Attractor

In the mathematical field of dynamical systems, an attractor is a set of numerical values toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed.

In finite-dimensional systems, the evolving variable may be represented algebraically as an n-dimensional vector. The attractor is a region in n-dimensional space. In physical systems, the n dimensions may be, for example, two or three positional coordinates for each of one or more physical entities; in economic systems, they may be separate variables such as the inflation rate and the unemployment rate.

If the evolving variable is two- or three-dimensional, the attractor of the dynamic process can be represented geometrically in two or three dimensions, (as for example in the three-dimensional case depicted to the right). An attractor can be a point, a finite set of points, a curve, a manifold, or even a complicated set with a fractal structure known as a strange attractor. If the variable is a scalar, the attractor is a subset of the real number line. Describing the attractors of chaotic dynamical systems has been one of the achievements of chaos theory.

Strange Attractors

This article is about the television episode. For the mathematical concept, see Strange attractor.

"Strange Attractors" is the sixth episode of the fourth season of the NBC science fiction drama series Heroes and sixty-fifth episode overall. The episode aired on October 26, 2009.

Plot

The scene opens with Matt Parkman making love to his wife Janice. Unbeknownst to Janice, however, Sylar is in control, which Matt realizes later. He is enraged, though Sylar says it's a warning. Matt tells Janice about his problem (without referring to Sylar by name), and urges her to leave with their baby. After leaving a message for Mohinder Suresh, he opens up a beer. He notices Sylar being affected by the alcohol and begins to drink more. As Matt continues to get more drunk, he notices Sylar beginning to disappear. As Sylar completely disappears, Matt's wife and his Alcoholics Anonymous partner walk in. Matt exclaims his triumph before passing out in front of them. Matt wakes up later, with he and his wife embracing and his AA partner telling him they need to start over. As Matt leaves, Sylar reveals that he has taken control over his body. Matt says he'll never get away with it, though Sylar just chuckles. A worried Janice sees him talking to and laughing at no one.

Strange

Strange may refer to:

Fiction

Music

Lorenz system

The Lorenz system is a system of ordinary differential equations (the Lorenz equations, note it is not Lorentz) first studied by Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditions. In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system which, when plotted, resemble a butterfly or figure eight.

Overview

In 1963, Edward Lorenz developed a simplified mathematical model for atmospheric convection. The model is a system of three ordinary differential equations now known as the Lorenz equations:

Here , , and make up the system state, is time, and , , are the system parameters. The Lorenz equations also arise in simplified models for lasers,dynamos,thermosyphons, brushless DC motors,electric circuits,chemical reactions and forward osmosis.

From a technical standpoint, the Lorenz system is nonlinear, three-dimensional and deterministic. The Lorenz equations have been the subject of hundreds of research articles, and at least one book-length study.

Animal Kingdom

Animal Kingdom may refer to:

In performing arts: