A Poincare recurrence occurs when the state of a volume-preserving flow map (e.g. 2-D image) returns to a close approximation of the initial condition after a period of time (usually very long). Theoretically, this is related to ergodic theory and the evolution of Hamiltonian systems [3]. As such, the dynamics of a Poincare recurrence can also be illustrated as a chaotic Poincare map (inset B, left) or a deterministic Baker’s map (inset B, right).
Next up, LinkedIn has a new feature that allows you to visualize your professional social network. It plots all of your first-order connections on the basis of shared connections and other attributes.
Now, similar techniques have been used to make the world’s first atomic-scale animated short film “A Boy and His Atom” [6]. A “Star Trek” logo is also possible [7].
[1] Google “Nick Cage vampire” for more information.
[2] Image/illustration is courtesy of the Max Planck institute for Complex Systems and Crutchfield, J. et.al Chaos. Scientific American, December (1986).
[3] it may also be the mechanism behind deja vu in “The Matrix” trilogy.
[4] Eigler, D.M. and Schweizer, E.K. Positioning single atoms with a scanning tunnelling microscope. Nature, 344, 524-526 (1990).
[5] Johnson, D. IBM Makes Smallest Movie Ever. IEEE Nanoclast Blog, May 1 (2013).
[6] Pachal, P. IBM Manipulates Atoms to Create the World’s Smallest Movie. Mashable, May 1 (2013).
IBM Research, “A Boy and His Atom”. YouTube, April 30 (2013).
[7] Kramer, M. IBM Warps Atoms into Crazy “Star Trek” Art. Space.com, May 3 (2013).
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