Abstract

Beyond their conventional concepts as some outcome of the system dynamics, Patterns and their Formation are regarded here as some substantial parts in description of the dynamics and flow of information in systems. Approach to a typical geometrical problem, for instance, comprises some sequential steps where the observed information of the system is rearranged, reorganized and reformulated to reach the final result. An algebra is introduced here to begin a systematic framework for sequential approaches to geometrical problems. The type of the objects suitable for different kinds of the problems, the way the objects successively match to get a more detailed description of the problem, and the summation operator which combines simultaneous segments of the information of the system are discussed. Based on such abstract clarification for the sequential description of systems, we then switch to reformulate practical examples in various fields from network dynamics to molecular decomposition, relativity and embryogenesis, and demonstrate how different sequential implementation of symmetry could lead to proper description for the dynamics in each of these examples.