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[[Image:Langtons Loop.png|frame|right|Langton's Loop, in the starting configuration.]]
 
'''Langton's loops''' are a particular "species" of [[artificial life]] in a [[cellular automaton]] created in 1984 by [[Christopher Langton]]. They consist of a loop of cells containing genetic information, which flows continuously around the loop and out along an "arm" (or [[pseudopod]]), which will become the daughter loop. The "genes" instruct it to make three left turns, completing the loop, which then disconnects from its parent.
 
== History ==
 
In 1952 [[John von Neumann]] created the first cellular automaton (CA) with the goal of creating a self-replicating machine.<ref name=TSRA>{{cite web| url=http://www.walenz.org/vonNeumann/index.html| title=''Theory of Self-Reproducing Automata.''| author=von Neumann, John| coauthors=Burks, Arthur W.| date=1966| publisher=www.walenz.org| format=Scanned book online| accessdate=2008-02-29 |archiveurl = http://web.archive.org/web/20080105213853/http://www.walenz.org/vonNeumann/index.html <!-- Bot retrieved archive --> |archivedate = 2008-01-05}}</ref> This automaton was necessarily very complex due to its computation- and construction-universality. In 1968 [[Edgar F. Codd]] reduced the number of states from 29 in [[von Neumann cellular automaton|von Neumann's CA]] to 8 in [[Codd's cellular automaton|his]].<ref name=Codd68>{{cite book|author = Codd, Edgar F.|title="Cellular Automata"|publisher=Academic Press, New York|year=1968}}</ref> When Christopher Langton did away with the universality condition, he was able to significantly reduce the automaton's complexity. Its self-replicating loops are based on one of the simplest elements in Codd's automaton, the periodic emitter.
 
== Specification ==
 
Langton's Loops run in a CA that has 8 states, and uses the [[von Neumann neighborhood]] with rotational symmetry. The [[State transition table|transition table]] can be found here: [http://code.google.com/p/ruletablerepository/wiki/TheRules#Self-replicating_loops].
 
As with [[Codd's cellular automaton|Codd's CA]], Langton's Loops consist of sheathed wires. The signals travel passively along the wires until they reach the open ends, when the command they carry is executed.
 
[[Image:Langtons Loop Colony.png|thumb|right|A colony of loops. The ones in the centre are "dead".]]
 
=== Colonies ===
 
Because of a particular property of the loops' "pseudopodia", they are unable to reproduce into the space occupied by another loop. Thus, once a loop is surrounded, it is incapable of reproducing, resulting in a [[coral]]-like colony with a thin layer of reproducing organisms surrounding a core of inactive "dead" organisms. Unless provided unbounded space, the colony's size will be limited. The maximum population will be [[asymptote|asymptotic]] to <math>\left \lfloor \frac{A}{121} \right \rfloor</math>, where ''A'' is the total area of the space in cells.
 
=== Encoding of the genome ===
 
The loops' genetic code is stored as a series of nonzero-zero state pairs. The standard loop's genome is illustrated in the picture at the top, and may be stated as a series of numbered states starting from the T-junction and running clockwise: 70-70-70-70-70-70-40-40. The '70' command advances the end of the wire by one cell, while the '40-40' sequence causes the left turn. State 3 is used as a temporary marker for several stages.
 
While the roles of states 0,1,2,3,4 and 7 are similar to Codd's CA, the remaining states 5 and 6 are used instead to mediate the loop replication process. After the loop has completed, state 5 travels counter-clockwise along the sheath of the parent loop to the next corner, causing the next arm to be produced in a different direction.  State 6 temporarily joins the genome of the daughter loop and initialises the growing arm at the next corner it reaches.
 
The genome is used a total of six times: once to extend the pseudopod to the desired location, four times to complete the loop, and again to [[DNA replication|transfer]] the genome into the daughter loop. Clearly, this is dependent on the fourfold [[rotational symmetry]] of the loop; without it, the loop would be incapable of containing the information required to describe it. The same use of symmetry for genome compression is used in many biological [[viruses]], such as the [[icosahedral symmetry|icosahedral]] [[adenovirus]].
 
