathematical model intended for the description and analysis of patterns. As buildingblocks for this model will serve certain simple but foundamental concepts: signs, configurations, and images. These are related by similarity, synonymity and deformation transformations. Using these concepts it is shown how patterns can be analysed into elementary parts, both pure patterns and deformed ones. As a result of such an analysis one gets a grammatical description of the image presented to the observer. For didactic reasons the grammatical construction is limited to a special but typical case; a more general grammer of patterns will be treated elsewhere. The introduction of the mathematical model is accompanied by a number of illustrative examples.