User:GUYTU6J/OCA:Glimmering Garden/Appendix 1: Miscellaneous construction practice

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Ambox notice.png The page contains 14 LifeViewers, which may make loading slow with poor internet connection. A custom color scheme is used.

This page documents miscellaneous constructions in the isotropic non-totalistic rule Glimmering Garden. Unless otherwise noted, they are built by user GUYTU6J. When downloading a pattern, hit Ctrl+C in the corresponding LifeViewer to get the rle.

Collection of simple stable 90-degree T-ship reflectors and duplicators as well as a grammar as of February 19, 2021, categorized by mod-4 timing and marked with recovery time (dotted numbers) in History format: (hit Alt+J before copy and pasting into a Golly pre-4.0 version)

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D.D.D2$50.D3.D7.D2$50.D3.D3.D.D.D2$50.D3.D7.D2$50.D3.D3.D.D.D! #C [[ THUMBNAIL WIDTH 800 HEIGHT 1400 ZOOM 2 ]]

Rule 110 unit cell

The following pattern consists of six gun-less Rule 110 unit cells built on September 14, 2020.[1] On-cells emit a T-ship to the right at period-1476.

x=295, y = 1048, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c:T0,1074 120bo$119bobo136bo$120bo136bobo$258bo2$130bo$129bobo12bo$130bo12bobo$ 144b2o$275bo$274bobo$9bo265bo$8bobo$9bo116bo$125bobo$126bo132bo$258bob o$259b2o4$82bo$74bo6bobo$73bobo6bo$74bo116bo$95bo94bobo75bo$88bo5bobo 94bo75bobo$15b2o70bobo5bo26b2o75bo68bo$bo12bobo44bo26b2o31bobo46bo27bo bo$obo12bo44bobo59bo31bo14bobo27bo$bo59bo91bobo14bo$108bo45bo25bo$107b obo6bo62bobo$108bo6bobo62bo$116bo$198bo$197bobo$198bo$262bo$261bobo$ 92bo169bo$91bobo$92bo78bo69bo$170bobo67bobo$171b2o68bo3$20bo$19bobo 219bo$20bo217bob2o$241bo51bo$6b2o284bobo$5bobo257b2o26bo$6bo26bo52bo 12bo165bobo$32bobo50bobo10bobo165bo$33bo52bo11b2o137bo$170bo65bobo41bo $169bobo65bo34bo6bobo$170bo100bobo6bo$272bo$157bo$156bobo69bo$157bo69b obo$181bo46bo$180bobo$5bo175bo40bo27b2o$4bobo214bobo20bo5bobo12bo$5bo 216bo20bobo5bo12bobo$244bo20bo4$175bo$174bobo37bo$175bo37bobo$214bo3$ 156bo14bo$155bobo12bobo55bo11bo$156bo14bo55bobo9bobo$206bo21bo11bo$ 205bobo$206bo4$220bo$219bobo$160bo14bo22bo21bo$159bobo12bobo20bobo$ 160bo14bo22bo2$179bo$178bobo$138bo40bo32bo$137bobo71bobo$138bo51bo21bo $189bobo$190bo$101bo$100bobo$101bo$204bo$87b2o114bobo$86bobo73b2o40bo$ 87bo26bo16bo30bobo$113bobo14bobo30bo$114bo16bo47bo$178bobo$82bo82bo13b o$81bobo80bobo$82bo82bo24bo$113bo75bobo$112bobo75bo$113bo$103bo$102bob o$103bo43b2o$129bo17bobo12bo$84bo14bo28bobo17bo12bobo$83bobo12bobo27b 2o32bo$84bo14bo9$80bo14bo$79bobo12bobo$80bo14bo4$104bo$103bobo$104bo6$ 89bo$88bobo$89bo3$94bo$93bobo$94bo27$120bo$119bobo136bo$120bo136bobo$ 258bo2$130bo$129bobo12bo$130bo12bobo$144b2o$275bo$274bobo$9bo265bo$8bo bo$9bo116bo$125bobo$126bo132bo$258bobo$259b2o4$82bo$74bo6bobo$73bobo6b o$74bo116bo$95bo94bobo75bo$88bo5bobo94bo75bobo$15b2o70bobo5bo26b2o75bo 68bo$bo12bobo44bo26b2o31bobo46bo27bobo$obo12bo44bobo59bo31bo14bobo27bo $bo59bo91bobo14bo$108bo45bo25bo$107bobo6bo62bobo$108bo6bobo62bo$116bo$ 198bo$197bobo$198bo$262bo$261bobo$92bo169bo$91bobo$92bo78bo69bo$170bob o67bobo$171b2o68bo3$20bo$19bobo219bo$20bo217bob2o$241bo51bo$6b2o284bob o$5bobo257b2o26bo$6bo26bo52bo12bo165bobo$32bobo50bobo10bobo165bo$33bo 52bo11b2o137bo$170bo65bobo41bo$169bobo65bo34bo6bobo$170bo100bobo6bo$ 272bo$157bo$156bobo69bo$157bo69bobo$181bo46bo$180bobo$5bo175bo40bo27b 2o$4bobo214bobo20bo5bobo12bo$5bo216bo20bobo5bo12bobo$244bo20bo4$175bo$ 174bobo37bo$175bo37bobo$214bo3$156bo14bo$155bobo12bobo55bo11bo$156bo 14bo55bobo9bobo$206bo21bo11bo$205bobo$206bo4$220bo$219bobo$160bo14bo 22bo21bo$159bobo12bobo20bobo$160bo14bo22bo2$179bo$178bobo$138bo40bo32b o$137bobo71bobo$138bo51bo21bo$189bobo$190bo$101bo$100bobo$101bo$204bo$ 87b2o114bobo$86bobo73b2o40bo$87bo26bo16bo30bobo$113bobo14bobo30bo$114b o16bo47bo$178bobo$82bo82bo13bo$81bobo80bobo$82bo82bo24bo$113bo75bobo$ 112bobo75bo$113bo$103bo$102bobo$103bo43b2o$129bo17bobo12bo$84bo14bo28b obo17bo12bobo$83bobo12bobo27b2o32bo$84bo14bo9$80bo14bo$79bobo12bobo$ 80bo14bo4$104bo$103bobo$104bo6$89bo$88bobo$89bo3$94bo$93bobo$94bo27$ 120bo$119bobo136bo$120bo136bobo$258bo2$130bo$129bobo12bo$130bo12bobo$ 144b2o$275bo$274bobo$9bo265bo$8bobo$9bo116bo$125bobo$126bo132bo$258bob o$259b2o4$82bo$74bo6bobo$73bobo6bo$74bo116bo$95bo94bobo75bo$88bo5bobo 94bo75bobo$15b2o70bobo5bo26b2o75bo68bo$bo12bobo44bo26b2o31bobo46bo27bo bo$obo12bo44bobo59bo31bo14bobo27bo$bo59bo91bobo14bo$108bo45bo25bo$107b obo6bo62bobo$108bo6bobo62bo$116bo$198bo$197bobo$198bo$262bo$261bobo$ 92bo169bo$91bobo$92bo78bo69bo$170bobo67bobo$171b2o68bo3$20bo$19bobo 219bo$20bo217bob2o$241bo51bo$6b2o284bobo$5bobo257b2o26bo$6bo26bo52bo 12bo165bobo$32bobo50bobo10bobo165bo$33bo52bo11b2o137bo$170bo65bobo41bo $169bobo65bo34bo6bobo$170bo100bobo6bo$272bo$157bo$156bobo69bo$157bo69b obo$181bo46bo$180bobo$5bo175bo40bo27b2o$4bobo214bobo20bo5bobo12bo$5bo 216bo20bobo5bo12bobo$244bo20bo4$175bo$174bobo37bo$175bo37bobo$214bo3$ 156bo14bo$155bobo12bobo55bo11bo$156bo14bo55bobo9bobo$206bo21bo11bo$ 