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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 | lastlast1=Sinha | firstfirst1=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 | lastlast1=Sinha | firstfirst1=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| pmid=11969770 }}</ref><ref>{{cite journal | lastlast1=Munakata | firstfirst1=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.
== ChaoGate ==
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==Research==
Recent research has shown how chaotic computers can be recruited in [[Fault tolerance|fault tolerant]] applications, by introduction of dynamic based fault detection methods.<ref>{{cite journal | lastlast1=Jahed-Motlagh | firstfirst1=Mohammad R. | last2=Kia | first2=Behnam | last3=Ditto | first3=William L. | last4=Sinha | first4=Sudeshna | title=Fault tolerance and detection in chaotic Computers | journal=International Journal of Bifurcation and Chaos | publisher=World Scientific Pub Co Pte Lt | volume=17 | issue=066 | year=2007 | issn=0218-1274 | doi=10.1142/s0218127407018142 | pages=1955–1968}}</ref> Also it has been demonstrated that multidimensional dynamical states available in a single ChaoGate can be exploited to implement parallel chaos computing,<ref name="Chua 2005">{{cite conference | lastlast1=Cafagna | firstfirst1=D. | last2=Grassi | first2=G. | title=Chaos-based computation via chua's circuit: parallel computing with application to the SR flip-flop |conference= International Symposium on Signals, Circuits and Systems|year=2005| publisher=IEEE | isbn=0-7803-9029-6 | doi=10.1109/isscs.2005.1511349 | volume=2|page=749-752}}</ref><ref>{{cite journal | lastlast1=Sinha | firstfirst1=Sudeshna | last2=Munakata | first2=Toshinori | last3=Ditto | first3=William L. | title=Parallel computing with extended dynamical systems | journal=Physical Review E | publisher=American Physical Society (APS) | volume=65 | issue=3 | date=2002-02-19 | issn=1063-651X | doi=10.1103/physreve.65.036214 | page=036214| pmid=11909219 }}</ref> and as an example, this parallel architecture can lead to constructing an [[SR flip-flop circuit|SR like memory element]] through one ChaoGate.<ref name="Chua 2005" /> As another example, it has been proved that any logic function can be constructed directly from just one ChaoGate.<ref>{{cite journal | lastlast1=Pourshaghaghi | firstfirst1=Hamid Reza | last2=Kia | first2=Behnam | last3=Ditto | first3=William | last4=Jahed-Motlagh | first4=Mohammad Reza | title=Reconfigurable logic blocks based on a chaotic Chua circuit | journal=Chaos, Solitons & Fractals | publisher=Elsevier BV | volume=41 | issue=1 | year=2009 | issn=0960-0779 | doi=10.1016/j.chaos.2007.11.030 | pages=233–244}}</ref>
Chaos allows order to be found in such diverse systems as the atmosphere, heart beating, fluids, seismology, metallurgy, physiology, or the behavior of a stock market.<ref>{{cite book |last1=Soucek |first1=Branko |title=Dynamic, Genetic, and Chaotic Programming: The Sixth-Generation Computer Technology Series |date=6 May 1992 |publisher=John Wiley & Sons, Inc |isbn=0-471-55717-X |page=11}}</ref>