== Comparison of related CA loops ==
 
{| class="wikitable" style="text-align:center"
|-
! CA !! number of states !! [[Neighbourhood (graph theory)|neighborhood]] !! number of cells (typical) !! replication period (typical) !! thumbnail
|-
| '''Langton's loops'''<ref name=Langton1984>{{cite journal|author=C. G. Langton|title=Self-reproduction in cellular automata|journal=Physica D|volume=10|pages=135–144|year=1984|doi=10.1016/0167-2789(84)90256-2}}</ref> (1984): The original self-reproducing loop.  || 8 || von Neumann || 86 || 151 || [[Image:Langtons Loop.png|none|100x100px]]
|-
| '''[[Byl's loop]]'''<ref name=Byl1989>{{cite journal|author=J. Byl|title=Self-Reproduction in small cellular automata|journal=Physica D|volume=34|pages=295–299|year=1989|doi=10.1016/0167-2789(89)90242-X}}</ref> (1989): By removing the inner sheath, Byl reduced the size of the loop. || 6 || von Neumann || 12 || 25 || [[Image:Byl Loop.png|none|100x100px]]
|-
| '''Chou-Reggia loop'''<ref name=Reggia1993>{{cite journal |url=http://www.sciencemag.org/content/259/5099/1282.short|author=J. A. Reggia, S. L. Armentrout, H.-H. Chou, and Y. Peng|title=Simple systems that exhibit self-directed replication|journal=Science|volume=259|pages=1282–1287|year=1993|doi=10.1126/science.259.5099.1282|pmid=17732248|issue=5099}}</ref> (1993): A further reduction of the loop by removing all sheaths. || 8 || von Neumann || 5 || 15 ||[[Image:Chou-Reggia Loop.png|none|100x100px]]
|-
| '''Tempesti loop'''<ref name=Tempesti1995>{{cite conference|url=http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.48.7578|author=G. Tempesti|title=A New Self-Reproducing Cellular Automaton Capable of Construction and Computation|booktitle=Advances in Artificial Life, Proc. 3rd European Conference on Artificial Life|location=Granada, Spain|year=1995|publisher=Lecture Notes in Artificial Intelligence, 929, Springer Verlag, Berlin|pages=555–563}}</ref> (1995): Tempesti added construction capabilities to his loop, allowing patterns to be written inside the loop after reproduction. || 10 || Moore || 148 || 304 || [[Image:Tempesti Loop.png|none|100x100px]]
|-
| '''Perrier loop'''<ref name=Perrier1996>{{cite journal|author=J.-Y. Perrier, M. Sipper, and J. Zahnd|title=Toward a viable, self-reproducing universal computer|journal=Physica D|volume=97|pages=335–352|year=1996|url=http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.21.3200|doi=10.1016/0167-2789(96)00091-7}}</ref> (1996): Perrier added a program stack and an extensible data tape to Langton's loop, allowing it to compute anything [[Computable function|computable]]. || 64 || von Neumann || 158 || 235 || [[Image:Perrier Loop.png|none|100x100px]]
|-
| '''SDSR loop'''<ref name=Sayama1998>{{cite conference|author=Hiroki Sayama|title=Introduction of Structural Dissolution into Langton's Self-Reproducing Loop|booktitle=Artificial Life VI: Proceedings of the Sixth International Conference on Artificial Life|pages=114–122|location=Los Angeles, California|year=1998|publisher=MIT Press}}</ref> (1998): With an extra structure-dissolving state added to Langton's loops, the SDSR loop has a limited lifetime and dissolves at the end of its life cycle. This allows continuous growth and turn-over of generations. || 9 || von Neumann || 86 || 151 || [[Image:SDSR Loop.png|none|100x100px]]
|-
| '''Evoloop'''<ref name=Sayama1999>{{cite conference|author=Hiroki Sayama|title=Toward the Realization of an Evolving Ecosystem on Cellular Automata|booktitle=Proceedings of the Fourth International Symposium on Artificial Life and Robotics (AROB 4th '99)|pages=254–257|location=Beppu, Oita, Japan|year=1999|url=http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.40.391}}</ref> (1999): An extension of the SDSR loop, Evoloop is capable of interaction with neighboring loops as well as of [[evolution]]. Often, the greatest selection pressure in a colony of Evoloops is the competition for space, and [[natural selection]] favors the smallest functional loop present. Further studies demonstrated more complexity than originally thought in the Evoloop system.<ref name=Salzberg2004>{{cite journal|author=Chris Salzberg and Hiroki Sayama|title=Complex genetic evolution of artificial self-replicators in cellular automata|journal=Complexity|volume=10|pages=33–39|year=2004|url=http://www3.interscience.wiley.com/journal/109860047/abstract|doi=10.1002/cplx.20060}}</ref> || 9 || von Neumann || 149 || 363 || [[Image:Evoloop closeup.png|none|100x100px]]
|-
| '''Sexyloop'''<ref name=Oros2007>{{cite conference|author=Nicolas Oros and C. L. Nehaniv|title=Sexyloop: Self-Reproduction, Evolution and Sex in Cellular Automata|booktitle=The First IEEE Symposium on Artificial Life (April 1-5, 2007, Hawaii, USA)|pages=130–138|year=2007|url=http://hdl.handle.net/2299/6711}}</ref> (2007): Sexyloop is a modification of Evoloop in which collisions often result in transfer of genetic material between loops. This increases diversity in evolution of new species of loops. || 10 || von Neumann || ? || ? ||
|}
 
