Difference between revisions of "Wire"

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Considerable effort has been spent on finding a way to turn a [[2c/3]] signal 90 or 180 degrees, since this would have been one way to prove that Life was omniperiodic. There is a known 2c/3 [[converter]] shown under [[signal elbow]], which converts a standard 2c/3 signal into a double-length signal. This is usable in some situations, but unfortunately it fails when its input is a double-length signal, so it cannot be used to complete two or more consecutive turns. It could only produce zigzag wires in any case rather than completing a loop, since the wire coming out of the elbow is a mirror image of the input wire.
Considerable effort has been spent on finding a way to turn a [[2c/3]] signal 90 or 180 degrees, since this would have been one way to prove that Life was omniperiodic. There is a known 2c/3 [[converter]] shown under [[signal elbow]], which converts a standard 2c/3 signal into a double-length signal. This is usable in some situations, but unfortunately it fails when its input is a double-length signal, so it cannot be used to complete two or more consecutive turns. It could only produce zigzag wires in any case rather than completing a loop, since the wire coming out of the elbow is a mirror image of the input wire.


In February {{year|2004}}, [[Noam Elkies]] discovered a [[glider synthesis]] of a reaction that can repeatably insert a signal into the upper end of a 2c/3 wire. See [[stable pseudo-Heisenburp]] for details. On September 11, {{year|2017}}, [[Martin Grant]] reduced the input reaction to five gliders or three gliders plus a [[Herschel]].<ref name="post50807" /> With the Herschel option the [[recovery time]] is 152 ticks. In 2011, a [[p11 double-length signal injector]] was found that allows signals to be injected periodically.
In February {{year|2004}}, [[Noam Elkies]] discovered a [[glider synthesis]] of a reaction that can repeatably insert a signal into the upper end of a 2c/3 wire. See [[stable pseudo-Heisenburp]] for details. In 2011, a [[p11 double-length signal injector]] was found that allows signals to be injected periodically.


Devices that extract a signal from a 2c/3 wire have also been built; currently the lowest repeat time of a standard 2c/3 signal receiver is 964 ticks,<ref name="post135690" /> and that of a double-length signal is 970 ticks,<ref name="post137526" /> both of which were achieved by [[Goldtiger997]] in {{year|2021}} by using complex [[staged recovery]] systems.
On September 11, {{year|2017}}, [[Martin Grant]] reduced the cost of the synchronized input to five gliders, or three gliders plus a [[Herschel]].<ref name="post50807" /> In {{year|2024}}, a double [[beehive push catalyst]] variant was found that uses only 4 gliders to activate a 2c/3 wire, with a recovery time of 56,<ref name="post179988" /> or just two [[pi heptomino]]s following each other on the same track. (See [[Tutorials/Catalyses#Beehive push catalyst replacements]]). Compact engineered solutions requiring just one input Herschel have been completed with [[recovery time]] 151 ticks<ref name="post180139" /> and 171 ticks<ref name="post179942" /> in March 2024, and with recovery time 132 ticks in April 2024.<ref name="post181846" /> The current fastest 2c/3 signal injector has a repeat time of 126.<ref name="post181888" />
 
Devices that extract a signal from a 2c/3 wire have also been built. Before 2024, the lowest repeat time of a standard 2c/3 signal receiver was 964 ticks,<ref name="post135690" /> and that of a double-length signal was 970 ticks,<ref name="post137526" /> both of which were achieved by [[Goldtiger997]] in {{year|2021}} by using complex [[staged recovery]] systems. On March 31, {{year|2024}}, [[Entity Valkyrie]] constructed a new [[pseudo-Heisenburp]] device with a repeat time of 742 ticks at both the input end (the highway robber) and the output end (the 2c/3 to glider converter).<ref name="post181579" /> On July 4, {{year|2024}}, Entity Valkyrie improved the repeat time at the receiver end to 708 ticks using an alternate [[bait]] proposed by [[Simon Ekström]].<ref name="post189015" /> On August 1, {{year|2025}}, [[TigerCub414]] built a receiver with a repeat time of 629 ticks;<ref name="post215428"/> on August 3, [[Entity Valkyrie]] improved the repeat time to 570 ticks using the same bait object.<ref name="post215500"/> Two days later, TigerCub414 improved the repeat time even further, to 504 ticks.<ref name="post215632"/>


