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Chaotic systems generate large numbers of patterns of behavior and are irregular because they switch between these patterns. They exhibit sensitivity to initial conditions which, in practice, means that chaotic systems can switch between patterns extremely fast.
Modern digital
A chaotic morphing logic gate consists of a generic [[Nonlinear system|nonlinear circuit]] that exhibits chaotic dynamics producing various patterns. A control mechanism is used to select patterns that correspond to different logic gates. The sensitivity to initial conditions is used to switch between different patterns extremely fast (well under a computer clock cycle).
== Chaotic
As an example of how chaotic morphing works, consider a generic chaotic system known as the [[
:<math>\qquad x_{n+1} = r x_n (1-x_n) </math>.
In this case, the value of {{math|''x''}} is chaotic when {{math|''r''}} >~ 3.57... and rapidly switches between different patterns in the value of {{math|''x''}} as one iterates the value of {{math|''n''}}. A simple threshold controller can control or direct the chaotic map or system to produce one of many patterns. The controller basically sets a threshold on the map such that if the iteration ("chaotic update") of the map takes on a value of {{math|''x''}} that lies above a given threshold value, {{math|''x''}}*,then the output corresponds to a 1, otherwise it corresponds to a 0. One can then reverse engineer the chaotic map to establish a lookup table of thresholds that robustly produce any of the logic gate operations.<ref>{{cite journal | last=Sinha | first=Sudeshna | last2=Ditto | first2=William | title=Dynamics Based Computation | journal=Physical Review Letters | publisher=American Physical Society (APS) | volume=81 | issue=10 | year=1998 | issn=0031-9007 | doi=10.1103/physrevlett.81.2156 | pages=2156–2159}}</ref><ref>{{cite journal | last=Sinha | first=Sudeshna | last2=Ditto | first2=William L. | title=Computing with distributed chaos | journal=Physical Review E | publisher=American Physical Society (APS) | volume=60 | issue=1 | date=1999-07-01 | issn=1063-651X | doi=10.1103/physreve.60.363 | pages=363–377}}</ref><ref>{{cite journal | last=Munakata | first=T. | last2=Sinha | first2=S. | last3=Ditto | first3=W.L. | title=Chaos computing: implementation of fundamental logical gates by chaotic elements | journal=IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications | publisher=Institute of Electrical and Electronics Engineers (IEEE) | volume=49 | issue=11 | year=2002 | issn=1057-7122 | doi=10.1109/tcsi.2002.804551 | pages=1629–1633}}</ref> Since the system is chaotic, we can then switch between various gates ("patterns") exponentially fast.
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The ''ChaoGate'' is an implementation of a chaotic morphing logic gate developed by the inventor of the technology William Ditto, along with [[Sudeshna Sinha]] and K. Murali.<ref>{{cite web | url=http://news.techeye.net/chips/scientists-use-chaos-theory-to-create-new-chip | title=Scientists use chaos theory to create new chip Chaogate holds exciting processing prospects | date=16 Nov 2010 | author=Matthew Finnegan | publisher=TechEYE.net | accessdate=October 15, 2012 | archive-url=https://web.archive.org/web/20140512225447/http://news.techeye.net/chips/scientists-use-chaos-theory-to-create-new-chip | archive-date=12 May 2014 | url-status=dead}}</ref><ref>"Method and apparatus for a chaotic computing module," W. Ditto, S. Sinha and K. Murali, US Patent Number 07096347 (August 22, 2006). {{US Patent|8,520,191}}</ref>
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==Research==
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