Rectifier: Difference between revisions

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|pname        = rectifier
|pname        = rectifier
|type        = Stable
|type        = Stable
|colour      = preserving
|c            = 59
|c            = 59
|bx          = 41
|bx          = 41
Line 12: Line 13:
|rulemin      = B3/S23
|rulemin      = B3/S23
|rulemax      = B3/S23
|rulemax      = B3/S23
|rulespecial  = [[Conway's Game of Life|Conway Life]]
|isorulemin  = B3/S23
|isorulemin  = B3/S23
|isorulemax  = B3/S23
|isorulemax  = B3/S23
|plaintext    = true
|plaintext    = true
|rle          = true
|rle          = true
|viewerconfig = #C [[ THUMBSIZE 3 ZOOM 12 HEIGHT 500 T 0 PAUSE 3 T 180 PAUSE 2 LOOP 181 ]]
|viewerconfig = #C [[ HEIGHT 470 WIDTH 600 THUMBSIZE 2 ZOOM 12 GPS 30 AUTOSTART OFF ]]
}}
}}
The '''rectifier''' is a [[Stable reflector|stable]] 180° [[glider]] [[reflector]] made up of two [[eater 1]]s, a [[block]], a [[beehive]], and an [[eater 3]]. The normal [[tub]]-stabilised eater 3 can be used here to reduce the [[population]], but the [[snake]]-stabilised eater 3 has a smaller [[bounding box]]. The rectifier is notable for its [[recovery time]] of 106 generations and small number of [[catalyst]]s. It can replace the [[boojum reflector]] in a large number of instances, although in some cases it cannot fit into the space provided due to the transparency of the beehive. It has several advantages over the boojum reflector:
The '''rectifier''' is a [[Stable reflector|stable]] 180° [[glider]] [[reflector]] made up of two [[eater 1]]s, a [[block]], a [[beehive]], and an [[eater 3]]. The normal [[tub]]-stabilised eater 3 can be used here to reduce the [[population]], but the [[snake]]-stabilised eater 3 has a smaller [[bounding box]]. The rectifier is notable for its [[recovery time]] of 106 generations and small number of [[catalyst]]s. It can replace the [[boojum reflector]] in a large number of instances, although in some cases it cannot fit into the space provided due to the transparency of the beehive. It has several advantages over the boojum reflector:
Line 25: Line 25:


The transparent beehive reaction was discovered by [[Paul Callahan]] in {{year|1996}}.
The transparent beehive reaction was discovered by [[Paul Callahan]] in {{year|1996}}.
{{EmbedViewer
|pname        = 169p106
|viewerconfig = #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 12 X 32 Y 25 THEME Book STARTFROM 106 GPS 15 AUTOSTART ]]
|position    = center
|caption      = Rectifier reflecting a p106 glider stream, shown with highlighted reaction [[envelope]]. A second rectifier is present outside the frame, forming a loop with five gliders
|style        = width:300px;
}}