205bobo$206bo4$220bo$219bobo$160bo14bo22bo21bo$159bobo12bobo20bobo$ 160bo14bo22bo2$179bo$178bobo$138bo40bo32bo$137bobo71bobo$138bo51bo21bo $189bobo$190bo$101bo$100bobo$101bo$204bo$87b2o114bobo$86bobo73b2o40bo$ 87bo26bo16bo30bobo$113bobo14bobo30bo$114bo16bo47bo$178bobo$82bo82bo13b o$81bobo80bobo$82bo82bo24bo$113bo75bobo$112bobo75bo$113bo$103bo$102bob o$103bo43b2o$129bo17bobo12bo$84bo14bo28bobo17bo12bobo$83bobo12bobo27b 2o32bo$84bo14bo9$80bo14bo$79bobo12bobo$80bo14bo4$104bo$103bobo$104bo6$ 89bo$88bobo$89bo3$94bo$93bobo$94bo27$120bo$119bobo136bo$120bo136bobo$ 258bo2$130bo$129bobo12bo$130bo12bobo$144b2o$275bo$274bobo$9bo265bo$8bo bo$9bo116bo$125bobo$126bo132bo$258bobo$259b2o4$82bo$74bo6bobo$73bobo6b o$74bo116bo$95bo94bobo75bo$88bo5bobo94bo75bobo$15b2o70bobo5bo26b2o75bo 68bo$bo12bobo44bo26b2o31bobo46bo27bobo$obo12bo44bobo59bo31bo14bobo27bo $bo59bo91bobo14bo$108bo45bo25bo$107bobo6bo62bobo$108bo6bobo62bo$116bo$ 198bo$197bobo$198bo$262bo$261bobo$92bo169bo$91bobo$92bo78bo69bo$170bob o67bobo$171b2o68bo3$20bo$19bobo$20bo$293bo$6b2o284bobo$5bobo257b2o26bo $6bo26bo52bo12bo165bobo$32bobo50bobo10bobo165bo$33bo52bo11b2o137bo$ 170bo65bobo41bo$169bobo65bo34bo6bobo$170bo100bobo6bo$272bo$157bo$156bo bo69bo$157bo69bobo$181bo46bo$180bobo$5bo175bo40bo27b2o$4bobo214bobo20b o5bobo12bo$5bo216bo20bobo5bo12bobo$244bo20bo4$175bo$174bobo37bo$175bo 37bobo$214bo3$156bo14bo$155bobo12bobo55bo11bo$156bo14bo55bobo9bobo$ 206bo21bo11bo$205bobo$206bo4$220bo$219bobo$160bo14bo22bo21bo$159bobo 12bobo20bobo$160bo14bo22bo2$179bo$178bobo$138bo40bo32bo$137bobo71bobo$ 138bo51bo21bo$189bobo$190bo$101bo$100bobo$101bo$204bo$87b2o114bobo$86b obo73b2o40bo$87bo26bo16bo30bobo$113bobo14bobo30bo$114bo16bo47bo$178bob o$82bo82bo13bo$81bobo80bobo$82bo82bo24bo$113bo75bobo$112bobo75bo$113bo $103bo$102bobo$103bo43b2o$129bo17bobo12bo$84bo14bo28bobo17bo12bobo$83b obo12bobo27b2o32bo$84bo14bo9$80bo14bo$79bobo12bobo$80bo14bo4$104bo$ 103bobo$104bo6$89bo$88bobo$89bo3$94bo$93bobo$94bo27$120bo$119bobo136bo $120bo136bobo$258bo2$130bo$129bobo12bo$130bo12bobo$144b2o$275bo$274bob o$9bo265bo$8bobo$9bo116bo$125bobo$126bo132bo$258bobo$259b2o4$82bo$74bo 6bobo$73bobo6bo$74bo116bo$95bo94bobo75bo$88bo5bobo94bo75bobo$15b2o70bo bo5bo26b2o75bo68bo$bo12bobo44bo26b2o31bobo46bo27bobo$obo12bo44bobo59bo 31bo14bobo27bo$bo59bo91bobo14bo$108bo45bo25bo$107bobo6bo62bobo$108bo6b obo62bo$116bo$198bo$197bobo$198bo$262bo$261bobo$92bo169bo$91bobo$92bo 78bo69bo$170bobo67bobo$171b2o68bo3$20bo$19bobo$20bo$293bo$6b2o284bobo$ 5bobo257b2o26bo$6bo26bo52bo12bo165bobo$32bobo50bobo10bobo165bo$33bo52b o11b2o137bo$170bo65bobo41bo$169bobo65bo34bo6bobo$170bo100bobo6bo$272bo $157bo$156bobo69bo$157bo69bobo$181bo46bo$180bobo$5bo175bo40bo27b2o$4bo bo214bobo20bo5bobo12bo$5bo216bo20bobo5bo12bobo$244bo20bo4$175bo$174bob o37bo$175bo37bobo$214bo3$156bo14bo$155bobo12bobo55bo11bo$156bo14bo55bo bo9bobo$206bo21bo11bo$205bobo$206bo4$220bo$219bobo$160bo14bo22bo21bo$ 159bobo12bobo20bobo$160bo14bo22bo2$179bo$178bobo$138bo40bo32bo$137bobo 71bobo$138bo51bo21bo$189bobo$190bo$101bo$100bobo$101bo$204bo$87b2o114b obo$86bobo73b2o40bo$87bo26bo16bo30bobo$113bobo14bobo30bo$114bo16bo47bo $178bobo$82bo82bo13bo$81bobo80bobo$82bo82bo24bo$113bo75bobo$112bobo75b o$113bo$103bo$102bobo$103bo43b2o$129bo17bobo12bo$84bo14bo28bobo17bo12b obo$83bobo12bobo27b2o32bo$84bo14bo9$80bo14bo$79bobo12bobo$80bo14bo4$ 104bo$103bobo$104bo6$89bo$88bobo$89bo3$94bo$93bobo$94bo27$120bo$119bob o136bo$120bo136bobo$258bo2$130bo$129bobo12bo$130bo12bobo$144b2o$275bo$ 274bobo$9bo265bo$8bobo$9bo116bo$125bobo$126bo132bo$258bobo$259b2o4$82b o$74bo6bobo$73bobo6bo$74bo116bo$95bo94bobo75bo$88bo5bobo94bo75bobo$15b 2o70bobo5bo26b2o75bo68bo$bo12bobo44bo26b2o31bobo46bo27bobo$obo12bo44bo bo59bo31bo14bobo27bo$bo59bo91bobo14bo$108bo45bo25bo$107bobo6bo62bobo$ 108bo6bobo62bo$116bo$198bo$197bobo$198bo$262bo$261bobo$92bo169bo$91bob o$92bo78bo69bo$170bobo67bobo$171b2o68bo3$20bo$19bobo$20bo$293bo$6b2o 284bobo$5bobo257b2o26bo$6bo26bo52bo12bo165bobo$32bobo50bobo10bobo165bo $33bo52bo11b2o137bo$170bo65bobo41bo$169bobo65bo34bo6bobo$170bo100bobo 6bo$272bo$157bo$156bobo69bo$157bo69bobo$181bo46bo$180bobo$5bo175bo40bo 27b2o$4bobo214bobo20bo5bobo12bo$5bo216bo20bobo5bo12bobo$244bo20bo4$ 175bo$174bobo37bo$175bo37bobo$214bo3$156bo14bo$155bobo12bobo55bo11bo$ 156bo14bo55bobo9bobo$206bo21bo11bo$205bobo$206bo4$220bo$219bobo$160bo 14bo22bo21bo$159bobo12bobo20bobo$160bo14bo22bo2$179bo$178bobo$138bo40b o32bo$137bobo71bobo$138bo51bo21bo$189bobo$190bo$101bo$100bobo$101bo$ 204bo$87b2o114bobo$86bobo73b2o40bo$87bo26bo16bo30bobo$113bobo14bobo30b o$114bo16bo47bo$178bobo$82bo82bo13bo$81bobo80bobo$82bo82bo24bo$113bo 75bobo$112bobo75bo$113bo$103bo$102bobo$103bo43b2o$129bo17bobo12bo$84bo 14bo28bobo17bo12bobo$83bobo12bobo27b2o32bo$84bo14bo9$80bo14bo$79bobo 12bobo$80bo14bo4$104bo$103bobo$104bo6$89bo$88bobo$89bo3$94bo$93bobo$ 94bo! #CXRLE Pos=-40,-537 #C [[ COLOR ALIVE 255 255 255 ]] #C [[ COLOR ALIVERAMP Aqua ]] #C [[ COLOR DEAD 0 128 64 ]] #C [[ COLOR DEADRAMP 64 128 0 ]] #C [[ THUMBNAIL WIDTH 800 HEIGHT 800 ZOOM 2 ]]