==5c/9 wire==
==5c/9 wire==
Line 44: Line 46:
It is possible to convert a 2c/3 wire signal into a 5c/9 signal; the viewer above shows the aforementioned five-glider input reaction for a 2c/3 signal and its subsequent conversion to 5c/9 signal. Another elementary 5c/9 signal injector involves a [[lumps of muck]] reaction,<ref name="post54568" /> which can be made from the synchronized [[2-glider collision]] at a repeat time of 62 ticks<ref name="post54617" />, a single Herschel with a much higher repeat time<ref name="post101243" />, or a fixed-period lumps of muck hassler that uses a specific catalyst (such as the p47).
It is possible to convert a 2c/3 wire signal into a 5c/9 signal; the viewer above shows the aforementioned five-glider input reaction for a 2c/3 signal and its subsequent conversion to 5c/9 signal. Another elementary 5c/9 signal injector involves a [[lumps of muck]] reaction,<ref name="post54568" /> which can be made from the synchronized [[2-glider collision]] at a repeat time of 62 ticks<ref name="post54617" />, a single Herschel with a much higher repeat time<ref name="post101243" />, or a fixed-period lumps of muck hassler that uses a specific catalyst (such as the p47).


However, no converter has yet been found for 5c/9 to 2c/3&ndash;or any other viable signal type, for that matter.
No elementary converter has yet been found for 5c/9 to 2c/3 &ndash; or any other viable signal type, for that matter. However, in November 2025, [[James Pascua]] completed a multistage composite converter for 5c/9 signals, which allowed for the completion of the first closed loop containing a segment of 5c/9 wire.<ref name="post221926" />


==c/2 wire==
==c/2 wire==
Line 54: Line 56:
|pname        = c2wire
|pname        = c2wire
|caption      = Diagonal c/2 wire
|caption      = Diagonal c/2 wire
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 HEIGHT 440 ZOOM 8 GPS 10 LOOP 50 PAUSE 2 ]]
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 HEIGHT 440 ZOOM 8 GPS 10 LOOP 40 PAUSE 2 ]]
|style        = width:300px;
|style        = width:300px;
}}
}}
Line 74: Line 76:
}}
}}


This wire must extend infinitely at the leading edge to avoid destruction, limiting its practical usefulness.
Another type of lightspeed wire is "beehive wire":  an orthogonal chain of beehives can be burned non-destructively at lightspeed, as described in the [[telegraph]] article.


