Chaos computing: Difference between revisions

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{{Short description|Computers using chaotic systems}}

In [[theoretical computer science]], '''Chaoschaos computing''' is the idea of using [[chaos theory|chaotic systems]] for [[computation]]. In particular, chaotic systems can be made to produce all types of [[logic gates]] and further allow them to be morphed into each other.

== Introduction ==

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Modern digital computers perform computations based upon digital logic operations implemented at the lowest level as [[logic gates]]. There are essentially seven basic logic functions implemented as logic gates: [[AND gate|AND]], [[OR gate|OR]], [[NOT gate|NOT]], [[NAND gate|NAND]], [[NOR gate|NOR]], [[XOR gate|XOR]] and [[XNOR gate|XNOR]].

A chaotic morphing logic gate consists of a generic [[Nonlinear system|nonlinear circuit]] 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 morphing ==

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:<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 | last1=Sinha | first1=Sudeshna |author2-link=William Ditto | 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| bibcode=1998PhRvL..81.2156S }}</ref><ref>{{cite journal | last1=Sinha | first1=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 | bibcode=1999PhRvE..60..363S }}</ref><ref>{{cite journal | last1=Munakata | first1=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") can be switch between exponentially fast.

== ChaoGate ==

[[File:Ditto Chaos Computing Example 1.jpg|thumb]]

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>

A chaotic computer, made up of a lattice of ChaoGates, has been demonstrated by Chaologix Inc.

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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 | last1=Jahed-Motlagh | first1=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=6 | year=2007 | issn=0218-1274 | doi=10.1142/s0218127407018142 | pages=1955–1968| bibcode=2007IJBC...17.1955J }}</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 | last1=Cafagna | first1=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|pagepages=749-752749–752}}</ref><ref>{{cite journal | last1=Sinha | first1=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 | bibcode=2002PhRvE..65c6214S }}</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 | last1=Pourshaghaghi | first1=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| bibcode=2009CSF....41..233P }}</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>

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== See also ==

* [[Chua's circuit]]

* [[Unconventional computing]]

== References ==