Phase meter

The following phase meter, built on January 6, 2021,[2] measures the phase difference between two T-ships. Advancing the bottom-left one by n generations ( 0 ≤ n ≤ 189 ) causes the pattern to emit n T-ships on the location marked with a ghost T-ship at period-1024:

x=303, y = 163, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c 207bo$206bobo$207bo6$201bobo$202bo2$202bo2$201bo$200bobo$201bo$288bo$ 287bobo$288bo3$200bo65bo$199bobo63bobo$200bo65bo$147bo$146bobo83bo$ 147bo83bobo31bo$205bo26bo31bobo$204bobo57b2o$205b2o2$219bo$218bobo$ 219bo$189bo$134bo46bo6bobo47bo$133bobo44bobo6bo47bobo$134bo46bo56bo2$ 195bo$153b2o39bobo73bo$152bobo13bo26b2o72bobo$153bo13bobo86bo13bo$168b o86bobo$256bo$152bo$151bobo$152bo$240bo$239bobo$240b2o3$199bo$198bobo$ 199bo11$193bo$192bobo$193bo$233bo$232bobo$233bo3$201b2o$201bobo78bo$ 202bo69bo$271bobo8bo$248b2o22bo8b3o$247bobo$186bo61bo36b2o$185bobo97bo bo$186bo64bo7bo26bo$227b2o21bobo5bobo$227bobo21bo7bo$228bo$291bo$204bo 85bobo$203bobo23bo61bo$204bo23bobo$229bo4$290bo$289bobo$290bo11$284bo$ 283bobo$284bo5$249bo$248bobo$249bo4$142b2o$137bo3bobo$136bobo3bo$137bo 2$156bo$155bobo$156bo86bo$242bobo$243bo8$3bo92b2o$ob2o92b3o$3bo92bo2$ 246b2o$201bo44bobo12bo$132bo67bobo44bo12bobo22b2o$131bobo67bo12bo46bo 22bobo$obobo87bo3bobobo3bobobo23bo80bobo69bo$214b2o$o3bo87bo3bo3bo3bo 3bo2$o3bo87bo3bobobo3bobobo192bo$300bobo$o3bo87bo3bo3bo7bo192bo2$obobo 87bo3bobobo3bobobo3$283bo$282bobo$283bo2$208bo$207bobo$208bo! #C [[ COLOR ALIVE 255 255 255 ]] #C [[ COLOR ALIVERAMP Aqua ]] #C [[ COLOR DEAD 0 128 64 ]] #C [[ COLOR DEADRAMP 64 128 0 ]] #C [[ THUMBNAIL WIDTH 800 HEIGHT 600 ZOOM 2 ]]

Caber tossers

The first caber tosser was completed on January 7, 2021,[3] where a c/2 T-ship approaches two 3c/20 spaceships and gets reflected on the same lane, which then is received by a stable regulator driven by p294 gun. The key boat is destroyed at generations 380, 2018, 5294, 11300, 22220, 42968, 81188, 152168, ..., liberating a T-ship at generations 3, 9, 20, 40, 78, 148, 278, 520, ... *294. The following pattern uses an optimized p294 gun.

x=119, y = 90, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c 34bo$33bobo$34bo$8bo$7bobo12bo$8bo12bobo$22b2o$52bo$51bobo11bo$52bo4$ 11bo24bo27bob4obo$10bobo16bo5bobo24b3o2bo2b3o$11bo16bobo5b2o26bob4obo$ 29bo29bo$58bobo$59bo2$65bo2$70bo$44b2o$4bo38bobo24bobo$3bobo38bo$4bo 61bo$47bo23bo3bo2bo2bo$23b2o21bobo20bo7bo$23bobo21bo21bo2b3obo2bo2bo$ 24bo44bo7bo$15bo55bo3bo2bo2bo$14bobo49bo$15bo9bo$24bobo43bobo$25bo$70b o13bo$83bobo$64bo19bo$63bobo3bo$64bo3bobo$69b2o3$75bo5bo$74bobo3bobo$ 68bo4b2o2bo3bo$67bobo4b2obo$68bo5bobo$20bo52b3o$19bobo51bo$20bo52bo2bo $67bo2b3ob3o$6b2o58b5o2bo$5bobo57bo2bobo2bo$6bo26bo15bo16bo2bo2b2o$32b obo13bobo15b3o$33bo15bo16b2o$67bobo$bo66b3o$obo51bo14bo$bo51bobo$54bo 19bo$73bobo31bo$74bo31bobo$107bo2$2bo$bobo35bo61bo$2bo35bobo59bobo$39b o60b2o3$40bo$39bobo75bo$40bo26bo48bobo$67b2obo46bo$67bo2$56b2o$8bo46bo bo$7bobo46bo$8bo2$55bo$54bobo$55bo$106bo$105bobo$106bo! #C [[ COLOR ALIVE 255 255 255 ]] #C [[ COLOR ALIVERAMP Aqua ]] #C [[ COLOR DEAD 0 128 64 ]] #C [[ COLOR DEADRAMP 64 128 0 ]] #C [[ THUMBNAIL WIDTH 800 HEIGHT 600 ZOOM 4 ]]

Previously, a design with only stable circuitry failed with 3c/20o spaceships. After the discovery of sparky 16c/34o spaceships, it becomes functional and even can be adjusted.[4]

x=69, y = 103, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c 2bo$b3o$b3o44$15bo$14bobo$15bo$11bo$10bobo$11bo$34bo$33bobo$34bo3$57bo $56b3o$56bo$55bo$54b3o3b2o$bo19b2o36bo$obo17bobo36bo$bo19bo38b2o2$66b 3o$20bo47bo$19bobo42bo3bo$20bo30bo2bo2bo2b2obo$24bo26b2obob2obob3o3bo$ 23bobo11b2o12bo2bo2bo2b2obo$24bo12b3o24bo3bo$37b2o29bo$10b2o54b3o$9bob o31b2o$10bo26bo5bobo$36bobo5bo12bo$37bo18bobo$57bo4$58bo2$66b3o$68bo$ 8bo55bo3bo$7bobo41bo2bo2bo2b2obo$8bo42b2obob2obob3o3bo$51bo2bo2bo2b2ob o$64bo3bo$68bo$66b3o2$60b2o$59bo$59bo$54b3o3b2o$55bo$56bo$56b3o$57bo! #C [[ COLOR ALIVE 255 255 255 ]] #C [[ COLOR ALIVERAMP Aqua ]] #C [[ COLOR DEAD 0 128 64 ]] #C [[ COLOR DEADRAMP 64 128 0 ]] #C [[ THUMBNAIL WIDTH 800 HEIGHT 600 ZOOM 4 ]]

In the pattern above, the n-th T-ship is emitted and arrive at the shown location at generation 1963*(33n-1)/16 for any natural number n. The multiplier 1963 can be adjusted to any odd number larger than 1963 by simply moving the components:

  • Moving the 16c/34o spaceship to the right for x cells adds 34x to the multiplier,
  • Moving the c/2 T-ship to the left for x cells adds 32x to the multiplier,
  • Moving the duplicator and 90-degree reflector to the left for x cells adds 2x to the multiplier.

Sqrtgun

The following sqrtgun was completed on January 18, 2021. [5] For any natural number n, the n-th T-ship is emitted at generation 4n2+1443n.

x=160, y = 160, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c 119bo$119bo$119bo9$140bo$139bobo$130bo9bo$129bobo$59bo70bo$58bobo$59bo $108bo49bo$107bobo47bobo$108bo49bo3$107bo$106bobo33bo$106b2o33bobo$ 142b2o2$48bo$47bobo$48bo3$69bo$64bo3bobo$63bobo3bo$63b2o2$109bo$108bob o$109bo$54bo$47bo5bobo$46bobo5bo$47bo2$53bo19bo$52bobo17bobo29bo$52b2o 19bo29bobo$29bo74bo$28bobo$29bo4$45bo$44bobo$44b2o36bo$81bobo$63bo18bo $62bobo$63bo4b2o$35bo23bo7bobo31b2o$19bo14bobo21bobo7bo26bo5bobo$18bob o14bo23bo34bobo5bo$19bo75bo2$34bo19bo48bo$33bobo17bobo46bobo$33b2o19bo 48bo$bo$obo$bo123bo$124bobo$66bo58bo$65bobo$17bo8bo39bo31bo$16bobo6bob o69bobo$16b2o8bo71bo$22bo$21bobo20bo$22bo20bobo$44bo$40bo$39bobo$40bo 4$109bo$108bobo$109bo$12bo19b2o$11bobo17bobo$12bo19bo55bo$87bobo3bo$ 88bo3bobo$31bo61b2o$30bobo$31bo122bo$153bobo$141bo12bo$140bobo$140b2o$ 35bo$34bobo$35bo2$21b2o$20bobo$21bo26bo59bo$47bobo57bobo$48bo59bo3$ 107bo$106bobo$106b2o39bo$63bo82bobo$62bobo82bo$63bo62bo$19bo105bobo$ 18bobo28b2o75bo$19bo28bobo$49bo26bo$75bobo$76bo5$113bo$112bobo$113bo2$ 47bo$46bobo$47bo67b2o$89bo20bo3bobo$88bobo18bobo3bo$89bo12bo7bo$101bob o$102b2o$131bo$117bo12bobo$117b2obo10bo$117bo$128bo$127bobo$128bo7$96b o25bo$95bobo17bo3bob2o$96bo17bobo5bo$115bo! #C [[ COLOR ALIVE 255 255 255 ]] #C [[ COLOR ALIVERAMP Aqua ]] #C [[ COLOR DEAD 0 128 64 ]] #C [[ COLOR DEADRAMP 64 128 0 ]] #C [[ THUMBNAIL WIDTH 800 HEIGHT 800 ZOOM 4 ]]

A prototype, as shown below, was completed on January 12, 2021. [6] The T-ship outputs are distributed in a similar fasion to those from a sqrtgun, but due to the dominating blinker puffers the overall population growth is linear.

x=123, y = 134, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c 9bo83b3o$8bobo81bo2bo17b3o$9bo82bo19bo2bo$92b3o4bo12bo$96bo2b2o11b3o4b o$97b3o16bo2b2o$57bo38bobo18b3o$56bobo36bo20bobo$57bo42b3o12bo$102bo 17b3o$99bo2bo19bo$98bo2bo17bo2bo$62b2o32bo21bo2bo$62b3o26bo4bo2bo16bo$ 62b2o32b3o12bo4bo2bo$91bo24b3o$15b2o73b3o18bo$14bobo93b3o$2bo12bo83bo$ bobo92bob2o19bo$2bo24bo71bo16bob2o$26bobo48bo41bo$27bo46bob2o3bo3bo11b o$77bo3bo3bo11bo$81bo3bo11bo$119bo$99bo16bob2o$82bo13bob2o19bo$62bo18b obo15bo$61bobo3bo14bo27b3o$40bo21bo3bobo21b3o18bo$39bobo25b2o22bo24b3o $40bo55b3o12bo4bo2bo$91bo4bo2bo16bo$96bo21bo2bo$41bo56bo2bo17bo2bo$40b obo56bo2bo19bo$41bo60bo17b3o$100b3o12bo$22bo72bo20bobo$21bobo3bo68bobo 18b3o$22bo3bobo68b3o16bo2b2o$27b2o67bo2b2o11b3o4bo$92b3o4bo12bo$92bo 19bo2bo$92bo2bo17b3o$93b3o$26bo$25bobo$26bo10$76bo$32bo42bobo$31bobo 42bo$32bo7$63bo$62bobo$63bo$70bo$69bobo$28b2o40bo$27bobo$15bo12bo$14bo bo$15bo$50bo$49bobo$50bo2$47bo$46bobo$47bo$73b2o$73bobo$68bo5bo12bo$ 63bo3bobo16bobo$62bobo3bo18bo$62b2o4$67bo$66bobo$54bo12bo$53bobo$53b2o $20bo$19bobo$20bo2$6b2o$5bobo$6bo26bo$32bobo$33bo2$bo$obo$bo$60bo$59bo bo$60bo3$2bo$bobo$2bo11$8bo$7bobo$8bo! #C [[ COLOR ALIVE 255 255 255 ]] #C [[ COLOR ALIVERAMP Aqua ]] #C [[ COLOR DEAD 0 128 64 ]] #C [[ COLOR DEADRAMP 64 128 0 ]] #C [[ THUMBNAIL WIDTH 800 HEIGHT 800 ZOOM 4 ]]

T-to-24c/48o converter, infinite distinct 48c/96o spaceship gun and T-to-rake converter

This is a stable converter that takes a T-ship and gives a 24c/48o spaceship at recovery time 142.

x=144, y = 273, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c 66bo10bo$65bobo8bobo$66bo10bo93$36bo70bo$35bobo68bobo$36bo70bo3$35bo 72bo$34bobo27bo14bo27bobo$34b2o27bobo12bobo27b2o$17bo46bo14bo46bo$16bo bo106bobo$17bo108bo8$30bo82bo$29bobo8bo62bo8bobo$30bo8bobo60bobo8bo$ 40bo62bo2$31bo80bo$30bobo78bobo$31bo80bo2$12bo118bo$11bobo3bo108bo3bob o$12bo3bobo106bobo3bo$4bo12b2o106b2o12bo$3bobo132bobo$4bo134bo8$40bo 62bo$39bobo60bobo$40bo62bo2$5bo132bo$4bobo130bobo$5b2o21bo86bo21b2o$ 27bobo84bobo$28bo86bo7$37b2o66b2o$37bobo64bobo$21bo16bo66bo16bo$20bobo 98bobo$21bo100bo$39bo64bo$38bobo62bobo$39bo64bo3$61bo20bo$60bobo18bobo $61bo20bo7$142bo$141bobo$129bo12bo$128bobo$128b2o$61bo$60bobo$61bo5$bo $obo$bo12bo$13bobo58bo$14b2o57bobo$74bo$135bo$77bo56bobo$76bobo56bo$ 77bo3$56bo$55bobo3bo$56bo3bobo$61b2o2$64b3o$8bo56bo$7bobo$8bo56bo68$ 64b3o$65bo2$65bo! #C [[ COLOR ALIVE 255 255 255 ]] #C [[ COLOR ALIVERAMP Aqua ]] #C [[ COLOR DEAD 0 128 64 ]] #C [[ COLOR DEADRAMP 64 128 0 ]] #C [[ THUMBNAIL WIDTH 800 HEIGHT 800 ZOOM 4 Y -20 ]]