==Gallery==
==Gallery==
Line 30: Line 38:
File:Rectifier_glider.png|An incoming glider (in green) and an outgoing glider (in red) 167 generations later
File:Rectifier_glider.png|An incoming glider (in green) and an outgoing glider (in red) 167 generations later
</gallery>
</gallery>
==SKOPs==
Rectifier loops comprise the majority of the [[SKOP|smallest known oscillators of a certain period]] for high periods. Here is a list of them up to period 200:
{| class="wikitable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
! Period
! Number of gliders
! [[Catagolue]] page
! Minimum population
|-
! {{period|109|brief}}
| 10
| {{LinkCatagolue|xp109_yzyzyzyzy7giligzyzyzyzyo178cydg9g0641u08k8zyzyzyzyf4s0gym1221w11zyzyzyzyh11y44ahhrzzzyzyzyzy8265ya696zzyzyzyzy642ezzzyzyzykokgzzyzyzyjogzyzyzyi101zzzyzyw361zzyzyu2a6zzzyzy5sg8zzypo4oya8ogzyq1yb1zzylm22k8zy5ggya111y631e8z4a40v18o1243ydc4ozy112iai3yg11zy41|patternname=link|style=raw}}
| {{cells|156}}
|-
! {{period|121|brief}}
| 10
| {{LinkCatagolue|xp121_yzyzyzyzymgiligzyzyzyzyzy0178cydg9g0641u08k8zyzyzyzyu4s0gym1221w11zyzyzyzyw11y7eaazzzyzyzyzymco4yb696zzzyzyzyzyh2a6zzzyzyzyvsg8zzzyzyzyqa64zzzyzyzy08okzzzyzyy42ezzzyzy9okgzzzypo4oyb86czyq1zzykkkszy5ggyn31e8z4a40v18o1243ydc4ozy112iai3yg11zy41|patternname=link|style=raw}}
| {{cells|156}}
|-
! {{period|131|brief}}
| 6
| {{LinkCatagolue|xp131_yzyzyzy8giligzyzyzyp178cydg9g0641u08k8zyzyzyg4s0gym1221w11zyzyzyi11y6ehrzzzyzyzyq696zyzyzy5742zzyzyzy1gcozzzzyzybog8zyzyc1zzyqgyf217zyp343zzylo8gzyl643y6c4ozg8g0s4w4aicydggy511z01w349b88cye1074zy3252|patternname=link|style=raw}}
| {{cells|136}}
|-
! {{period|137|brief}}
| 2
| {{LinkCatagolue|xp137_yzymgiligzyzy0178cydg9g0641u08k8zyu4s0gym1221w11zyw11y7eaazyp696zzyzy1696zyk557y7o8gz0gwo8w8k4oyo32z121078imggpye31e8zy34a4|patternname=link|style=raw}}
| {{cells|116}}
|-
! {{period|139|brief}}
| 6
| {{LinkCatagolue|xp139_yzyzyzyegiligzyzyzyv178cydg9g0641u08k8zyzyzym4s0gym1221w11zyzyzyo11y7eaazzzyzyzyw696zyzyzy94cazzzyzyzy4217zzzzyzyee84zzzyzy9532zyp696zzzyk557y7o8gz0gwo8w8k4oyo32z121078imggpye31e8zy34a4|patternname=link|style=raw}}
| {{cells|136}}
|-
! {{period|149|brief}}
| 2
| {{LinkCatagolue|xp149_yzypgiligzyzy3178cydg9g0641u08k8zyx4s0gym1221w11zyz11y64arzypg8gzyp121zyzy4696zylc8gzyl31y762sgz8k80u2gg2596ydo8gzy01245k46yg32zy3121|patternname=link|style=raw}}
| {{cells|116}}
|-
! {{period|151|brief}}
| 6
| {{LinkCatagolue|xp151_yzyzyzyngiligzyzyzyzy1178cydg9g0641u08k8zyzyzyv4s0gym1221w11zyzyzyx11y6ehrzzzyzyzyzy2696zzyzyzyf742zzyzyzybgcozzzzzyzygog8zyzyh1zzyzyc217zyqgzyp343zzylo8gzyl643y6c4ozg8g0s4w4aicydggy511z01w349b88cye1074zy3252|patternname=link|style=raw}}
| {{cells|136}}
|-
! {{period|153|brief}}
| 2
| {{LinkCatagolue|xp153_yzyqgiligzyzy4178cydg9g0641u08k8zyy4s0gym1221w11zyz011y64arzyqgzyp343zyzy5696zylogzyl621y6c4ozg8g0s4w4aicydggy511z01w349b88cye1074zy3252|patternname=link|style=raw}}
| {{cells|116}}
|-
! {{period|157|brief}}
| 2
| {{LinkCatagolue|xp157_yzyrgiligzyzy5178cydg9g0641u08k8zyz4s0gym1221w11zyzw11y7eaazzyp696zyzy6696zzyk557y7o8gz0gwo8w8k4oyo32z121078imggpye31e8zy34a4|patternname=link|style=raw}}
| {{cells|116}}
|-
! {{period|161|brief}}
| 2
| {{LinkCatagolue|xp161_y2giligz8k80u1460g9gydc871zy011w1221ymg0s4zykaaey711zzyzy7ciczyp696zzyzxggy7eaazyz04701ymg88gwggzyzy6gs26yd1i10c4gf0252zyzys19l91|patternname=link|style=raw}}
| {{cells|116}}
|-
! {{period|163|brief}}
| 6
