Measuring static complexity

The concept of pattern is introduced, formally defined, and used to analyze various measures of the complexity of finite binary sequences and other objects. The standard Kolmogoroff-Chaitin-Solomonoff complexity measure is considered, along with Bennett's logical depth, Koppel's sophistication', and Chaitin's analysis of the complexity of geometric objects. The pattern-theoretic point of view illuminates the shortcomings of these measures and leads to specific improvements, it gives rise to two novel mathematical concepts--orders of complexity and levels of pattern, and it yields a new measure of complexity, the structural complexity, which measures the total amount of structure an entity possesses