Frustration in Complexity

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Science  18 Apr 2008:
Vol. 320, Issue 5874, pp. 322-323
DOI: 10.1126/science.1156940

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  1. Three manifestations of dynamical frustration.

    (Top) Geometric frustration. In this schematic of the Lorenz attractor (a butterfly structure in three-dimensional phase space, corresponding to the long-term behavior of a chaotic flow), we can see the interplay between stretching (outward spirals) and folding (arrows directed toward the two fixed points). (Middle) Scale frustration. The global motion is generally counterclockwise, but parts of the system may rotate in the clockwise direction. (Bottom) Computational frustration. Through complex interactions between the infinite memory tape, the state transition rules of the computing head, the back-and-forth motion (arrows), and the machine rewriting on the memory tape, a Turing machine can perform extremely complex computations—or may never stop computing.