With the construction of sqrtgun, a related infinite distinct 48c/96o spaceship gun (as in Pattern of the Year 2018) can be made:[5]

x=240, y = 226, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c 119bo$119bo$119bo9$140bo$139bobo$130bo9bo$129bobo$59bo70bo$58bobo$59bo $108bo49bo$107bobo47bobo$108bo49bo3$107bo$106bobo33bo$106b2o33bobo$ 142b2o2$48bo$47bobo$48bo3$69bo$64bo3bobo$63bobo3bo$63b2o2$109bo$108bob o$109bo$54bo$47bo5bobo$46bobo5bo$47bo2$53bo19bo$52bobo17bobo29bo$52b2o 19bo29bobo$29bo74bo$28bobo$29bo4$45bo$44bobo$44b2o36bo$81bobo$63bo18bo $62bobo$63bo4b2o$35bo23bo7bobo31b2o$19bo14bobo21bobo7bo26bo5bobo$18bob o14bo23bo34bobo5bo$19bo75bo2$34bo19bo48bo$33bobo17bobo46bobo$33b2o19bo 48bo$bo$obo$bo123bo$124bobo$66bo58bo$65bobo$17bo8bo39bo31bo$16bobo6bob o69bobo$16b2o8bo71bo$22bo$21bobo20bo$22bo20bobo$44bo$40bo$39bobo$40bo 4$109bo$108bobo$109bo$12bo19b2o$11bobo17bobo$12bo19bo55bo$87bobo3bo$ 88bo3bobo$31bo61b2o$30bobo$31bo122bo$153bobo$141bo12bo$140bobo49bo$ 140b2o49bobo$35bo156bo$34bobo$35bo133bo$168bobo$21b2o146bo$20bobo$21bo 26bo59bo$47bobo57bobo$48bo59bo$151bo$150bobo$107bo43bo$106bobo$106b2o 39bo$63bo82bobo36b2o$62bobo82bo19bo17bobo$63bo62bo39bobo17bo12bo$19bo 105bobo38b2o30bobo$18bobo28b2o75bo72bo$19bo28bobo$49bo26bo$75bobo$76bo 117b2o$194bobo3bo$195bo3bobo$200bo2$113bo67bo$112bobo65bobo$113bo67bo$ 118b3o$47bo70b3o$46bobo70bo$47bo67b2o$89bo20bo3bobo$88bobo18bobo3bo$ 89bo12bo7bo$101bobo$102b2o$131bo$130bobo$131bo2$128bo28bo$127bobo26bob o$128bo28bo68bo$225bobo$216bo9bo11bo$156bo19bo38bobo19bobo$155bobo17bo bo38bo21bo$155b2o19bo2$96bo$95bobo17bo$96bo17bobo$115bo6$166bo$165bobo $166bo$162bo$161bobo$162bo4$216bo21bo$215bobo19bobo$216bo9bo11bo$225bo bo$226bo16$181bo$180bobo$181bo2$200bo$195bo3bobo$194bobo3bo$194b2o4$ 199bo$178b2o18bobo$178bobo5bo12bo$179bo5bobo$185b2o3$163bo$162bobo$ 163bo5$181bo$180bobo$181bo2$192bo$191bobo$192bo! #C [[ COLOR ALIVE 255 255 255 ]] #C [[ COLOR ALIVERAMP Aqua ]] #C [[ COLOR DEAD 0 128 64 ]] #C [[ COLOR DEADRAMP 64 128 0 ]] #C [[ THUMBNAIL WIDTH 800 HEIGHT 800 ZOOM 2 X 70 Y -50 ]]

An associated stable converter, completed on January 30, takes a T-ship and gives a 24c/48o siderake at recovery time 589. Reducing the recovery time would result in a rise in bounding box.

x=251, y = 116, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c 42bo130bo$41bobo128bobo$42bo100bo29bo$72bo69bobo$71bobo68bobo$72bo70bo 3$71bo72bo$70bobo27bo14bo27bobo$70b2o27bobo12bobo27b2o$100bo14bo2$31bo 152bo$30bobo150bobo$31bo152bo3$52bo110bo$47bo3bobo108bobo3bo$46bobo3bo 110bo3bobo$30bo15b2o120b2o15bo$29bobo44bo62bo44bobo$30bo44bobo60bobo 44bo$34bo41bo62bo41bo$19bo13bobo144bobo48bo$18bobo13bo146bo48bobo$19bo 211bo5$bo247bo$obo80bo48bo115bobo$bo80bobo46bobo115bo$83bo48bo$63bo88b o$23b2o19bo17bobo86bobo17bo19b2o$17bo5bobo17bobo17bo14bo58bo14bo17bobo 17bobo31bo8bo$16bobo5bo19bo32bobo56bobo32bo19bo31bobo6bobo$16b2o60bo 58bo86bo8b2o$62bo90bo74bo$25bo35bobo88bobo35bo21bo14bobo$24bobo34b2o 90b2o34bobo19bobo14bo$25bo15bo132bo15bo21bo$40bobo130bobo$41bo51bo28bo 51bo$92bobo26bobo$27b2o64bo28bo64b2o$26bobo158bobo4bo$27bo26bo106bo26b o4bobo$53bobo104bobo31bo$54bo106bo$78bo58bo$77bobo56bobo78b2o19bo$67bo 10bo58bo10bo61bo6bobo17bobo$66bobo78bobo59bobo6bo19bo$67bo80bo60b2o$ 138bo$137bobo79bo$138bo79bobo$4bo20bo164bo28bo$3bobo12bo5bobo162bobo$ 4bo12bobo5bo164bo$18b2o$156bo$155bobo$156bo4$79bo60bo80b2o$78bobo12bo 45bobo78bobo$79bo12bobo45b2o79bo$93b2o3$237bo$12bo223bobo$11bobo223bo$ 12bo4$125bo93bo$124bobo91bobo$125bo93bo2$87bo$86bobo35bo$87bo35bobo$ 123b2o$200bo$87bo111bobo$84bob2o112bo$87bo$151bo$150bobo46bo$151bo46bo bo$198b2o2$135bo$134bobo81bo$129bo5bo81bobo$128bobo87bo$129bo2$144bo$ 143bobo$144bo4$205bo$204bobo$205bo! #C [[ COLOR ALIVE 255 255 255 ]] #C [[ COLOR ALIVERAMP Aqua ]] #C [[ COLOR DEAD 0 128 64 ]] #C [[ COLOR DEADRAMP 64 128 0 ]] #C [[ THUMBNAIL WIDTH 1100 HEIGHT 600 ZOOM 4 Y -20 ]]

