https://en.wikipedia.org/wiki/Attractor
Visual representation of a strange attractor. Another visualization of the same 3D attractor is this video.Code capable of rendering this is available.. In the mathematical field of dynamical systems, an attractor is a set of states 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

https://ocw.mit.edu/courses/12-006j-nonlinear-dynamics-chaos-fall-2022/mit12_006jf22_lec19.pdf
Learn about the properties and examples of strange attractors, which are aperiodic, fractal, and chaotic sets of points in phase space. See how dissipation, stretching, and folding create the sensitivity to initial conditions and the non-integer dimension of strange attractors.

https://hypertextbook.com/chaos/strange/
Strange attractors are complex structures that emerge from iterated mappings of multiple-dimensional spaces. Learn how they are formed, how they differ from fixed points and cycles, and how they can be explored with fractal and chaotic flows.

https://www.dynamicmath.xyz/strange-attractors/
Learn about strange attractors, regions or shapes that display sensitive dependence on initial conditions, and explore various systems of equations that generate them. Click on the images to see the Lorenz attractor, the Langford attractor, the Rössler attractor and more.

https://www.stsci.edu/~lbradley/seminar/attractors.html
Learn about strange attractors, the complex and unpredictable patterns that arise from simple nonlinear equations. See examples of Lorenz, Rössler and Hénon attractors and how they differ from periodic orbits.

https://mathworld.wolfram.com/StrangeAttractor.html
An attracting set that has zero measure in the embedding phase space and has fractal dimension. Trajectories within a strange attractor appear to skip around randomly. A selection of strange attractors for a general quadratic map. are illustrated above, where the letters to stand for coefficients of the quadratic from to 1.2 in steps of 0.1

https://sprott.physics.wisc.edu/fractals/booktext/SABOOK.HTM
Nearly all strange attractors are fractals but not all fractals arise from strange attractors. The Hénon map produces an object with a fractal dimension that is a fraction intermediate between one and two.

https://dspace.mit.edu/bitstream/handle/1721.1/84612/12-006j-fall-2006/contents/lecture-notes/lecnotes10.pdf
Learn how strange attractors are formed by dissipation, stretching and folding of phase space trajectories. See examples of the Rössler and Lorenz attractors and their properties.

https://www.ams.org/notices/200607/what-is-ruelle.pdf
The strange attractor A is visualized when a computer plots the points xn = fnx0 with almost any initial value x0 in U. The figures show. two-dimensional example corresponding to the Hénon attractor, and a three-dimensional example corresponding to Smale's solenoid. It turns out that. small change in the values of a and b can destroy the

https://www.sciencedirect.com/topics/engineering/strange-attractor
An interesting example of this is the so-called strange attractor. Strange attractors arise in the study of nonlinear dynamics and chaotic systems. In these systems, the usual types of dynamic motion—equilibrium, periodic motion, and quasi-periodic motion—are not present. Instead, the system exhibits chaotic motion.

https://sprott.physics.wisc.edu/SA.HTM
My book, Strange Attractors: Creating Patterns in Chaos (ISBN 1-55851-298-5), describes a simple method for generating an endless succession of beautiful fractal patterns by iterating simple maps and ordinary differential equations with coefficients chosen automatically by the computer. It contains over 350 examples of such patterns.

https://annex.exploratorium.edu/complexity/lexicon/strange.html
A Strange Attractor is a geometrical shape in phase space that represents the limited region of phase space ultimately occupied by all trajectories of a dynamical system . Strange Attractors have a orderly appearance. Their limited extent implies that the system is not simply exhibiting random behavior.

https://uwaterloo.ca/applied-mathematics/future-undergraduates/what-you-can-learn-applied-mathematics/dynamical-systems/strange-attractors
Learn what strange attractors are and how they arise from nonlinear dynamical systems. See examples of strange attractors, such as the Lorenz attractor, and their physical interpretation.

