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Between order and chaos

A Corrigendum to this article was published on 03 June 2013

This article has been updated


What is a pattern? How do we come to recognize patterns never seen before? Quantifying the notion of pattern and formalizing the process of pattern discovery go right to the heart of physical science. Over the past few decades physics’ view of nature’s lack of structure—its unpredictability—underwent a major renovation with the discovery of deterministic chaos, overthrowing two centuries of Laplace’s strict determinism in classical physics. Behind the veil of apparent randomness, though, many processes are highly ordered, following simple rules. Tools adapted from the theories of information and computation have brought physical science to the brink of automatically discovering hidden patterns and quantifying their structural complexity.

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Figure 1: ε-machines for four information sources.

© 1994 Elsevier

Figure 2: Structure versus randomness.
Figure 3: Complexity–entropy diagrams.

Change history

  • 17 May 2013

    In the version of this Review Article originally published online there were several errors. In the section entitled 'Complicated yes, but is it complex?', seventh paragraph, the subscripts should appear as follows: past X:t; future Xt:; and blocks Xt:t'. All instances of x:l should appear as x0:l. In the section entitled 'Applications', in the third and seventh paragraphs, x: should appear as x0:. In the caption of Fig. 1d, the distributions should be listed as Pr(A, B, C, D), and panel d should have been attributed to ref. 45. These errors have now been corrected in the PDF and HTML versions of the Review Article.


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I thank the Santa Fe Institute and the Redwood Center for Theoretical Neuroscience, University of California Berkeley, for their hospitality during a sabbatical visit.

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Correspondence to James P. Crutchfield.

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Crutchfield, J. Between order and chaos. Nature Phys 8, 17–24 (2012).

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