A strange attractor is a semi-stable pattern with no fixed location that appears randomly in chaotic systems. It involves non-integer dimensional values and can predict features of a model without assigning a specific location. It can result in almost infinite complex trajectories and ornate patterns.
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 involves the formation of semi-stable patterns with no fixed spatial location. An equation that includes a strange attractor must incorporate non-integer dimensional values, resulting in a pattern of trajectories that appear 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 dynamical system that increases the probability of other components approaching a specific field or point as they approach a certain distance from the attractor. After passing within a certain distance of the attractor, these components will adopt a stable configuration and resist small disturbances in the system. For example, the lowest point of a pendulum’s arc is a simple attractor. A spatial model of the phases of a pendulum plots a series of points that grow closer to the lowest point each time their trajectory passes them, until they cluster around the lowest point in a stable configuration. Minor disturbances to the system, such as a bumped table, will not disturb this stability much.
A strange attractor is special in that it can predict certain features of a chaotic model in great detail without being able to assign a specific spatial location to the model. A simple example in nature is convection currents in a closed 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 with great precision the general behavior and the magnitude of the convection currents inside the gas. The chaotic nature of the turbulence equations, however, causes currents to appear randomly within the gas. The exact location of any future convection current is theoretically impossible to predict in such a system.
Patterns can become even more exotic in the case of theoretical models involving 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 give rise to ornate and otherworldly patterns. Such equations, when computer mapped onto a three-dimensional manifold, are sometimes valued as objects of beauty in their own right.
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