==References==
==References==
Line 119: Line 121:
|author = Sphenocorona
|author = Sphenocorona
|date  = July 28, 2020
|date  = July 28, 2020
}}</ref>
<ref name="post179942">{{LinkForumThread
|format = ref
|title  = Re: Faster 2c/3 Wires
|p      = 179942
|author = Entity Valkyrie
|date  = March 8, 2024
}}</ref>
<ref name="post179988">{{LinkForumThread
|format = ref
|title  = Re: Faster 2c/3 Wires
|p      = 179988
|author = EvinZL
|date  = March 10, 2024
}}</ref>
<ref name="post180139">{{LinkForumThread
|format = ref
|title  = Re: Faster 2c/3 Wires
|p      = 180139
|author = Dave Greene
|date  = March 12, 2024
}}</ref>
<ref name="post181579">{{LinkForumThread
|format = ref
|title  = Re: Faster 2c/3 Wires
|p      = 181579
|author = Entity Valkyrie
|date  = March 31, 2024
}}</ref>
<ref name="post181846">{{LinkForumThread
|format = ref
|title  = Re: Faster 2c/3 Wires
|p      = 181846
|author = C. R. Hilton
|date  = April 4, 2024
}}</ref>
<ref name="post181888">{{LinkForumThread
|format = ref
|title  = Re: Faster 2c/3 Wires
|p      = 181888
|author = Adam P. Goucher
|date  = April 5, 2024
}}</ref>
<ref name="post189015">{{LinkForumThread
|format = ref
|title  = Re: Faster 2c/3 Wires
|p      = 189015
|author = Entity Valkyrie
|date  = July 4, 2024
}}</ref>
<ref name="post215428">{{LinkForumThread
|format = ref
|title  = Re: Faster 2c/3 Wires
|p      = 215428
|author = TigerCub414
|date  = August 1, 2025
}}</ref>
<ref name="post215500">{{LinkForumThread
|format = ref
|title  = Re: Faster 2c/3 Wires
|p      = 215500
|author = Entity Valkyrie
|date  = August 3, 2025
}}</ref>
<ref name="post215632">{{LinkForumThread
|format = ref
|title  = Re: Faster 2c/3 Wires
|p      = 215632
|author = TigerCub414
|date  = August 5, 2025
}}</ref>
<ref name="post221926">{{LinkForumThread
|format = ref
|title  = Re: Stable signal converters
|p      = 221926
|author = James Pascua
|date  = November 27, 2025
}}</ref>
}}</ref>
</references>
</references>

Latest revision as of 14:56, 14 April 2026

A wire is a repeating pattern that a signal can travel along without making any permanent change to the pattern.[1] If instead the pattern is destroyed by the travelling signal (i.e. it burns from one end) it is a fuse.[2]

The first documented wire was discovered by Dean Hickerson in March 1997 while studying some period-3 oscillators found by Achim Flammenkamp. It transmits signals that travel through the wire diagonally at two-thirds of the speed of light. This was the inspiration for Hickerson's drifter search program, which led to the discovery of a 5c/9 wire a month later.

Hickerson also used his program to search for a wire signal elbow, hoping to use it to construct a fast signal loop and solve the omniperiodicity problem; this effort was unsuccessful for Life, with the closest match being a 2c/3 signal elbow found in July 1997 that turned a single signal into a reflected double signal.

Signals on wires are harder to manipulate as compared to signals in a vacuum, especially in the form of gliders, for which there is a rich and growing toolkit.[3]

2c/3 wire

2c/3 wire was discovered by Dean Hickerson in 1997. It can be found in the misc section of jslife under the name signals 2c3d.[4]

x = 69, y = 66, rule = B3/S23 41bo$6bo32b2o$4bobo33b2o$5b2o2$34bo$33bo$33b3o2$25bo$23b3o$22bo$22b2o 6$26bo4b2o$25bobobo2bo$26b2ob3o2$26b6o$25bo6bo$25bo2b5o$23bobobo7bo$ 23b2o2bo2b6o$27bobo$26b2obo2b6o$29bobo6bo$bo27bobo2b5o$b2o27b2obo7bo$o bo30bo2b6o$33bobo$32b2obo2b6o$35bobo6bo$5bo29bobo2b5o$5b2o29b2obo7bo$ 4bobo32bo2b6o$39bobo$38b2obo2b6o$41bobo6bo$41bobo2b5o$42b2obo7bo$45bo 2b6o$45bobo$44b2obo2b6o$47bobo6bo$47bobo2b5o$48b2obo7bo$51bo2b6o$51bob o$50b2obo2b6o$53bobo6bo$53bobo2b5o$54b2obo7bo$57bo2b6o$57bobo$56b2obo 2b6o$59bobo6bo$59bobo2b3obo$60b2obo3bo$63bo2bo$63bobo$62b2obobo$66b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART THUMBSIZE 2 HEIGHT 600 WIDTH 600 X 8 Y 4 ZOOM 8 GPS 10 LOOP 128 PAUSE 2 ]]
Diagonal 2c/3 wire
(click above to open LifeViewer)
RLE: here Plaintext: here

Each signal is made up of two half-signals that can be separated from each other by an arbitrary number of ticks.

