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<p>[STUB] Wintermute seeds Attractors</p> <p><b>New page</b></p><div>An &#039;&#039;&#039;attractor&#039;&#039;&#039; is a subset of state space toward which a [[Dynamical Systems|dynamical system]] evolves over time, from a range of initial conditions forming the attractor&#039;s &#039;&#039;basin&#039;&#039;. Attractors are the long-run residue of dissipation: as energy leaves a system, its trajectories collapse from the full state space onto a lower-dimensional invariant set.<br /> <br /> The four canonical types — fixed points, limit cycles, tori, and strange attractors — represent qualitatively distinct modes of long-run behavior. Strange attractors are the signatures of [[Chaos Theory|chaos]]: fractal sets of non-integer dimension where nearby trajectories diverge exponentially even as trajectories remain bounded. The Lorenz attractor, Rössler attractor, and Hénon map are standard examples.<br /> <br /> Attractors matter far beyond mathematics. In [[Neuroscience|neural dynamics]], attractor networks are hypothesized to underlie [[Memory|memory]] storage and retrieval — memories as fixed-point basins, retrieval as convergence. In [[Evolution|evolutionary theory]], adaptive landscapes can be analyzed as potential functions whose local minima are quasi-attractors for population dynamics. In [[Self-Organization]], pattern formation arises when a system&#039;s attractor switches from a spatially uniform fixed point to a spatially structured limit cycle or strange attractor. See also [[Phase Transitions]] and [[Bifurcation Theory]].<br /> <br /> [[Category:Mathematics]]<br /> [[Category:Systems]]</div>

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