Wolfram Computation Meets Knowledge

Wolfram Summer School


Rafal Kicinger

Summer School

Class of 2003


Originally from Poland, Rafal is a PhD student in the School of Information Technology and Engineering at George Mason University, Virginia. In 1999 he completed his masters degree in structural engineering at Warsaw University of Technology, Poland. In addition to evolutionary computation, dynamical systems and chaos theory, Rafal’s research interests include “inventive engineering design” — looking for innovative approaches to conceptual design problems in engineering. In this vein he hopes to find ways to apply A New Kind of Science methodology, believing that interesting design concepts can emerge, based on local interactions of simple programs representing simple design/decision rules. Lindenmayer systems, Turing machines and Cellular automata are among the systems he plans to investigate in the context of possible engineering design applications.

Project: Using Cellular Automata to Design Structural Systems in Tall Buildings

The goal of this project was to introduce NKS to engineering design problems and estimate a true potential of this approach. It was an initial step in exploring the world of simple programs for engineering design applications as well as introducing a novel methodology presented in Wolfram’s A New Kind of Science.

The motivation for this project is based on the fact that even designers of complex and sophisticated engineering systems (bridges, tall buildings, etc.) use only a very small set of design/decision rules to develop design concepts. It is hence author’s belief that even very complex designs of engineering systems can be modeled using simple programs like cellular automata (CAs).

Two potential ways of attacking this problem are based on the following observations. First, one of the important problems in engineering design is the problem of topological optimum design, where one seeks the optimal configuration of design elements satisfying some constraints, and minimizing, or maximizing, a certain objective function, e.g. maximum deflection of a steel structure. This search for the optimal configuration of design elements sometimes yields very interesting patterns. It is author’s belief that the search for such interesting structural patterns can be vastly enhanced using cellular automata and other simple programs. Second, it is usually the case that engineering designs have very simple and repetitive forms. On the other hand, cellular automata, or other simple programs, can generate both very simple and repetitive behavior as well as complex forms and configurations. It is definitely worth exploring whether the complex forms of engineering systems will be better than traditional design. Hence, it is worth exploring the true potential of this approach to engineering design.

The project had two major objectives: exploration of the space of simple programs that can provide interesting models of engineering systems, as well as identification of potential interesting patterns and their further analysis. The initial exploration of the space of simple programs has been focused on one dimensional elementary CAs and two dimensional 5-color 9-neighbor totalistic CAs.

Elementary CAs have been used to generate designs of structural systems in tall buildings. These experiments were performed using all 256 elementary CAs. The goal of these experiment was to design the most rigid structural system in a tall building. The fitness of every design was measured by the maximum displacement of the structure.

Elementary CA evolved wind bracing configurations in tall buildings. Each configuration was represented as a two-dimensional array with the number of rows corresponding to the number of stories, and a number of columns equal to the number of bays in a tall building. The array consisted of binary numbers where the value 0 corresponded to the absence of a wind bracing element at a particular position in the array, whereas value 1 corresponded to the wind bracing of type X.

A structural system in a tall building is a complex system consisting of various structural elements consisting of not only wind bracings but also beams, columns and ground connections. In the simplified model used in these experiments only wind bracings were evolved. All other elements’ characteristics were kept constant throughout all runs. Thus, only fixed columns, pinned beams, and fixed ground connection were used. Also, only two types of cross-sections were used; one for all beams and columns, and one for all wind bracings.

The fitness of each design concepts generated by a CA was evaluated by a structural analysis package called SODA developed by Acronym Software Inc. The fitness of a design was equal to the maximum displacement of the steel structure and measured at the topmost right node. Each structure was loaded with wind load, as well as dead and love loads determined according to the commonly used American design codes. Each experiment consisted of the run of an elementary CA starting with a random initial condition and evolved for the number of generations equal to the number of stories in a tall building. 8 sets of random initial conditions have been used for each elementary rule. Also, an initial condition consisting of a single black cell (single wind bracing element) in the middle bay have been used. In the experiments 36-story buildings have been used with 7 bays. The story height was equal to 14 feet and bay width was 20 feet.

Results of these experiments have shown that elementary CAs can generate some interesting structural patterns. These patterns included both traditionally used patterns for this class of buildings like vertical and horizontal trusses, but also some novel arrangements of wind bracings characterized by high fitness values. Elementary rule 109 generated the best design concept when starting with a single black cell. It also produced very interesting structural pattern. When random initial conditions were used, several elementary CAs generated the same pattern consisting of the multibay vertical truss located in 5 middle bays. This pattern was generated by the elementary CA with rules 232, 233, 236, and 237.

In another set of experiments 2D cellular automata were used. In this case the original representation was extended and included 3 more types of wind bracings: left diagonal bracing, right diagonal bracing, and simple X bracing. They were represented as integers with values 2, 3, and 4 respectively. The 5-color 9-neighbor totalistic CA rules were picked randomly. Also, initial conditions were generated randomly as a two-dimensional array of integer values with range 0-4. Each CA was evolved for 100 steps and at each step evaluated in terms of its fitness.

The results of these experiments have shown that 2D CAs can also generate interesting structural patterns. The best fitness value obtained in these experiments was worse compared to the best fitness from previous experiments with elementary CAs. However, only very limited search was performed including only 15 2D CA rules and much larger number of experiments in necessary to fully estimate the true potential of this approach.

Favorite Three-Color Cellular Automaton

Rule Chosen: 3549372511747

Reason: I’ve decided to choose this particular automaton because it exhibits very interesting behavior at the border of class 1 and class 2 behavior and because that everybody will be looking at class 4 behavior so it would be nice to do something else.

The coexistence of the two classes is visible here and it would be worthwhile to try to analyze it. I have done some simple analysis of the behavior of this CA.

Additional Information

Kicinger, R. “Cellular Automata in Structural Design.” Presentation at NKS 2004, Boston, MA, 2004. [abstract]