May 10, 2013

Celebrity Recurrence, Professional Graphs, and Nano-Self-Expression

This has been cross-posted to my micro-blog, Tumbld Thoughts:


First up, it’s time for internet memes to meet mathematical concepts. On the left is a conceptual piece I am calling “The Cage Recurrence”. This is based on the Nick Cage vampire urban legend [1]. The transformations in the image are based on the Poincare recurrence (inset A), originally developed by Henri Poincare [2].

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.


The network tends to cluster by workplace/community, but my network includes a lot of people that do not fall into any one category (as do most, I would imagine). InMaps uses programming tools such as Hadoop for handling large datasets and Processing for visualization. Fun!


Finally, here is a feature on nanoscale movies. In 1990, Don Eigler and other researchers at IBM [4] were able to assemble the letters “I-B-M” out of Xenon atoms using scanning tunneling microscopy (STM) [5].



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]. 


NOTES:

[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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