Structural Design using Cellular Automata

Traditional parallel methods for structural design do not scale well. This paper discusses the application of massively scalable cellular automata (CA) techniques to structural design. There are two sets of CA rules, one used to propagate stresses and strains, and one to perform design analysis. These rules can be applied serially,periodically,or concurrently, and Jacobi or Gauss- Seidel style updating can be done. These options are compared with respect to convergence,speed, and stability

Empirical Encounters with Computational Irreducibility and Unpredictability

There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up and slowdown phenomena in small Turing machines. We present the results of a test that may spur experimental approaches to the notion of computational irreducibility. The test involves a systematic attempt to outrun the computation of a large number of small Turing machines (all 3 and 4 state, 2 symbol) by means of integer sequence prediction using a specialized function finder program. This massive experiment prompts an investigation into rates of convergence of decision procedures and the decidability of sets in addition to a discussion of the (un)predictability of deterministic computing systems in practice. We think this investigation constitutes a novel approach to the discussion of an epistemological question in the context of a computer simulation, and thus represents an interesting exploration at the boundary between philosophical concerns and computational experiments.Comment: 18 pages, 4 figure

Design and application of convergent cellular automata

Systems made of many interacting elements may display unanticipated emergent properties. A system for which the desired properties are the same as those which emerge will be inherently robust. Currently available techniques for designing emergent properties are prohibitively costly for all but the simplest systems. The self-assembly of biological cells into tissues and ultimately organisms is an example of a natural dynamic distributed system of which the primary emergent behaviour is a fully operational being. The distributed process that co-ordinates this self-assembly is morphogenesis. By analysing morphogenesis with a cellular automata model we deduce a means by which this self-organisation might be achieved. This mechanism is then adapted to the design of self-organising patterns, reliable electronic systems and self-assembling systems. The limitations of the design algorithm are analysed, as is a means to overcome them. The cost of this algorithm is discussed and finally demonstrated with the design of a reliable arithmetic logic unit and a self-assembling, self-repairing and metamorphosising robot made of 12,000 cells

Exclusive Queueing Process with Discrete Time

In a recent study [C Arita, Phys. Rev. E 80, 051119 (2009)], an extension of the M/M/1 queueing process with the excluded-volume effect as in the totally asymmetric simple exclusion process (TASEP) was introduced. In this paper, we consider its discrete-time version. The update scheme we take is the parallel one. A stationary-state solution is obtained in a slightly arranged matrix product form of the discrete-time open TASEP with the parallel update. We find the phase diagram for the existence of the stationary state. The critical line which separates the parameter space into the regions with and without the stationary state can be written in terms of the stationary current of the open TASEP. We calculate the average length of the system and the average number of particles

Layered Cellular Automata

Layered Cellular Automata (LCA) extends the concept of traditional cellular automata (CA) to model complex systems and phenomena. In LCA, each cell's next state is determined by the interaction of two layers of computation, allowing for more dynamic and realistic simulations. This thesis explores the design, dynamics, and applications of LCA, with a focus on its potential in pattern recognition and classification. The research begins by introducing the limitations of traditional CA in capturing the complexity of real-world systems. It then presents the concept of LCA, where layer 0 corresponds to a predefined model, and layer 1 represents the proposed model with additional influence. The interlayer rules, denoted as f and g, enable interactions not only from adjacent neighboring cells but also from some far-away neighboring cells, capturing long-range dependencies. The thesis explores various LCA models, including those based on averaging, maximization, minimization, and modified ECA neighborhoods. Additionally, the implementation of LCA on the 2-D cellular automaton Game of Life is discussed, showcasing intriguing patterns and behaviors. Through extensive experiments, the dynamics of different LCA models are analyzed, revealing their sensitivity to rule changes and block size variations. Convergent LCAs, which converge to fixed points from any initial configuration, are identified and used to design a two-class pattern classifier. Comparative evaluations demonstrate the competitive performance of the LCA-based classifier against existing algorithms. Theoretical analysis of LCA properties contributes to a deeper understanding of its computational capabilities and behaviors. The research also suggests potential future directions, such as exploring advanced LCA models, higher-dimensional simulations, and hybrid approaches integrating LCA with other computational models.Comment: This thesis represents the culmination of my M.Tech research, conducted under the guidance of Dr. Sukanta Das, Associate Professor at the Department of Information Technology, Indian Institute of Engineering Science and Technology, Shibpur, West Bengal, India. arXiv admin note: substantial text overlap with arXiv:2210.13971 by other author