| {{LinkCatagolue|xp163_yzyzyzywgiligzyzyzyzya178cydg9g0641u08k8zyzyzyzy14s0gym1221w11zyzyzyzy311yccczzyzyzyzy74kczyzyzyxe84ya696zzzzzzzyzyzy5gcozyzyvco4zzzzzzzypg8gyag8ozyp1210okgy81zzygoozyy62sgz8k80u2gg2596ydo8gzy01245k46yg32zy3121|patternname=link|style=raw}}
| {{cells|136}}
|-
! {{period|167|brief}}
| 6
| {{LinkCatagolue|xp167_y2giligz8k80u1460g9gydc871zy011w1221ymg0s4zylrhha4y411zzzyp696zzzyzyh163zzyzyj6a2zzzzzzyzyzyk8aczzyzyzymocgzzzyzyzyzyeciczzzyzyzyzy6ggy44ahhrzyzyzyzy44701ymg88gwggzyzyzyzydgs26yd1i10c4gf0252zyzyzyzyz19l91|patternname=link|style=raw}}
| {{cells|136}}
|-
! {{period|169|brief}}
| 2
| {{LinkCatagolue|xp169_yzyugiligzyzy8178cydg9g0641u08k8zyzx4s0gym1221w11zyzy111y64arzzypg8gzyp121yg696zzylc8gzyl31y762sgz8k80u2gg2596ydo8gzy01245k46yg32zy3121|patternname=link|style=raw}}
| {{cells|116}}
|-
! {{period|173|brief}}
| 2
| {{LinkCatagolue|xp173_yzyvgiligzyzy9178cydg9g0641u08k8zyzy04s0gym1221w11zyzy211y64arzzyqgzyp343yh696zzylogzyl621y6c4ozg8g0s4w4aicydggy511z01w349b88cye1074zy3252|patternname=link|style=raw}}
| {{cells|116}}
|-
! {{period|178|brief}}
| 5
| {{LinkCatagolue|xp178_yzyzyzylgiligzyzyzyzx178cy6ggy1g9g0641u08k8zyzyzyt4s0gyd1311y11221w11zyzyzyv11yccczzyzyzyr6c2zyzyzyzy0696zyzyzyq2a6zzzzzzzyzyl265zzyzyk217zzzypo4ozyq1zzyln112szy5ggya3221y531e8z4a40v18o1243ydc4ozy112iai3yg11zy41|patternname=link|style=raw}}
| {{cells|148}}
|-
! {{period|179|brief}}
| 6
| {{LinkCatagolue|xp179_yzyzyzyzy5giligzyzyzyzym178cydg9g0641u08k8zyzyzyzyd4s0gym1221w11zyzyzyzyf11yccczzzyzyzyzy5ca8y3217y1696zzzzzzzzzyzyzx4cay4532zzzzzzzzzyp696y1e84y3153zzzyg33yco8gz0gwo8w8k4oyo32z121078imggpye31e8zy34a4|patternname=link|style=raw}}
| {{cells|136}}
|-
! {{period|181|brief}}
| 2
| {{LinkCatagolue|xp181_y2giligz8k80u1460g9gydc871zy011w1221ymg0s4zykaaey711zzzyp696yjciczzzyzy4ggy7eaazyzy24701ymg88gwggzyzybgs26yd1i10c4gf0252zyzyx19l91|patternname=link|style=raw}}
| {{cells|116}}
|-
! {{period|183|brief}}
| 6
| {{LinkCatagolue|xp183_yzyzyzyzy8giligzyzyzyzyp178cydg9g0641u08k8zyzyzyzyg4s0gym1221w11zyzyzyzyi11yccczzzyzyzyzy9e84y14kcy2696zzzzzzzzzyzyzy2co4y1gcozzzzzzzzzypg8gy2okgy1g8ozyp121yc1zzygoozyy62sgz8k80u2gg2596ydo8gzy01245k46yg32zy3121|patternname=link|style=raw}}
| {{cells|136}}
|-
! {{period|191|brief}}
| 6
| {{LinkCatagolue|xp191_yzyzyzyzyegiligzyzyzyzyv178cydg9g0641u08k8zyzyzyzym4s0gym1221w11zyzyzyzyo11y6ehrzzzyzyzyzyw696zzzzyzyzyz742zzyzyzyvgcozzzzzzzyzyqog8zyzyr1zzyzym217zzzyqgzyp343zzylo8gzyl643y6c4ozg8g0s4w4aicydggy511z01w349b88cye1074zy3252|patternname=link|style=raw}}
| {{cells|136}}
|-
! {{period|193|brief}}
| 2
| {{LinkCatagolue|xp193_yzyz0giligzyzye178cydg9g0641u08k8zyzy54s0gym1221w11zyzy711y64arzzzyqgyn696zyp343zzylogzyl621y6c4ozg8g0s4w4aicydggy511z01w349b88cye1074zy3252|patternname=link|style=raw}}
| {{cells|116}}
|-
! {{period|194|brief}}
| 5
| {{LinkCatagolue|xp194_yzyzyzyvgiligzyzyzyzy9178cydg9g0641u08k8zyzyzyzy04s0gym1221w11zyzyzyzy211y44ahhrzzzyzyzyzya696zzzzyzyzybca8zzyzyzy9gcozzzzzzzzyzy2742zypo4ozyq1y8a64zzygcczy5ggyn31e8z4a40v18o1243ydc4ozy112iai3yg11zy41|patternname=link|style=raw}}
| {{cells|137}}
|-
! {{period|197|brief}}
| 2
| {{LinkCatagolue|xp197_yzyzwgiligzyzyf178cydg9g0641u08k8zyzy64s0gym1221w11zyzy811y7eaazzzyzyg696zyp696zzzyk557y7o8gz0gwo8w8k4oyo32z121078imggpye31e8zy34a4|patternname=link|style=raw}}
| {{cells|116}}
|}
Most prime-period SKOPs are rectifier loops, because there's no currently known lower-population way to close a loop using only [[stable]] circuitry.
==See also==
[[User:Galoomba/Skopje|List of smallest-population known oscillators]] for periods up to 2048, tracked by the [[Skopje]] project


