General Pattern Theory

An introduction to pattern theory, a concept which aims to create mathematical knowledge representations of complex systems, analyze the mathematical properties of the resulting regular structures, and apply them to practically occurring patterns in nature and the man-made world.
The aim of pattern theory is to create mathematical knowledge representations of complex systems, analyse the mathematical properties of the resulting regular structures, and to apply them to practically occuring patterns in nature and the man-made world. Starting from an algebraic formulation of such representations they are studied in terms of their topological, dynamical and probabilistic aspects. Patterns are expressed through their typical behaviour as well as
through their variability around their typical form. Employing the representations (regular structures) algorithms are derived for the understanding, recognition, and restoration of observed patterns. The algorithms are investigated through computer experiments.