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Any [[oscillator]] in which [[spaceship]]s (typically [[glider]]s) travel in a loop. The simplest example is the p60 one shown below using two [[pentadecathlon]]s. Pulling the pentadecathlons further apart allows any period of the form 60+120n to be achieved - this is the simplest proof of the existence of oscillators of arbitrarily large period.  
{{Glossary}}
A '''relay''' is an [[oscillator]] in which [[spaceship]]s (typically [[glider]]s) travel in a loop. The simplest example is the [[p60 glider shuttle]] shown below using two [[pentadecathlon]]s. Pulling the pentadecathlons further apart allows any period of the form {{nowrap|60 + 120''n''}} to be achieved. This is the simplest proof of the existence of oscillators of arbitrarily large period.  


[[File:Pentadecathlon relay.gif|center]]
{{EmbedViewer
|pname        = p60glidershuttle
|viewerconfig = #C [[ WIDTH 800 THUMBSIZE 2 ZOOM 18 GPS 5 AUTOSTART ]]
|position    = center
|caption      = pentadecathlon relay ([[p60 glider shuttle]])
|style        = width:300px;
}}


From [http://www.argentum.freeserve.co.uk/lex_r.htm#relay The Life Lexicon]
==Table of adjustable relays==
Note that for a glider relay supporting periods of the form <tt>c<sub>1</sub>+c<sub>0</sub>*n</tt>, if the following conditions are met:
*gliders are reflected 180º between two ends without offsetting their [[lane]],
*the oscillating components at its ends (when the gliders are removed) have a period divisible by <tt>2</tt> but not <tt>4</tt> (such as [[unices]] in the [[p42 glider shuttle]]),
then using two copies of the relay, whose gliders reflect off each other in a [[rephaser]], to provide a set of oscillators of the form <tt>c<sub>2</sub>+c<sub>0</sub>*n</tt>, where <tt>c<sub>2</sub> ≡ c<sub>1</sub> + {{frac|c<sub>0</sub>|2}} ([[Modular congruence|mod]] c<sub>0</sub>)</tt>
{|class="wikitable" style="text-align: center"
!relay!!periods!!population
|-
|[[Buckaroo]] loop||<tt>{{LinkCatagolue|xp30_ggy0g8gcy5c871z11x1243czyc742g0ozy8g8ow2587oy666zy723|name=30|style=raw}} + 120*n</tt>||51
|-
|[[p60 glider shuttle]]||<tt>60 + 120*n</tt>||29
|-
|[[6 bits]]||<tt>75 + 120*n</tt>||49
|-
|[[106P135]]||<tt>135 + 120*n</tt>||106
|-
|[[Metamorphosis II]]||<tt>60 + 360*n</tt>||150
|-
|[[Gallus]] ([[34P7]] version)||<tt>{{LinkCatagolue|xp42_33j71t8ggz678u0h43108k8xcczx223333y184swccwcczx66w66y6oooo88zy666x2520go4h0f2sczyf112ngspoo|name=42|style=raw}} + 56*n</tt>||105
|-
|[[Ocellus]]||<tt>90 + 24*n</tt>||92
|-
|[[Silverstream]]<ref>{{LinkForumThread|format=ref|f=2|t=1437|p=133626|title=Re: Oscillator Discussion Thread|author=Freywa|date=July 16, 2021}}</ref>||<tt>90 + 120*n</tt>||106
|-
|[[p42 glider shuttle]]||<tt>42 + 24*n</tt>||143
|-
|[[p50 glider shuttle]]||<tt>50 + 40*n</tt>||<tt>188 if n = 0 else {{LinkCatagolue|xp90_y535asgs4cw4a4x4a4zggxow111w4ac673y1j11d92s0g8gz12lms1g8gya3452w23whzwj20ce710gydosc0hi1z01210gg01ryd3520eqbgz02520fg4c01i20261goock8y37w123zy319l91w8k811c8e2ek9h1zyl11|name=183|style=raw}}</tt>
|-
|[[p43 Snark loop]]||<tt>43 + n</tt>||228
|-
|[[p49 bouncer loop]]<br />(using the {{LinkCatagolue|xp7_oe1ugmmy0o8z6s1mas9wcs0ar4k8zw1169d59e1230e91|name=74-cell variant|style=raw}} of the [[p7 pipsquirter]])<br />(1 glider)||<tt>{{LinkCatagolue|xp140_04s0gg0s48c4oyagy1g08o6pajk46z5b8ml0fc115fkr1eoy1g06511y111w662q5kczx146y0rq2u1s6y0123w66wgbb8fhca7ar453zy08oy1oo01yc11j2g2311zy112308kcyeepxq40ggzy4gg0ggyf346x1074zwg88mlplc2s5ll2woowggy1oe1ugmmy0o8zwdb8ngpo011011y18o121y06s1mas9wcs0ar4k8zwo8bik6o6413y1311y61169d59e1230e91zy1101|name=140|style=raw}} + 56*n</tt>||365
|-
|(2 gliders)||<tt>{{LinkCatagolue|xp70_04s0gg0s48c4oyagy1g08o6pajk46z5b8ml0fc115fkr1eoy1g06511y111w662q5kczx146y0rq2u1s6y0123w66wgbb8fhca7ar453zy08oy1o8g1yc11j2g2311zy112308mw16syaepxq40ggzy4gg2gi01yd346x1074zwg88mlplc2s5ll2woowggy1oe1ugmmy0o8zwdb8ngpo011011y18o121y06s1mas9wcs0ar4k8zwo8bik6o6413y1311y61169d59e1230e91zy1101|name=70|style=raw}} + 28*n</tt>||370
|-
|(4 gliders)||<tt>{{LinkCatagolue|xp35_04s0gg0s48c4oyagy1g08o69ajk46z5b8mh4f03tt7gl1e8gy0g06511y111ggijaq5kczx146x1qq2u1s53x1irw66wgbb8fgd1b2r453zy08oy1oo01y3101y2113464311zy112308kc04cayakc80ca40ggzy4g8o8gyg66x1074zwg88mhl1c2s5ll2woo01mjy0g8e1ugmmy0o8zwdb8nkjj321011y18o121x35s1a2oefg0s82r4k8zwo8bik5o6413y1311y61169d59e1230e91zy1101|name=35|style=raw}} + 14*n</tt>||380
|-
|(5 gliders)||<tt>{{LinkCatagolue|xp28_04s0gg0s48c4oyagy1g08o6pajk46z5b8ml0b831dhgv1eoy1g06511y111w60aq5kczx146y0rq2u1t6y0123w66wgbb8fhe998r453zy08oy1oo01w8oky06a2y0113212311zy112308kcy1gy7gcowca40ggzy4gg0ggw123y1gy566x1074zwg88m555s3s5ll2woke7313gxoe1ugmmy0o8zwdb8nk1p011011y18o33y16t1u22d0g4k0ar4k8zwo8bik6o6413y1311y61169d59e1230e91zy1101|name=28|style=raw}} + {{LinkCatagolue|xp84_yu4s0gg0s48c4oyagy1g08o6pajk46zyt5b8ml0fc115fkr1eoy1g06511y111w662q5kczyw146y0rq2u1s6y0123w66wgbb8fhca7ar453zyzy41yc113202311zyzy4654ydca40ggzyzyf42ey166x1074zzzymca8zyx84szw8oy1oozx12308kczy2gg0ggy2ko8zg88mlplc2s5ll2woowggy1oe1ugmmy0o8zdb8ngpo011011y18o121y06s1mas9wcs0ar4k8zo8bik6o6413y1311y61169d59e1230e91zx101|name=56|style=raw}}*n</tt>||385
|}
 
==See also==
* {{CategoryLink|Relays}}
* [[Shuttle]]
 
== External links ==
* {{LinkLexicon|lex_r.htm#relay}}

Latest revision as of 03:34, 21 April 2024

A relay is an oscillator in which spaceships (typically gliders) travel in a loop. The simplest example is the p60 glider shuttle shown below using two pentadecathlons. Pulling the pentadecathlons further apart allows any period of the form 60 + 120n to be achieved. This is the simplest proof of the existence of oscillators of arbitrarily large period.

x = 35, y = 7, rule = B3/S23 2bo4bo$2ob4ob2o$2bo4bo$16bo$17b2o8bo4bo$16b2o7b2ob4ob2o$27bo4bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 800 THUMBSIZE 2 ZOOM 18 GPS 5 AUTOSTART ]]
pentadecathlon relay (p60 glider shuttle)
(click above to open LifeViewer)
RLE: here Plaintext: here

Table of adjustable relays

Note that for a glider relay supporting periods of the form c1+c0*n, if the following conditions are met:

  • gliders are reflected 180º between two ends without offsetting their lane,
  • the oscillating components at its ends (when the gliders are removed) have a period divisible by 2 but not 4 (such as unices in the p42 glider shuttle),

then using two copies of the relay, whose gliders reflect off each other in a rephaser, to provide a set of oscillators of the form c2+c0*n, where c2 ≡ c1 + c02 (mod c0)

relay periods population
Buckaroo loop 30 + 120*n 51
p60 glider shuttle 60 + 120*n 29
6 bits 75 + 120*n 49
106P135 135 + 120*n 106
Metamorphosis II 60 + 360*n 150
Gallus (34P7 version) 42 + 56*n 105
Ocellus 90 + 24*n 92
Silverstream[1] 90 + 120*n 106
p42 glider shuttle 42 + 24*n 143
p50 glider shuttle 50 + 40*n 188 if n = 0 else 183
p43 Snark loop 43 + n 228
p49 bouncer loop
(using the 74-cell variant of the p7 pipsquirter)
(1 glider)		 140 + 56*n 365
(2 gliders) 70 + 28*n 370
(4 gliders) 35 + 14*n 380
(5 gliders) 28 + 56*n 385

See also

  1. ↑ Freywa (July 16, 2021). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
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