Wire
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]
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]
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,[10] and that of a double-length signal was 970 ticks,[11] 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).[12]
5c/9 wire
5c/9 wire was discovered by Dean Hickerson in 1997.
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.[13]
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,[14] which can be made from the synchronized 2-glider collision at a repeat time of 62 ticks[15], a single Herschel with a much higher repeat time[16], 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–or any other viable signal type, for that matter.
c/2 wire
c/2 wire was discovered by Hartmut Holzwart in 2003.
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).
Several lightspeed signals travel through a zebra stripes wire (click above to open LifeViewer) RLE: here Plaintext: here |
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
- ↑ Nathaniel Johnston, Dave Greene. Conway's Game of Life: Mathematics and Construction (2022), Section 4.5.1.
- ↑ Nathaniel Johnston, Dave Greene. Conway's Game of Life: Mathematics and Construction (2022), Section 4.5.2, pp. 103.
- ↑ Nathaniel Johnston, Dave Greene. Conway's Game of Life: Mathematics and Construction (2022), Section 4.7.
- ↑ Jason Summers' jslife pattern collection. Retrieved on June 6, 2022.
- ↑ Martin Grant (September 11, 2017). Re: Stable signal converters (discussion thread) at the ConwayLife.com forums
- ↑ EvinZL (March 10, 2024). Re: Faster 2c/3 Wires (discussion thread) at the ConwayLife.com forums
- ↑ Dave Greene (March 12, 2024). Re: Faster 2c/3 Wires (discussion thread) at the ConwayLife.com forums
- ↑ Entity Valkyrie (March 8, 2024). Re: Faster 2c/3 Wires (discussion thread) at the ConwayLife.com forums
- ↑ C. R. Hilton (April 4, 2024). Re: Faster 2c/3 Wires (discussion thread) at the ConwayLife.com forums
- ↑ Goldtiger997 (September 12, 2021). Re: Faster 2c/3 Wires (discussion thread) at the ConwayLife.com forums
- ↑ Goldtiger997 (November 11, 2021). Re: Faster 2c/3 Wires (discussion thread) at the ConwayLife.com forums
- ↑ Entity Valkyrie (March 31, 2024). Re: Faster 2c/3 Wires (discussion thread) at the ConwayLife.com forums
- ↑ "Dean Hickerson's signal-injector collection".
- ↑ Adam P. Goucher (January 2, 2018). Re: Interacting with LoM (discussion thread) at the ConwayLife.com forums
- ↑ Chris Cain (January 3, 2018). Re: Interacting with LoM (discussion thread) at the ConwayLife.com forums
- ↑ Sphenocorona (July 28, 2020). Re: The Hunting of the Elementary Conduits (discussion thread) at the ConwayLife.com forums
External links
- Stable 2c/3 signal receiver at Game of Life News. Posted by Dave Greene on February 7, 2005.
- Wire at the Life Lexicon
- 2c/3 wire at the Life Lexicon
- 5c/9 wire at the Life Lexicon
- Lightspeed wire at the Life Lexicon