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Über dieses Buch

This book addresses the intellectual foundations, function, modeling approaches and complexity of cellular automata; explores cellular automata in combination with genetic algorithms, neural networks and agents; and discusses the applications of cellular automata in economics, traffic and the spread of disease. Pursuing a blended approach between knowledge and philosophy, it assigns equal value to methods and applications.



Chapter 1. The Conceptual Origin of Cellular Automata

Since ancient Greece, simplicity has always been a beacon for scientists to the truth. Aristotle said in his book of “metaphysics” that: “an academic theory with less principles is more accurate than those alike with more complimentary principles”. Later, some scientific pioneers inherited and developed the thought of Aristotle. For example, British philosopher William Occam proposed the famous “Occam razor”, that was: “entities should not be multiplied unnecessarily.” His logic was that we should shave off unmercifully those that are redundant and useless.” In modern times, Newton (Newton) unified the complex principles of universe and earth movements with simple Three Laws of Motion and the Law of Universal Gravitation. He put forward in “the mathematical principle of natural philosophy” that: “Nature does nothing in vain, and more is in vain when less will serve; for Nature is pleased with simplicity, and affects not the pomp of superfluous causes”. In the era of relativity, Albert Einstein liked simplicity more in thinking.
Xuewei Li, Jinpei Wu, Xueyan Li

Chapter 2. The Working Principle of Cellular Automata

What exactly is life? How do we define the essential difference between a life system and a non-living one? This has been a long-lasting question for scientific research. In the 1950s, a famous mathematician and computer scientist Von Neumann proposed that self-reproduction is the unique characteristic of living things, and also the necessary condition for anything to be considered life. At that time, the mechanism of biological self-reproduction was not fully understood yet, therefore, such a theory demonstrated Von Neumann’s genius foresight.
Xuewei Li, Jinpei Wu, Xueyan Li

Chapter 3. Model Building Method of Cellular Automata

Mathematical models apply mathematical ways of thinking to simplify and abstract problems needing to be solved, and use mathematical symbols, formulas, diagrams to describe the essential characteristics and inherent rules of things. When people solve a specific problem, they do not rely on observations and experiments, but turn the problem into a mathematical topic and use mathematical analytic method to find the answer. For example, the variations of the electric current and voltage of a circuit system do not need to be actually measured, but are obtained by establishing a mathematical model of differential equation according to the laws of electromagnetics, and then substituting known data for the unknowns in the model for a solution.
Xuewei Li, Jinpei Wu, Xueyan Li

Chapter 4. The Complexity of Cellular Automata

Numerous complex systems exist in nature. The structure of every single component of these systems may be very simple, but because the existence of certain connections (or so called coupling) among various parts, the eventual display of the overall state is quite complex. Cellular automata are the ideal mathematical model for studying complex systems. Through modeling based on the complex system of cellular automata, we can simulate complex systems’ evolutionary phenomena and mechanisms. But at a deeper level, although the evolution of cellular automata simulates the phenomena of the development and the variation of complex systems, for model building itself, it is not capable of analyzing the ultimate cause for complex systems in generating complexity. The mechanism of the generation of complexity is still unknown and indescribable. Only by further analyzing and describing the mechanism of the generation of cellular automata’s complexity, can we explain and analyze the complexity of various systems in depth.
Xuewei Li, Jinpei Wu, Xueyan Li

Chapter 5. Cellular Genetic Algorithms

In this chapter, we introduce the applications of cellular automata in genetic algorithms. In the traditional sense, genetic algorithms (GA) originated from Darwin’s evolution theory. Borrowing from the natural law of “survival of the fittest”, through the genetic operations of selection, crossover and mutation, the individual’s adaptability gets improved. One important feature of genetic algorithms is that the optimization process is not dependent on gradient information, which makes it especially suitable for dealing with complex and nonlinear problems which are difficult to be solved by general searching methods.
Xuewei Li, Jinpei Wu, Xueyan Li

Chapter 6. Cellular Neural Networks

As stated in the chapter of Cellular Genetic Algorithm, an individual cell plays the roles of both “chromosome” and “gene”. Though the roles are different, they all reflect the function of “information transmission by the rules” and the intelligent form of the cells. To continue thinking along this path, may the cellular automata continue to play the role of some elements in other intelligent algorithms so as to realize some complex operations of the intelligent algorithm by using “computing by the rules” of the cells? If the answer is “yes”, then what are the characteristics of such a smart algorithm? Where is the linking point? What will be the effect? If not, where are the difficulties? Will this be able to provide some ideas for the improvement of the intelligent algorithm?
Xuewei Li, Jinpei Wu, Xueyan Li

Chapter 7. Agent-Cellular Automata

In the previous two chapters (“Cellular Genetic Algorithm” and “Cellular Neural Networks”), we have seen that self-adaptive individuals distributed within the cellular lattice play roles of genes, chromosomes, and neurons respectively. The ability of learning among individual cells is strengthened, and at the same time the function of traditional artificial intelligence algorithm is realized. Next, we might as well consider this question—when individuals in the cellular space have different rules of evolution and learning, or they can move by themselves, or individual evolution rules change with time, can we give these individuals human characteristics such as emotions, beliefs, roles, consciousness, etc., and eventually make the space of cellular automata form a “real world” participated in by intelligent agents?
Xuewei Li, Jinpei Wu, Xueyan Li

Chapter 8. The Application Fields of Cellular Automata

Cellular automata theory is a kind of new ideas, different from the traditional thoughts and methods on treating system problems. For many problems that were difficult for traditional methods to find a solution, cellular automaton has made new progresses. For more than 20 years to date, a variety of applications based on the idea of cellular automaton has been booming, they can be roughly summarized as follows: ➀ Simulation of phenomena in the fields of physics and chemistry; ➁ modeling of biological organisms; ➂ high speed computing; ➃ image processing and pattern recognition; ➄ military combat simulation; ➅ simulation of the transportation, epidemics and stock investors’ behavior; ➆ applications in geographical and ecological areas such as land use scenarios, waste water, exhaust gas diffusion, as well as the dynamic changes of biological species.
Xuewei Li, Jinpei Wu, Xueyan Li

Chapter 9. Concluding Remarks—Looking to the Future

In the process of modeling the real world, an important question is: should the model be as abstract as possible or as realistic as possible? Should it describes as generally as possible, or depicts as specifically as possible? One thought is that the prerequisite of grasping the overall functionality of a system is to analyze in-depth the units which comprise the system; another thought believes that the so called “individuals” have relatively strong disorderliness and randomness, thus cannot completely represent the overall behavior of the system. Constant occurrence of complexity, on the other hand, will make it difficult to discover new laws. For the first thought, the mode of construction of its system analysis is from top to bottom. The framework is basically composed of mathematical equations with relatively fewer parameters and environmental changes. It is a highly linear modeling method. For the second thought, its mode of construction of system analysis is from bottom up; the framework of the model is composed of adaptive agents, with relative more parameters and environmental uncertainty. It is a highly nonlinear modeling method. Then, what role do the research and application of cellular automata play in the clash of the two different thoughts of modeling?
Xuewei Li, Jinpei Wu, Xueyan Li
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