==External links==
==External links==

Latest revision as of 16:32, 26 February 2026

Rectifier
x = 41, y = 33, rule = B3/S23 bobo7bo$2b2o6bobo$2bo7bobo$11bo12$20b2o$20b2o2$2b2o$bobo$bo$2o$31b2o$ 30bo2bo2b2o$30bobo4bo$11b2o18bo5bob2o$10bobo21b2obobo$10bo23bo2bo2bo$ 9b2o20bo4bo2b2o$31b5o2$33b2obo$33bob2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ HEIGHT 470 WIDTH 600 THUMBSIZE 2 ZOOM 12 GPS 30 AUTOSTART OFF ]]
View static image
Pattern type Stable reflector
Number of cells 59
Bounding box 41 × 33
Angle 180°
Repeat time 106
Colour Colour-preserving
Discovered by Adam P. Goucher
Year of discovery 2009

The rectifier is a stable 180° glider reflector made up of two eater 1s, a block, a beehive, and an eater 3. The normal tub-stabilised eater 3 can be used here to reduce the population, but the snake-stabilised eater 3 has a smaller bounding box. The rectifier is notable for its recovery time of 106 generations and small number of catalysts. It can replace the boojum reflector in a large number of instances, although in some cases it cannot fit into the space provided due to the transparency of the beehive. It has several advantages over the boojum reflector:

  • it has a much lower recovery time, allowing certain guns to be compacted;
  • its passive bounding box is slightly smaller, so it can further compact many glider guns;
  • its output path is free of catalysts, enabling it to be used as a merge device.

The transparent beehive reaction was discovered by Paul Callahan in 1996.

x = 108, y = 86, rule = B3/S23 8bo$7bobo$8bo2$6b5o$5bo4bo20b2o$4bo2bo23bo$bo2bob2o21bobo$obobo5bo18b 2o$bo2bo4bobo8bo$4b2o2bo2bo7bobo$9b2o8bo2bo$18bo2bo18b2o$17b2o3b2o16bo $15b2o5b2o6bo7bobo$15bo6bo8b2o5b2o$16bo3bo9b2o$16bo3bo$17b3o4$29b2o$ 29b2o$30bo5$36b2o$36bobo$36bo$26b3ob3o$28b4o$28b3o$29bo6$56bobo$57b2o$ 57bo9$77bo$76bobo$76bobo$77bo$62b3o$62bo$63bo7$85b2o2$82b2o3bo$82bo4bo $82bo$68b2o13bo2bo$67bobo$67bo$66b2o$97b2o$96bo2bo2b2o$96bobo4bo2bo$ 77b2o18bo5bobobo$76bobo21b2obo2bo$76bo23bo2bo$75b2o20bo4bo$97b5o2$99bo $98bobo$99bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 12 X 32 Y 25 THEME Book STARTFROM 106 GPS 15 AUTOSTART ]]
Rectifier reflecting a p106 glider stream, shown with highlighted reaction envelope. A second rectifier is present outside the frame, forming a loop with five gliders
(click above to open LifeViewer)
RLE: here Plaintext: here
  • An incoming glider (in green) and an outgoing glider (in red) 167 generations later
    An incoming glider (in green) and an outgoing glider (in red) 167 generations later

SKOPs

Rectifier loops comprise the majority of the smallest known oscillators of a certain period for high periods. Here is a list of them up to period 200:

Period Number of gliders Catagolue page Minimum population
109 10 link 156
121 10 link 156
131 6 link 136
137 2 link 116
139 6 link 136
149 2 link 116
151 6 link 136
153 2 link 116
157 2 link 116
161 2 link 116
163 6 link 136
167 6 link 136
169 2 link 116
173 2 link 116
178 5 link 148
179 6 link 136
181 2 link 116
183 6 link 136
191 6 link 136
193 2 link 116
194 5 link 137
197 2 link 116

Most prime-period SKOPs are rectifier loops, because there's no currently known lower-population way to close a loop using only stable circuitry.

See also

List of smallest-population known oscillators for periods up to 2048, tracked by the Skopje project

Glider-accepting devices in stationary signal circuitry
(Talk · Edit · Links)
Stable
Reflectors
Pulse dividers
(Period multipliers)
G-to-X (mostly
glider-to-Herschel)
Memory cells / Factories
Eaters
Periodic
Reflectors
90-degree
180-degree
Pentadecathlon(s) (as in 6 bits) · 3-block-1-tub reflector (as in Ocellus or Gallus) · Pre-pond reflector · Hotcrystal0 reaction · p8 glider reflector
5× pulse divider: Quinti-Snark (p5 quinti-Snark)
0-degree
G-to-H
Concepts
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