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What Is a Strange Attractor?

Todd Podzemny
Todd Podzemny

A strange attractor is a concept in chaos theory that is used to describe the behavior of chaotic systems. Unlike a normal attractor, a strange attractor predicts the formation of semi-stable patterns that lack a fixed spatial position. An equation that includes a strange attractor must incorporate non-integer dimensional values, resulting in a pattern of trajectories that seem to appear randomly within the system. Strange attractors appear in both natural and theoretical diagrams of phase space models.

An attractor is a component in a dynamic system that increases the likelihood that other components will draw closer to a specific field or point when they approach within a certain distance of the attractor. After they have passed within a certain distance of the attractor, these components will adopt a stable configuration and resist minor disturbances in the system. For example, the lowest point in the arc of a pendulum is a simple attractor. A phase space model of a pendulum will chart a series of points growing closer to the low point each time their trajectory takes them past it, until they cluster around the low point in a stable configuration. Minor disturbances to the system, such as a jostled table, will not greatly disturb this stability.

Woman holding a book
Woman holding a book

A strange attractor is special in that it can predict certain characteristics of a chaotic pattern in great detail without being able to assign a specific spatial location to the pattern. A simple example in nature is the convection currents in an enclosed box filled with a gas and placed over a uniform heating element. The initial state of the system can be described by a few simple equations, which can predict the general behavior and magnitude of the convection currents within the gas over time with great precision. The chaotic nature of turbulence equations, however, causes the currents to appear randomly within the gas. The exact location of any future convection current is theoretically impossible to predict in such a system.

The patterns can become even more exotic in the case of theoretical models that involve a fractal dimension. In these cases, the presence of a strange attractor results in a series of semi-random trajectories of almost infinite complexity. Mapping even a simple equation containing a fractal dimension can result in ornate and otherworldly patterns. Such equations, when computer mapped to a three-dimensional manifold, are sometimes valued as objects of beauty in their own right.

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