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'''Chaos 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.


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== Introduction ==
 
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 [[computer]]s 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]] 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 ==
 
As an example of how chaotic morphing works, lets take a generic chaotic system known as the [[Logistic map]]. This nonlinear map is very well studied for its chaotic behavior and its functional representation is given by:
 
:<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. Since the system is chaotic, we can then switch between various gates ("patterns") 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]].<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}}</ref>
 
A Chaotic computer, made up of a lattice of ChaoGates, has been demonstrated by Chaologix Inc.
 
==Research==
 
Recent research has shown how chaotic computers can be recruited in Fault Tolerant applications, by introduction of dynamic based fault detection methods.<ref>"Fault tolerance and detection in chaotic Computers" M.R. Jahed-Motlagh, B. Kia, W.L. Ditto and S. Sinha, International Journal of Bifurcation and Chaos 17, 1955-1968(2007)</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">"Chaos-based computation via Chua's circuit: parallel computing with application to the SR flip-flop"D. Cafagna, G. Grassi, International Symposium on Signals, Circuits and Systems, ISSCS 2005, Volume: 2, 749-752 (2005)</ref><ref>
"Parallel computing with extended dynamical systems" S. Sinha, T. Munakata and W.L. Ditto
Physical Review E, 65 036214 [1-7](2002)</ref> and as an example, this parallel architecture can lead to constructing an 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>"Reconfigurable logic blocks Based on a chaotic Chua circuit," H. R. Pourshaghaghi, B. Kia, W. Ditto and M. R. Jahed-Motlagh, to be published in CHAOS, SOLITONS & FRACTALS</ref>
 
== References ==
 
<references/>
 
"The 10 Coolest Technologies You’ve Never Heard Of – Chaos Computing," PC Magazine, Vol. 25, No. 13, page p.&nbsp;66, August 8, 2006.
[http://www.pcmag.com/article2/0,2704,1990288,00.asp]
 
"Logic from Chaos," MIT Technology Review, June 15, 2006.
[http://www.technologyreview.com/Biztech/16989/]
 
"Method and apparatus for a chaotic computing module," W. Ditto, S. Sinha and K. Murali, US Patent Number 07096347 (August 22, 2006).[http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO2&Sect2=HITOFF&p=1&u=%2Fnetahtml%2FPTO%2Fsearch-bool.html&r=2&f=G&l=50&co1=AND&d=PTXT&s1=ditto.INNM.&OS=IN/ditto&RS=IN/ditto]
 
http://www.chaologix.com/
 
"Exploiting the controlled responses of chaotic elements to design configurable hardware," W. L. Ditto and S. Sinha, Philosophical Transactions of the Royal Society London A, 364, pp.&nbsp;2483–2494 (2006) {{doi|10.1098/rsta.2006.1836}}.
 
"Chaos Computing: ideas and implementations" William L. Ditto, K. Murali and S. Sinha, Philosophical Transactions of the Royal Society London A, (2007) {{doi|10.1098/rsta.2007.2116}}.
 
"Experimental realization of the fundamental NOR Gate using a chaotic circuit," K. Murali, Sudeshna Sinha and William L. Ditto Phys. Rev. E 68, 016205 (2003).
 
"Implementation of NOR gate by a chaotic Chua’s circuit," K. Murali, Sudeshna Sinha and William L. Ditto, Int. J. of Bifurcation and Chaos, Vol. 13, No. 9, pp.&nbsp;1–4, (2003).
 
"Fault tolerance and detection in chaotic Computers" M.R. Jahed-Motlagh, B. Kia, W.L. Ditto and S. Sinha, International Journal of Bifurcation and Chaos 17, 1955-1968(2007)
 
"Chaos-based computation via Chua's circuit: parallel computing with application to the SR flip-flop"D. Cafagna, G. Grassi, International Symposium on Signals, Circuits and Systems, ISSCS 2005, Volume: 2, 749-752 (2005)
 
"Parallel computing with extended dynamical systems" S. Sinha, T. Munakata and W.L. Ditto
Physical Review E, 65 036214 [1-7](2002)
 
"Reconfigurable logic blocks Based on a chaotic Chua circuit," H. R. Pourshaghaghi, B. Kia, W. Ditto and M. R. Jahed-Motlagh, to be published in CHAOS, SOLITONS & FRACTALS
 
{{DEFAULTSORT:Chaos Computing}}
[[Category:Classes of computers]]

Latest revision as of 06:32, 21 April 2013

Template:Multiple issues

Chaos computing is the idea of using 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

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 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, OR, NOT, NAND, NOR, XOR and XNOR.