Considerable effort has been spent on finding a way to turn a 2c/3 signal 90 or 180 degrees, since this would have been one way to prove that Life was omniperiodic. There is a known 2c/3 converter shown under signal elbow, which converts a standard 2c/3 signal into a double-length signal. This is usable in some situations, but unfortunately it fails when its input is a double-length signal, so it cannot be used to complete two or more consecutive turns. It could only produce zigzag wires in any case rather than completing a loop, since the wire coming out of the elbow is a mirror image of the input wire.

In February 2004, Noam Elkies discovered a glider synthesis of a reaction that can repeatably insert a signal into the upper end of a 2c/3 wire. See stable pseudo-Heisenburp for details. In 2011, a p11 double-length signal injector was found that allows signals to be injected periodically.

On September 11, 2017, Martin Grant reduced the cost of the synchronized input to five gliders, or three gliders plus a Herschel.[5] In 2024, a double beehive push catalyst variant was found that uses only 4 gliders to activate a 2c/3 wire, with a recovery time of 56,[6] or just two pi heptominos following each other on the same track. (See Tutorials/Catalyses#Beehive push catalyst replacements). Compact engineered solutions requiring just one input Herschel have been completed with recovery time 151 ticks[7] and 171 ticks[8] in March 2024, and with recovery time 132 ticks in April 2024.[9] The current fastest 2c/3 signal injector has a repeat time of 126.[10]

Devices that extract a signal from a 2c/3 wire have also been built. Before 2024, the lowest repeat time of a standard 2c/3 signal receiver was 964 ticks,[11] and that of a double-length signal was 970 ticks,[12] both of which were achieved by Goldtiger997 in 2021 by using complex staged recovery systems. On March 31, 2024, Entity Valkyrie constructed a new pseudo-Heisenburp device with a repeat time of 742 ticks at both the input end (the highway robber) and the output end (the 2c/3 to glider converter).[13] On July 4, 2024, Entity Valkyrie improved the repeat time at the receiver end to 708 ticks using an alternate bait proposed by Simon Ekström.[14] On August 1, 2025, TigerCub414 built a receiver with a repeat time of 629 ticks;[15] on August 3, Entity Valkyrie improved the repeat time to 570 ticks using the same bait object.[16] Two days later, TigerCub414 improved the repeat time even further, to 504 ticks.[17]

5c/9 wire

5c/9 wire was discovered by Dean Hickerson in 1997.

x = 91, y = 86, rule = B3/S23 41bo$6bo32b2o$4bobo33b2o$5b2o2$34bo$33bo$33b3o2$25bo$23b3o$22bo$22b2o 6$26bo4b2o$25bobobo2bo$26b2ob3o2$26b6o$25bo6bo$25bo2b5o$23bobobo7bo$ 23b2o2bo2b6o$27bobo8bo3b2o$26b2obo2b7o2bo2bo$29bobo7b3obobo$bo27bobo2b 5o3bobobob2o$b2o27b2obo6bo3bobobobo$obo30bo2b6o2bobo2b2o$33bobo6bobobo $32b2obo2b4obo2b5o$35bobo3bobobo4bo$5bo29bobobo3bobob2o$5b2o29bobob4ob o2b2o$4bobo31bo7bo3bo$38bob6ob3o3bo$37b2obo4bobo2b4o$40bo2bo3bobo6bo$ 40bobob4obo2b5o$39b2obo6bobo5b2o$42bob4obo2bob2obobo$42bobo2bob2obobob o2bo$41b2o2bo2bo3bobo4bob2o$43b2o4b4ob2o2b2o2bo$43bo3bobo6bo3bo$44b4ob ob5ob3o3bo$48bobo4bobo2b4o$46bo3bo2bo3bobo6bo$46b2o2bobob4obo2b5o$49b 2obo6bobo5b2o$52bob4obo2bob2obobo$52bobo2bob2obobobo2bo$51b2o2bo2bo3bo bo4bob2o$53b2o4b4ob2o2b2o2bo$53bo3bobo6bo3bo$54b4obob5ob3o3bo$58bobo4b obo2b4o$56bo3bo2bo3bobo6bo$56b2o2bobob4obo2b5o$59b2obo6bobo5b2o$62bob 4obo2bob2obobo$62bobo2bob2obobobo2bo$61b2o2bo2bo3bobo4bob2o$63b2o4b4ob 2o2b2o2bo$63bo3bobo6bo3bo$64b4obob5ob3o3bo$68bobo4bobo2b4o$66bo3bo2bo 3bobo6bo$66b2o2bobob4obo2b5o$69b2obo6bobo5b2o$72bob4obo2bob2obo2bo$72b obo2bob2obobobo2b2o$71b2o2bo2bo3bobo$73b2o4b4ob2o$73bo3bobo6bo$74b4obo b5obo$78bobo4bobo$76bo3bo2bo3b2o$76b2o2bobob3o2bo$79b2obo5bo$83bob3o$ 84b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART THUMBSIZE 2 HEIGHT 600 WIDTH 600 X 8 Y 4 ZOOM 6 GPS 10 LOOP 180 PAUSE 2 ]]
Diagonal 5c/9 wire
(click above to open LifeViewer)
RLE: here Plaintext: here