== References ==
 
<references/>
 
== See also ==
 
* [[Artificial life]]
* [[Cellular automaton]]
* [[Christopher Langton]]
* [[Codd's cellular automaton]]
* [[Conway's game of life]]
* [[Langton's ant]]
* [[von Neumann cellular automaton]]
 
== External links ==
{{commonscat|Self-replicating loops}}
* [http://www.youtube.com/watch?v=2iDc4C6vbcc Video] of Chris Langton demonstrating self reproducing loops.
* [http://necsi.edu/postdocs/sayama/sdsr/java/ visual representation] of several of the self-replicating loops in a [[Java applet]]
* The [http://code.google.com/p/ruletablerepository/ Rule Table Repository] has the transition tables for many of the CA mentioned above.
* [http://golly.sourceforge.net Golly] - supports Langton's Loops along with the [[Conway's Game of Life|Game of Life]], and other rulesets.
 
{{DEFAULTSORT:Langton's Loops}}
[[Category:Artificial life]]
[[Category:Cellular automaton rules]]

Revision as of 11:14, 11 April 2013

Langton's Loop, in the starting configuration.

Langton's loops are a particular "species" of artificial life in a cellular automaton created in 1984 by Christopher Langton. They consist of a loop of cells containing genetic information, which flows continuously around the loop and out along an "arm" (or pseudopod), which will become the daughter loop. The "genes" instruct it to make three left turns, completing the loop, which then disconnects from its parent.

History

In 1952 John von Neumann created the first cellular automaton (CA) with the goal of creating a self-replicating machine.[1] This automaton was necessarily very complex due to its computation- and construction-universality. In 1968 Edgar F. Codd reduced the number of states from 29 in von Neumann's CA to 8 in his.[2] When Christopher Langton did away with the universality condition, he was able to significantly reduce the automaton's complexity. Its self-replicating loops are based on one of the simplest elements in Codd's automaton, the periodic emitter.

Specification

Langton's Loops run in a CA that has 8 states, and uses the von Neumann neighborhood with rotational symmetry. The transition table can be found here: [1].

As with Codd's CA, Langton's Loops consist of sheathed wires. The signals travel passively along the wires until they reach the open ends, when the command they carry is executed.

