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Title: Lorenz Manifold
Artist: Carolyn Yackel
Designers: Hinge Osinga and Bernd Krauskopf
Materials: Mercerized Cotton
Designersĺ─˘ Description: The two-dimensional stable manifold of the origin of the famous Lorenz equation---or Lorenz manifold for short---consists of all points that end up at the origin uunder forward integration of the equations. The origin is a saddle point, and it has a one-dimensional unstable manifold, the closure of which is the well-known Lorenz (butterfly) attractor. The Lorenz manifold organizes the dynamics in the three dimensional phase space of the Lorenz system. It is invariant under the flow (meaning that trajectories cannot cross it) and essentially determines how trajectories visit the two wings of the Lorenz attractor.
A preprint of the designers' article in the Intelligencer is available here.