https://encyclopediaofmath.org/wiki/Strange_attractor
The expression "complicated structure" is rather indefinite, as is the term "strange attractor". For smooth dynamical systems two types of strange attractors which are preserved by small perturbations have been theoretically studied — attractors which are hyperbolic sets (cf. Hyperbolic set ), and the Lorenz attractor , which gave rise to the

https://www.exploratorium.edu/snacks/strange-attractor
Strange Attractor. The attraction and repulsion of magnets produces entrancing, unpredictable motion. Patterns of order can be found in apparently disordered systems. This pendulum—a magnet swinging over a small number of fixed magnets—is a very simple system that shows chaotic motion for some starting positions of the pendulum. The search

https://science.howstuffworks.com/math-concepts/chaos-theory4.htm
An attractor describes a state to which a dynamical system evolves after a long enough time. Systems that never reach this equilibrium, such as Lorenz's butterfly wings, are known as strange attractors. Additional strange attractors, corresponding to other equation sets that give rise to chaotic systems, have since been discovered.

https://www.cambridge.org/core/books/dynamical-systems-and-fractals/strange-attractors/9B3FB12D23D625A9EFCA45BE4B3B4746
The Strange Attractor. Because of its aesthetic qualities, the Feigenbaum diagram has acquired the nature of a symbol. Out of allegedly dry mathematics, a fundamental form arises. It describes the connection between two concepts, which have hitherto seemed quite distinct: order and chaos, differing from each other only by the values of a

https://www.marksmath.org/visualization/LorenzExperiment/
The Lorenz attractor. The Lorenz attractor is a strange attractor living in 3D space that relates three parameters arising in fluid dynamics. It is one of the Chaos theory's most iconic images and illustrates the phenomenon now known as the Butterfly effect or (more technically) sensitive dependence on initial conditions.

https://fractalfoundation.org/OFC/OFC-7-1.html
The basic concept of a simple attractor is that it is the solution or pattern of behavior that a system reaches. It is a way of visualizing the outcome of a system for any given starting values. To give a simple example, imagine a pendulum. If you pull it off to the side (the starting condition) and release it, the pendulum will swing back and

https://annex.exploratorium.edu/complexity/CompLexicon/strange.html
A chaotic attractor is a set of states in a system's state space with very special properties. First of all, the set is an attracting set. So that the system, starting with its initial condition in the appropriate basin, eventually ends up in the set. Even if the system is perturbed off the attractor, it eventually returns. Second, and most

https://en.wikipedia.org/wiki/Chaos_theory
Strange attractors occur in both continuous dynamical systems (such as the Lorenz system) and in some discrete systems (such as the Hénon map). Other discrete dynamical systems have a repelling structure called a Julia set, which forms at the boundary between basins of attraction of fixed points. Julia sets can be thought of as strange repellers.

https://www.chaos-math.org/en/chaos-vii-strange-attractors.html
A strange attractor! Understanding the Lorenz attractor is quite a task! How do the internal dynamics behave? Birman, Guckenheimer et Williams proposed a model in the 1970's that one can construct with nothing more than a strip of paper. With this simple model we can look at the dynamics in discrete time.

https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Graduate_Classical_Mechanics_(Fowler)/23%3A_Damped_Driven_Pendulum-_Period_Doubling_and_Chaos/23.03%3A_Lyapunov_Exponents_and_Dimensions_of_Strange_Attractors
In 1979, Kaplan and Yorke conjectured that the dimensionality of the strange attractor followed from the Lyapunov exponents taking part in its creation. In our case—the driven damped pendulum—there are only two relevant exponents, λ1 > 0 λ 1 > 0 , λ2 < 0 λ 2 < 0 and λ1 +λ2 = −2β λ 1 + λ 2 = − 2 β. A plausibility argument is

https://www.merriam-webster.com/dictionary/strange%20attractor
A strange attractor is a pattern of order in a chaotic system that seems to attract the system toward it. Learn more about this mathematical concept, its history, and how to use it in a sentence.