Oscillators have been found that inject signals of various periods including 9, 10, 11, and 47 into a 5c/9 wire.[18]

It is possible to convert a 2c/3 wire signal into a 5c/9 signal; the viewer above shows the aforementioned five-glider input reaction for a 2c/3 signal and its subsequent conversion to 5c/9 signal. Another elementary 5c/9 signal injector involves a lumps of muck reaction,[19] which can be made from the synchronized 2-glider collision at a repeat time of 62 ticks[20], a single Herschel with a much higher repeat time[21], or a fixed-period lumps of muck hassler that uses a specific catalyst (such as the p47).

No elementary converter has yet been found for 5c/9 to 2c/3 – or any other viable signal type, for that matter. However, in November 2025, James Pascua completed a multistage composite converter for 5c/9 signals, which allowed for the completion of the first closed loop containing a segment of 5c/9 wire.[22]

c/2 wire

c/2 wire was discovered by Hartmut Holzwart in 2003.

x = 50, y = 50, rule = B3/S23 bo$obo$bobo$2bobo$3bobo$5bo$7bo$3bo3bo$7b2o$4b3o3bo$8b3o$9b2o$12bo$12b obo2$13bobo$14bobo$15bobo2bo$16bo5bo$17b2o3bo$22bo$19b3o$21bobo$23b2o$ 22b3o2$25b2o$28bo$26bo2bo$28bobo$29bobo$30bobo$31bobo$32bobo$33bobo$ 34bobo$35bobo$36bobo$37bobo$38bobo$39bobo$40bobo$41bobo$42bobo$43bobo$ 44bobo$45bobo$46bobo$47bobo$48bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART THUMBSIZE 2 HEIGHT 440 ZOOM 8 GPS 10 LOOP 40 PAUSE 2 ]]
Diagonal c/2 wire
(click above to open LifeViewer)
RLE: here Plaintext: here

Both halves of the signal (the non-uniform portion of the pattern) are needed, since the wire is offset by one cell between the two half signals.

It is technically possible to use Extrementhusiast's construction and detection mechanisms from 2018 to complete a c/2 diagonal telegraph pattern that can send one bit of information every few thousand ticks. Or a somewhat higher transmission rate can be arranged with a mechanism similar to the one used in Louis-François Handfield's high-bandwidth telegraph. No complete c/2 diagonal telegraph has been built to date.

