Cellular automaton 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. The primary classifications of cellular automata as outlined by Wolfram are numbered one to four. Overview The red cells are the von Neumann neighborhood for the blue cell, while the extended neighborhood includes the pink cells as well. A torus, a toroidal shape History
Percolation threshold Percolation threshold is a mathematical term related to percolation theory , which is the formation of long-range connectivity in random systems. Below the threshold a giant connected component does not exist; while above it, there exists a giant component of the order of system size. In engineering and coffee making , percolation represents the flow of fluids through porous media, but in the mathematics and physics worlds it generally refers to simplified lattice models of random systems or networks (graphs), and the nature of the connectivity in them. [ edit ] Percolation models The most common percolation model is to take a regular lattice, like a square lattice, and make it into a random network by randomly "occupying" sites (vertices) or bonds (edges) with a statistically independent probability p . In the systems described so far, it has been assumed that the occupation of a site or bond is completely random—this is the so-called Bernoulli percolation. [ edit ] 2-Uniform Lattices
Swarm behaviour A flock of auklets exhibit swarm behaviour From a more abstract point of view, swarm behaviour is the collective motion of a large number of self-propelled entities. From the perspective of the mathematical modeller, it is an emergent behaviour arising from simple rules that are followed by individuals and does not involve any central coordination. Swarm behaviour was first simulated on a computer in 1986 with the simulation program boids. This program simulates simple agents (boids) that are allowed to move according to a set of basic rules. The model was originally designed to mimic the flocking behaviour of birds, but it can be applied also to schooling fish and other swarming entities. Models In recent decades, scientists have turned to modeling swarm behaviour to gain a deeper understanding of the behaviour. Mathematical models Early studies of swarm behaviour employed mathematical models to simulate and understand the behaviour. Evolutionary models Agents
NetLogo NetLogo is an agent-based programming language and integrated modeling environment. About The NetLogo environment enables exploration of emergent phenomena. It comes with an extensive models library including models in a variety of domains, such as economics, biology, physics, chemistry, psychology, system dynamics. NetLogo allows exploration by modifying switches, sliders, choosers, inputs, and other interface elements. Beyond exploration, NetLogo allows authoring of new models and modification of existing models. NetLogo is freely available from the NetLogo website. NetLogo was designed and authored by Uri Wilensky, director of Northwestern University's Center for Connected Learning and Computer-Based Modeling. Its lead developer is Seth Tisue. Books A number of books have been published about NetLogo. The books include: Steven F. Online courses Technical foundation User interface Examples HubNet External links References
Home | Santa Fe Institute Fractal Figure 1a. The Mandelbrot set illustrates self-similarity. As the image is enlarged, the same pattern re-appears so that it is virtually impossible to determine the scale being examined. Figure 1b. The same fractal magnified six times. Figure 1c. Figure 1d. Fractals are distinguished from regular geometric figures by their fractal dimensional scaling. As mathematical equations, fractals are usually nowhere differentiable. An infinite fractal curve can be conceived of as winding through space differently from an ordinary line, still being a 1-dimensional line yet having a fractal dimension indicating it also resembles a surface.:48:15 There is some disagreement amongst authorities about how the concept of a fractal should be formally defined. Introduction The word "fractal" often has different connotations for laypeople than mathematicians, where the layperson is more likely to be familiar with fractal art than a mathematical conception. History Figure 2.
Encyclopedia of Complexity and Systems Science Assembles 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
Euler equations (fluid dynamics) In fluid dynamics, the Euler equations are a set of equations governing inviscid flow. They are named after Leonhard Euler. The equations represent conservation of mass (continuity), momentum, and energy, corresponding to the Navier–Stokes equations with zero viscosity and without heat conduction terms. Historically, only the continuity and momentum equations have been derived by Euler. However, fluid dynamics literature often refers to the full set – including the energy equation – together as "the Euler equations". The Euler equations can be applied to compressible as well as to incompressible flow – using either an appropriate equation of state or assuming that the divergence of the flow velocity field is zero, respectively. During the second half of the 19th century, it was found that the equation related to the conservation of energy must at all times be kept, while the adiabatic condition is a consequence of the fundamental laws in the case of smooth solutions. where and or
The Proactive Web Era : Intelligent Web and Intelligent Services are knocking at the door ! | The Transcendent Man's Blog Translated from the french original article : It is only 22 years old ( Birth of the Web by Tim Berneers Lee 89 ) but now, the Web or World Wide Web is passing a new milestone in its life. A new generation of Web services is coming, a generation that will go beyond your expectations and your needs. A generation of Intelligent Services, like Siri just announced by Apple, or launched in 2009 by NTT DoCoMo in Japan with Mobile Personal Assistant iConcier. This generation of Intelligent services will know you so well that it will bring you an everyday life Personal Assistant. This step, called the Web intelligent, will bring about a new kind of web: a "Proactive Web!" Indeed, look at your use of the Web today … you go to it, you ask all sorts of questions and wait for a response (mail, web, social, chat, etc). The future will be way different. Remember: Like this:
Agent-Based Computational Economics (Tesfatsion) Growing Economies from the Bottom Up Welcome to the ACE Website Agent-based computational economics (ACE) is the computational modeling of economic processes (including whole economies) as open-ended dynamic systems of interacting agents. Here "agent" refers broadly to a bundle of data and methods representing an entity residing within the dynamic system. Examples of possible agents include: individuals (e.g., consumers and producers); social groupings (e.g., families, firms, communities, and government agencies); institutions (e.g., markets and regulatory systems); biological entities (e.g., crops, livestock, and forests); and physical entities (e.g., infrastructure, weather, and geographical regions). ACE modeling is analogous to a culture-dish laboratory experiment for a virtual world. Current ACE research divides roughly into four strands differentiated by objective. subscribe (unsubscribe) acenewslist youremailaddress end with your actual email address in place of youremailaddress.
University of Michigan, Center for the Study of Complex Systems