T-to-c/4o spaceship converter and c/4o 180-degree reflector

The device has a recovery time of 137 ticks due to the edge-shooter, and it is moderately edge-shooting.[7]

x=248, y = 140, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c 31bo$30bobo$31bo93bo$124bobo$125bo5$143bo$142bobo$143bo3$36b2o$35bobo 35bo53bo$36bo35bobo51bobo$73bo43bo9b2o$19bo96bobo3bo$18bobo14bo81bo3bo bo$19bo14bobo85bo$35bo5$23bo20bo52bo$22bobo12bo5bobo34bo15bobo$23bo12b obo5bo26bo7bobo15bo$37b2o31bobo7bo$70b2o4bo$75bobo33b2o19bo$57bo18bo 34bobo17bobo$56bobo53bo19bo$57bo2$110bo2bo$25bo83bob2obo$24bobo83bo2bo $17bo7bo$16bobo94bo$17bo94bobo$113bo$66bo19b2o$65bobo17bobo$66bo19bo5b o64bo$91bobo3bo58bobo$35bo56bo3bobo58bo$34bobo48bo11b2o$35bo48bobo27bo $85bo27bobo$114bo$17bo92bo$16bobo90bobo$17bo92bo2$128bo$127bobo$49bo 78bo26bo8bo$36bo11bobo103bobo6bobo$35bobo11bo104b2o8bo$36bo123bo$75b2o 64bo17bobo$50bo23bobo63bobo17bo$49bobo23bo65bo$23bo26b2o48bo19b2o$22bo bo74bobo17bobo$23bo76bo19bo$91bo$90bobo$91bo27bo57bo68b2o$118bobo56b2o bo64b3o$119bo57bo68b2o2$150bo19b2o$73bo75bobo17bobo$72bobo75bo19bo$45b o27bo$12bo31bobo$11bobo31bo123bo$12bo155bobo$169bo2$30bo$29bobo$30bo6$ 12bo$11bobo$12bo7bo$19bobo$20bo3$103bo$102bobo$103bo2$116b2o$32b2o82bo bo$18bo12bobo56bo26bo$17bobo12bo56bobo$18bo71bo9$119bo$118bobo$119bo$ 16bo$11bo3bobo$10bobo3bo$11bo2$159b2o$158bobo$159bo4$175bo$174bobo$ 175bo$bo19b2o$obo17bobo$bo19bo2$157bo$20bo135bobo$19bobo135bo$20bo! #C [[ COLOR ALIVE 255 255 255 ]] #C [[ COLOR ALIVERAMP Aqua ]] #C [[ COLOR DEAD 0 128 64 ]] #C [[ COLOR DEADRAMP 64 128 0 ]] #C [[ THUMBNAIL WIDTH 800 HEIGHT 800 ZOOM 4 X -30 Y -20 ]]

With the discovery of a c/4o-to-2T converter using a custom catalyst, it can be modified into a 180-degree reflector:[8]

x=177, y = 140, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c 31bo$30bobo$31bo93bo$124bobo$125bo5$143bo$142bobo$143bo3$36b2o$35bobo 35bo53bo$36bo35bobo51bobo$73bo43bo9b2o$19bo96bobo3bo$18bobo14bo81bo3bo bo$19bo14bobo85bo$35bo5$23bo20bo52bo$22bobo12bo5bobo34bo15bobo$23bo12b obo5bo26bo7bobo15bo$37b2o31bobo7bo$70b2o4bo$75bobo33b2o19bo$57bo18bo 34bobo17bobo$56bobo53bo19bo$57bo2$110bo2bo$25bo83bob2obo$24bobo83bo2bo $17bo7bo$16bobo94bo$17bo94bobo$113bo$66bo19b2o$65bobo17bobo$66bo19bo5b o64bo$91bobo3bo58bobo$35bo56bo3bobo58bo$34bobo48bo11b2o$35bo48bobo27bo $85bo27bobo$114bo$17bo92bo$16bobo90bobo$17bo92bo$169b3ob3o$128bo41b2ob 2o$127bobo41bobo$49bo78bo26bo8bo$36bo11bobo103bobo6bobo$35bobo11bo104b 2o8bo$36bo123bo$75b2o64bo17bobo$50bo23bobo63bobo17bo$49bobo23bo65bo$ 23bo26b2o48bo19b2o$22bobo74bobo17bobo$23bo76bo19bo$91bo$90bobo$91bo27b o$118bobo$119bo$175bo$150bo19bo3bobo$73bo75bobo17bobo3bo$72bobo75bo19b ob3o$45bo27bo97bo2bo$12bo31bobo$11bobo31bo122bo$12bo154bobo$168bo2$30b o$29bobo$30bo6$12bo$11bobo$12bo7bo$19bobo$20bo3$103bo$102bobo$103bo2$ 116b2o$32b2o82bobo$18bo12bobo56bo26bo$17bobo12bo56bobo$18bo71bo9$119bo $118bobo$119bo$16bo$11bo3bobo$10bobo3bo$11bo2$159b2o$158bobo$159bo4$ 175bo$174bobo$175bo$bo19b2o$obo17bobo$bo19bo2$157bo$20bo135bobo$19bobo 135bo$20bo! #C [[ COLOR ALIVE 255 255 255 ]] #C [[ COLOR ALIVERAMP Aqua ]] #C [[ COLOR DEAD 0 128 64 ]] #C [[ COLOR DEADRAMP 64 128 0 ]] #C [[ THUMBNAIL WIDTH 800 HEIGHT 800 ZOOM 4 Y -20 ]]