A chaotic morphing logic gate consists of a generic 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 Morphing

As an example of how chaotic morphing works, lets take a generic chaotic system known as the Logistic map. This nonlinear map is very well studied for its chaotic behavior and its functional representation is given by:

xn+1=rxn(1xn)

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There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

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If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

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A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

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There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

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Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer.*,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. Since the system is chaotic, we can then switch between various gates ("patterns") exponentially fast.

ChaoGate

File:Ditto Chaos Computing Example 1.jpg

The ChaoGate is an implementation of a chaotic morphing logic gate developed by the inventor of the technology William Ditto.[1]

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

Research

Recent research has shown how chaotic computers can be recruited in Fault Tolerant applications, by introduction of dynamic based fault detection methods.[2] Also it has been demonstrated that multidimensional dynamical states available in a single ChaoGate can be exploited to implement parallel chaos computing,[3][4] and as an example, this parallel architecture can lead to constructing an SR like memory element through one ChaoGate.[3] As another example, it has been proved that any logic function can be constructed directly from just one ChaoGate.[5]

References

  1. Template:Cite web
  2. "Fault tolerance and detection in chaotic Computers" M.R. Jahed-Motlagh, B. Kia, W.L. Ditto and S. Sinha, International Journal of Bifurcation and Chaos 17, 1955-1968(2007)
  3. 3.0 3.1 "Chaos-based computation via Chua's circuit: parallel computing with application to the SR flip-flop"D. Cafagna, G. Grassi, International Symposium on Signals, Circuits and Systems, ISSCS 2005, Volume: 2, 749-752 (2005)
  4. "Parallel computing with extended dynamical systems" S. Sinha, T. Munakata and W.L. Ditto Physical Review E, 65 036214 [1-7](2002)
  5. "Reconfigurable logic blocks Based on a chaotic Chua circuit," H. R. Pourshaghaghi, B. Kia, W. Ditto and M. R. Jahed-Motlagh, to be published in CHAOS, SOLITONS & FRACTALS

"The 10 Coolest Technologies You’ve Never Heard Of – Chaos Computing," PC Magazine, Vol. 25, No. 13, page p. 66, August 8, 2006. [1]

"Logic from Chaos," MIT Technology Review, June 15, 2006. [2]

"Method and apparatus for a chaotic computing module," W. Ditto, S. Sinha and K. Murali, US Patent Number 07096347 (August 22, 2006).[3]

http://www.chaologix.com/

"Exploiting the controlled responses of chaotic elements to design configurable hardware," W. L. Ditto and S. Sinha, Philosophical Transactions of the Royal Society London A, 364, pp. 2483–2494 (2006) 21 year-old Glazier James Grippo from Edam, enjoys hang gliding, industrial property developers in singapore developers in singapore and camping. Finds the entire world an motivating place we have spent 4 months at Alejandro de Humboldt National Park..

"Chaos Computing: ideas and implementations" William L. Ditto, K. Murali and S. Sinha, Philosophical Transactions of the Royal Society London A, (2007) 21 year-old Glazier James Grippo from Edam, enjoys hang gliding, industrial property developers in singapore developers in singapore and camping. Finds the entire world an motivating place we have spent 4 months at Alejandro de Humboldt National Park..

"Experimental realization of the fundamental NOR Gate using a chaotic circuit," K. Murali, Sudeshna Sinha and William L. Ditto Phys. Rev. E 68, 016205 (2003).

"Implementation of NOR gate by a chaotic Chua’s circuit," K. Murali, Sudeshna Sinha and William L. Ditto, Int. J. of Bifurcation and Chaos, Vol. 13, No. 9, pp. 1–4, (2003).

"Fault tolerance and detection in chaotic Computers" M.R. Jahed-Motlagh, B. Kia, W.L. Ditto and S. Sinha, International Journal of Bifurcation and Chaos 17, 1955-1968(2007)

"Chaos-based computation via Chua's circuit: parallel computing with application to the SR flip-flop"D. Cafagna, G. Grassi, International Symposium on Signals, Circuits and Systems, ISSCS 2005, Volume: 2, 749-752 (2005)

"Parallel computing with extended dynamical systems" S. Sinha, T. Munakata and W.L. Ditto Physical Review E, 65 036214 [1-7](2002)

"Reconfigurable logic blocks Based on a chaotic Chua circuit," H. R. Pourshaghaghi, B. Kia, W. Ditto and M. R. Jahed-Motlagh, to be published in CHAOS, SOLITONS & FRACTALS