Complex Systems

From Meander Designs to a Routing Application Using a Shape Grammar to Cellular Automata Methodology Download PDF

Thomas H. Speller, Jr.
Systems Engineering and Operations Research Department
Volgenau School of Engineering
George Mason University
Fairfax, VA 22030

Abstract

The usefulness of a methodology that integrates shape grammar for capturing design information with cellular automata for computational output of a design solution space is demonstrated in this paper. The application domain is the ornamental artwork known as Chinese lattices or meanders, a subject of earlier interest in shape grammar studies. In this study, a specification for a Chinese lattice is used for creating a shape grammar to capture the model's rules of self-organization, which are then transcribed into cellular automata to physically generate a catalog of designs that meet the requirements of this particular meander style. Then, the study compares the use of a probabilistic (evolutionary computation) technique against complete enumeration for managing the search for unique designs. In consideration of the finding of a very large number of rule solutions for a design specification which produced only a very small number of graphically unique architectures, the question is raised as to whether a more efficient search process other than brute force enumeration can be used. Finally, the meander study is extended to a real engineering system, demonstrating the applicability of the shape grammar to cellular automata (SG -> CA) methodology for finding the most efficient system architecture solutions for a comparable routing/circuit problem. System architectures addressing an underground heating specification are automatically generated and evaluated, resulting in a group of design alternatives displaying the best piping layouts for the given requirements.