A colony of loops. The ones in the centre are "dead".

Colonies

Because of a particular property of the loops' "pseudopodia", they are unable to reproduce into the space occupied by another loop. Thus, once a loop is surrounded, it is incapable of reproducing, resulting in a coral-like colony with a thin layer of reproducing organisms surrounding a core of inactive "dead" organisms. Unless provided unbounded space, the colony's size will be limited. The maximum population will be asymptotic to , where A is the total area of the space in cells.

Encoding of the genome

The loops' genetic code is stored as a series of nonzero-zero state pairs. The standard loop's genome is illustrated in the picture at the top, and may be stated as a series of numbered states starting from the T-junction and running clockwise: 70-70-70-70-70-70-40-40. The '70' command advances the end of the wire by one cell, while the '40-40' sequence causes the left turn. State 3 is used as a temporary marker for several stages.

While the roles of states 0,1,2,3,4 and 7 are similar to Codd's CA, the remaining states 5 and 6 are used instead to mediate the loop replication process. After the loop has completed, state 5 travels counter-clockwise along the sheath of the parent loop to the next corner, causing the next arm to be produced in a different direction. State 6 temporarily joins the genome of the daughter loop and initialises the growing arm at the next corner it reaches.

The genome is used a total of six times: once to extend the pseudopod to the desired location, four times to complete the loop, and again to transfer the genome into the daughter loop. Clearly, this is dependent on the fourfold rotational symmetry of the loop; without it, the loop would be incapable of containing the information required to describe it. The same use of symmetry for genome compression is used in many biological viruses, such as the icosahedral adenovirus.

Comparison of related CA loops

CA number of states neighborhood number of cells (typical) replication period (typical) thumbnail
Langton's loops[3] (1984): The original self-reproducing loop. 8 von Neumann 86 151
Byl's loop[4] (1989): By removing the inner sheath, Byl reduced the size of the loop. 6 von Neumann 12 25
Chou-Reggia loop[5] (1993): A further reduction of the loop by removing all sheaths. 8 von Neumann 5 15
Tempesti loop[6] (1995): Tempesti added construction capabilities to his loop, allowing patterns to be written inside the loop after reproduction. 10 Moore 148 304
Perrier loop[7] (1996): Perrier added a program stack and an extensible data tape to Langton's loop, allowing it to compute anything computable. 64 von Neumann 158 235
SDSR loop[8] (1998): With an extra structure-dissolving state added to Langton's loops, the SDSR loop has a limited lifetime and dissolves at the end of its life cycle. This allows continuous growth and turn-over of generations. 9 von Neumann 86 151
Evoloop[9] (1999): An extension of the SDSR loop, Evoloop is capable of interaction with neighboring loops as well as of evolution. Often, the greatest selection pressure in a colony of Evoloops is the competition for space, and natural selection favors the smallest functional loop present. Further studies demonstrated more complexity than originally thought in the Evoloop system.[10] 9 von Neumann 149 363
Sexyloop[11] (2007): Sexyloop is a modification of Evoloop in which collisions often result in transfer of genetic material between loops. This increases diversity in evolution of new species of loops. 10 von Neumann ? ?

References

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    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  8. ↑ 55 years old Systems Administrator Antony from Clarence Creek, really loves learning, PC Software and aerobics. Likes to travel and was inspired after making a journey to Historic Ensemble of the Potala Palace.

    You can view that web-site... ccleaner free download
  9. ↑ 55 years old Systems Administrator Antony from Clarence Creek, really loves learning, PC Software and aerobics. Likes to travel and was inspired after making a journey to Historic Ensemble of the Potala Palace.

    You can view that web-site... ccleaner free download
  10. ↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  11. ↑ 55 years old Systems Administrator Antony from Clarence Creek, really loves learning, PC Software and aerobics. Likes to travel and was inspired after making a journey to Historic Ensemble of the Potala Palace.

    You can view that web-site... ccleaner free download

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