Lightspeed wire

The zebra stripes agar can be used to form a wire. Below are several signals which can travel through such a wire at lightspeed (one cell to the right per generation).

x = 147, y = 40, rule = B3/S23:T147,40 13$2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo 2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo 2bo2bo2bo2bo$147o2$13o2b10o2b120o$12b2o10b2o40bo13bo13bo12bo$12o3b9o3b 12o2b24o4b11o4b10o3b10o4b14o2b20o$38b2o11bo12bo14bo15bo10bo2bo10bo3b2o $12o3b11o3b10o2b9o4b11o4b11o4b10o3b10o4b9o5bo3b18o$12b2o12b2o22bo14bo 14bo13bo12bo13bo2b2o$13o2b12o2b96o2b20o2$147o$2bo2bo2bo2bo2bo2bo2bo2bo 2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo 2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART THUMBSIZE 2 HEIGHT 360 WIDTH 800 GPS 10 LOOP 138 ZOOM 6 ]]
Several lightspeed signals travel through a zebra stripes wire
(click above to open LifeViewer)
RLE: here Plaintext: here

Another type of lightspeed wire is "beehive wire": an orthogonal chain of beehives can be burned non-destructively at lightspeed, as described in the telegraph article.

References

  1. ↑ Nathaniel Johnston, Dave Greene. Conway's Game of Life: Mathematics and Construction (2022), Section 4.5.1.
  2. ↑ Nathaniel Johnston, Dave Greene. Conway's Game of Life: Mathematics and Construction (2022), Section 4.5.2, pp. 103.
  3. ↑ Nathaniel Johnston, Dave Greene. Conway's Game of Life: Mathematics and Construction (2022), Section 4.7.
  4. ↑ Jason Summers' jslife pattern collection. Retrieved on June 6, 2022.
  5. ↑ Martin Grant (September 11, 2017). Re: Stable signal converters (discussion thread) at the ConwayLife.com forums
  6. ↑ EvinZL (March 10, 2024). Re: Faster 2c/3 Wires (discussion thread) at the ConwayLife.com forums
  7. ↑ Dave Greene (March 12, 2024). Re: Faster 2c/3 Wires (discussion thread) at the ConwayLife.com forums
  8. ↑ Entity Valkyrie (March 8, 2024). Re: Faster 2c/3 Wires (discussion thread) at the ConwayLife.com forums
  9. ↑ C. R. Hilton (April 4, 2024). Re: Faster 2c/3 Wires (discussion thread) at the ConwayLife.com forums
  10. ↑ Adam P. Goucher (April 5, 2024). Re: Faster 2c/3 Wires (discussion thread) at the ConwayLife.com forums
  11. ↑ Goldtiger997 (September 12, 2021). Re: Faster 2c/3 Wires (discussion thread) at the ConwayLife.com forums
  12. ↑ Goldtiger997 (November 11, 2021). Re: Faster 2c/3 Wires (discussion thread) at the ConwayLife.com forums
  13. ↑ Entity Valkyrie (March 31, 2024). Re: Faster 2c/3 Wires (discussion thread) at the ConwayLife.com forums
  14. ↑ Entity Valkyrie (July 4, 2024). Re: Faster 2c/3 Wires (discussion thread) at the ConwayLife.com forums
  15. ↑ TigerCub414 (August 1, 2025). Re: Faster 2c/3 Wires (discussion thread) at the ConwayLife.com forums
  16. ↑ Entity Valkyrie (August 3, 2025). Re: Faster 2c/3 Wires (discussion thread) at the ConwayLife.com forums
  17. ↑ TigerCub414 (August 5, 2025). Re: Faster 2c/3 Wires (discussion thread) at the ConwayLife.com forums
  18. ↑ "Dean Hickerson's signal-injector collection".
  19. ↑ Adam P. Goucher (January 2, 2018). Re: Interacting with LoM (discussion thread) at the ConwayLife.com forums
  20. ↑ Chris Cain (January 3, 2018). Re: Interacting with LoM (discussion thread) at the ConwayLife.com forums
  21. ↑ Sphenocorona (July 28, 2020). Re: The Hunting of the Elementary Conduits (discussion thread) at the ConwayLife.com forums
  22. ↑ James Pascua (November 27, 2025). Re: Stable signal converters (discussion thread) at the ConwayLife.com forums

External links


Retrieved from "https://conwaylife.com/w/index.php?title=Wire&oldid=172406"