Attractor

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An '''attractor''' is a set to which a dynamical system evolves over time. This is can a point, a curve or manifold to which a system tends to move. If the manifold is chaotic, then it is a strange attractor. If it is a temporary attractor in the dynamical behaviour of a system, it can be called a transient attractor. Seen from another point of view, an attractor is a set of points which 'attracts' orbits and trajectories. == Strange Attractor == Strange attractors in a dynamical system (described by one or more differential or difference equations) are bounded regions of phase space which have a fractal dimension. Trajectories within a strange attractor appear to skip around randomly. Examples of strange attractors include the Hénon attractor, Rössler attractor, and the Lorenz attractor. == Social Attractor == What is a “social attractor” ? Perhaps a macroscopic pattern of organization or special micro-macro link which arises inevitably through repeated interactions on microscopic scale. The pattern of a “social attractor” may be considered as the character of a social group (or the personality of the person who represents the group). Depending on the preferences, likes and dislikes, people are drawn to certain groups. A Wikipedia article about religiosity and intelligence says for example: “people with a low intelligence are more easily drawn toward religions, which give answers that are certain, while people with a high intelligence are more skeptical”. (There is also a passage in the bible which reads ‘Blessed are the poor in spirit, for theirs is the kingdom of heaven’). Religions can be characterized as a kind of social attractor in many ways, they are also a basic form of social organization for societies and groups. A group itself can be an attractor for discussions in the group. A typical attractor for discussions and conversations in social groups are common features of the members: if a few members of a group come together and start to discuss topics, they will sooner or later start discussing certain common features and properties of the group, even if they have met originally for a completely different reason, for example a birthday, a marriage, or a death of a member: * Neighbors will discuss the neighborhood * Employees will discuss the company * Relatives will discuss the family No matter why the group members came together in the first place, in the end they discussed always something which they all had in common: for example the neighborhood, the company or the family. == Books == * Steven Strogatz, Nonlinear dynamics and chaos : with applications to physics, biology, chemistry, and engineering, Perseus Books, 1994 * Julien C. Sprott, [http://sprott.physics.wisc.edu/SA.HTM Strange Attractors: Creating Patterns in Chaos] == Links == * Wikipedia entry for [http://en.wikipedia.org/wiki/Attractor attractor] * MathWorld entry for [http://mathworld.wolfram.com/Attractor.html attractor] * Scholarpedia entry for [http://www.scholarpedia.org/article/Attractor attractor]

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