The concept was originally discovered in the 1940s by Stanislaw Ulam and John von Neumann while they were contemporaries at Los Alamos National Laboratory. While studied by some throughout the 1950s and 1960s, it was not until the 1970s and Conway's Game of Life, a two-dimensional cellular automaton, that interest in the subject expanded beyond academia. In the 1980s, Stephen Wolfram engaged in a systematic study of one-dimensional cellular automata, or what he calls elementary cellular automata; his research assistant Matthew Cook showed that one of these rules is Turing-complete. Wolfram published A New Kind of Science in 2002, claiming that cellular automata have applications in many fields of science. These include computer processors and cryptography. The primary classifications of cellular automata as outlined by Wolfram are numbered one to four. Overview A torus, a toroidal shape Cellular automata are often simulated on a finite grid rather than an infinite one. History
Automate cellulaireUn article de Wikipédia, l'encyclopédie libre. À gauche, une règle locale simple : une cellule passe d'un état (i) au suivant (i+1) dans le cycle d'états dès que i+1 est présent dans au moins 3 cellules voisines. À droite, le résultat (complexe) de l'application répétée de cette règle sur une grille de cellules. Un automate cellulaire consiste en une grille régulière de « cellules » contenant chacune un « état » choisi parmi un ensemble fini et qui peut évoluer au cours du temps. Étudiés en mathématiques et en informatique théorique, les automates cellulaires sont à la fois un modèle de système dynamique discret et un modèle de calcul. Exemples[modifier | modifier le code] Les automates cellulaires les plus simples[modifier | modifier le code] Chacune des cellules pouvant prendre deux états, il existe 23=8 configurations (ou motifs) possibles d'un tel voisinage. Les automates de cette famille sont dits « élémentaires ». où chaque ligne est le résultat de la ligne précédente. -uplet où : dans
Self-organizationSelf-organization occurs in a variety of physical, chemical, biological, robotic, social and cognitive systems. Common examples include crystallization, the emergence of convection patterns in a liquid heated from below, chemical oscillators, swarming in groups of animals, and the way neural networks learn to recognize complex patterns. Overview The most robust and unambiguous examples of self-organizing systems are from the physics of non-equilibrium processes. Sometimes the notion of self-organization is conflated with that of the related concept of emergence, because "[t]he order from chaos, presented by Self-Organizing models, is often interpreted in terms of emergence". Properly defined, however, there may be instances of self-organization without emergence and emergence without self-organization, and it is clear from the literature that the phenomena are not the same. Self-organization usually relies on three basic ingredients: Principles of self-organization
Bees algorithmIn computer science and operations research, the Bees Algorithm is a population-based search algorithm which was developed in 2005. It mimics the food foraging behaviour of honey bee colonies. In its basic version the algorithm performs a kind of neighbourhood search combined with global search, and can be used for both combinatorial optimization and continuous optimization. The only condition for the application of the Bees Algorithm is that some measure of topological distance between the solutions is defined. The effectiveness and specific abilities of the Bees Algorithm have been proven in a number of studies.  The Bees Algorithm is inspired by the foraging behaviour of honey bees. Honey bees foraging strategy in nature A colony of honey bees can extend itself over long distances (over 14 km)  and in multiple directions simultaneously to harvest nectar or pollen from multiple food sources (flower patches). The Bees Algorithm Applications See also
Forget Dunbar’s Number, Our Future Is in Scoble’s NumberFebruary 16, 2009 by Hutch Carpenter Photo credit: Mark Wallace I probably don’t know about your latest job project. I don’t know what your kids are up to. But I do know you’ve got a really strong take about where social software helps companies. Why? From Wikipedia, here’s what Dunbar’s Number is: Dunbar’s number is a theoretical cognitive limit to the number of people with whom one can maintain stable social relationships. This is a recurring issue in social networks. I like to break it people down into three types. Three Types of Social Network Participants I’m oversimplifying here, but this is a useful way to segment how people view their social network participation: Close Friends: These folks view social networks as sites for staying up to date on a limited set of close connections. Information Seekers: These folks, including me, expand beyond those with whom they have a pre-existing connection. Power Networkers: These folks amass thousands of connections. Then there are the rest of us.
The Nature of Code“To play life you must have a fairly large checkerboard and a plentiful supply of flat counters of two colors. It is possible to work with pencil and graph paper but it is much easier, particularly for beginners, to use counters and a board.” — Martin Gardner, Scientific American (October 1970) In this chapter, we’re going to take a break from talking about vectors and motion. In fact, the rest of the book will mostly focus on systems and algorithms (albeit ones that we can, should, and will apply to moving bodies). In the previous chapter, we encountered our first Processing example of a complex system: flocking. 7.1 What Is a Cellular Automaton? First, let’s get one thing straight. In Chapters 1 through 6, our objects (mover, particle, vehicle, boid) generally existed in only one “state.” A cellular automaton is a model of a system of “cell” objects with the following characteristics. The cells live on a grid. Figure 7.1 7.2 Elementary Cellular Automata 1) Grid. Figure 7.2 2) States.
Encyclopedia of Complexity and Systems ScienceAssembles for the first time the concepts and tools for analyzing complex systems in a wide range of fields Reflects the real world by integrating complexity with the deterministic equations and concepts that define matter, energy, and the four forces identified in nature Benefits a broad audience: undergraduates, researchers and practitioners in mathematics and many related fields Encyclopedia of Complexity and Systems Science provides an authoritative single source for understanding and applying the concepts of complexity theory together with the tools and measures for analyzing complex systems in all fields of science and engineering. The science and tools of complexity and systems science include theories of self-organization, complex systems, synergetics, dynamical systems, turbulence, catastrophes, instabilities, nonlinearity, stochastic processes, chaos, neural networks, cellular automata, adaptive systems, and genetic algorithms. Content Level » Research Show all authors
Why the Theory of Evolution ExistsIntroduction to the Mathematics of Evolution Chapter 1 Why the Theory of Evolution Exists "In the preface to the proceedings of the [Wistar] symposium, Dr. Kaplan commented about the importance of mathematics in such matters as theorizing about origins [of life]. He said that to construct a history of thought without profound study of the mathematical ideas of successive efforts is comparable to omitting the part of Ophelia from Shakespeare's play, Hamlet" 's Enigma, Luther D. Introduction Many times students hear that the theory of evolution is a "proven fact of science." The reality is that the theory of evolution is NOT a proven fact of science. For example, the theory of evolution requires that life be created from simple chemicals. Such a conversion has never been demonstrated and such a conversion has never been proven to be possible. Even the simplest life on earth, which does not require a host, is far too complex to form by a series of accidents. Science Phillip E. "Naturalism" (Mr.