Quadratic sawtooth

The following quadratic sawtooth was constructed on February 13, 2021.[9]

x=391, y = 373, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c 145b2o5b2o10b2o5b2o$144bob2o3b2obo8bob2o3b2obo$144b3o5b3o8b3o5b3o$145b o7bo10bo7bo$149bo18bo$148b3o16b3o4$147bo3bo14bo3bo$149bo18bo$135b3o10b 3o16b3o10b3o$93bo41bobo10b3o16b3o10bobo41bo$92bobo40bo4b2o6b3o16b3o6b 2o4bo40bobo$93bo42b2o3b2o6bo18bo6b2o3b2o12bo29bo$123bo15b3o6bobo16bobo 6b3o14bobo$122bobo15bo8bo18bo8bo15bobo$123bo24b3o16b3o24bo$149bo18bo$ 148b3o16b3o$122bo72bo$121bobo27bo14bo27bobo$121b2o27bobo12bobo27b2o$ 151bo14bo2$82bo152bo$81bobo150bobo$82bo152bo3$103bo110bo$98bo3bobo108b obo3bo$97bobo3bo110bo3bobo$81bo15b2o120b2o15bo$80bobo44bo62bo44bobo$ 81bo44bobo60bobo44bo$85bo41bo62bo41bo$70bo13bobo144bobo48bo$69bobo13bo 146bo48bobo$70bo211bo5$52bo247bo$51bobo80bo48bo115bobo$52bo80bobo46bob o115bo$134bo48bo$114bo88bo$74b2o19bo17bobo86bobo17bo19b2o$68bo5bobo17b obo17bo14bo58bo14bo17bobo17bobo31bo8bo$67bobo5bo19bo32bobo56bobo32bo 19bo31bobo6bobo$67b2o60bo58bo86bo8b2o$113bo90bo74bo$76bo35bobo88bobo 35bo21bo14bobo$75bobo34b2o90b2o34bobo19bobo14bo$76bo15bo132bo15bo21bo$ 91bobo130bobo$92bo51bo28bo51bo$143bobo26bobo$78b2o64bo28bo64b2o$77bobo 158bobo4bo$78bo26bo106bo26bo4bobo$104bobo104bobo31bo$105bo106bo$129bo 58bo$128bobo56bobo78b2o19bo$118bo10bo58bo10bo61bo6bobo17bobo$117bobo 78bobo59bobo6bo19bo$118bo80bo60b2o$189bo$188bobo79bo$189bo79bobo$55bo 20bo164bo28bo$54bobo12bo5bobo162bobo$55bo12bobo5bo164bo$69b2o$207bo$ 206bobo$207bo4$130bo60bo80b2o$129bobo12bo45bobo78bobo$130bo12bobo45b2o 79bo$144b2o3$288bo56bo$63bo223bobo54bobo$62bobo223bo56bo$63bo4$270bo$ 269bobo$270bo2$138bo184bo$137bobo160bo21bobo$138bo160bobo21bo$300bo$ 251bo$250bobo85b2o$200bo50bo86bobo$199bobo137bo12bo$200bo150bobo$250bo 101bo$249bobo84bo$249b2o84bobo$336bo$189bo$188bobo78bo69bo$189bo78bobo 67bobo$269bo69bo$306b2o$305bobo$293bo12bo11bo$275bo16bobo22bobo3bo$ 274bobo16bo24bo3bobo$195bo79bo47b2o$194bobo$195bo$256bo$255bobo77bo$ 256bo77bobo$193bo128bo12bo$192bobo126bobo$193bo127b2o2$212bo$207bo3bob o50bo$206bobo3bo50bobo$206b2o56bo3$285bo$280bo3bobo$279bobo3bo$279b2o 3$328bo$327bobo$328bo$340b2o$316bo18bo3bobo$315bobo16bobo3bo$316bo12bo 5bo$328bobo$329b2o$356bo$355bobo6bo$356bo6bobo$364bo$353bo$352bobo$ 353bo5$333bo$332bobo42bo$333bo42bobo$340bo36bo$339bobo$340bo$357b2o$ 357bobo$358bo3$359bo$358bobo$257bo69bo31bo$256bobo67bobo$208bo48bo69bo $207bobo$208bo$256bo55bo$255bobo53bobo$255b2o55bo$335b2o$197bo137bobo 3bo$196bobo137bo3bobo$197bo143bo$283bo$282bobo37bo$283bo37bobo$108bo 88bo124bo$107bobo86bobo$108bo88bo69bo100b2o$266bobo99bobo3b2o$87bo173b o5bo101bo3bo2bo$86bobo171bobo111b2o$87bo173bo43b2o$97bo84bo122bobo47bo $96bobo82bobo92bo29bo12bo34bobo$97bo84bo92bobo40bobo3bo14bo15bo$209b2o 65bo42bo3bobo12bobo$115bo93bobo112bo14bo$114bobo65bo27bo12bo$115bo65bo bo20bo17bobo$182bobo18bobo17bo120bo$183bo20bo138bobo$344bo32b3o$376bo 2bo$88bo287bob2o$87bobo109bo$88b2o108bobo174bo$198b2o174b2obo$375b3o$ 376bo$331bo$330bobo55b2o$331bo55b2obo$388b3o$381bo7bo$371bobobob3o5bo$ 371b4ob5o4b2o$368bo2bobobob3o5bo$367bobo11bo7bo$368bo19b3o$387b2obo$ 388b2o9$388b2o$387b2obo$368bo19b3o$367bobo11bo7bo$368bo2bobobob3o5bo$ 371b4ob5o4b2o$371bobobob3o5bo$381bo7bo$388b3o$304b2o25bo55b2obo$304bob o23bobo55b2o$305bo25bo$376bo$375b3o$374b2obo$289bo85bo$288bobo$289bo 86bob2o$376bo2bo$344bo32b3o$343bobo$344bo2$306bo$305bobo16bo14bo$306bo 16bobo12bobo$324bo14bo15bo$354bobo$355bo2$374bo$369bo3bobo$368bobo3bo$ 368b2o2$322bo$321bobo$322bo2$341bo$336bo3bobo$335bobo3bo$335b2o2$61bo$ 60bobo$61bo$69bo$68bobo256bo$69bo256bobo$327bo31bo$358bobo$359bo2$87bo $79bo6bobo269bo$8bo5bo12bo5bo45b2obo4bo269bobo$7b3o3b3o10b3o3b3o44bo 277b2o$6b2obobobob2o8b2obobobob2o304bo$11bo18bo33b2o273bobo$63bobo5bo 268bo36bo$11bo18bo33bo5bobo260bo42bobo$2bo3bo9bo8bo9bo3bo31b2o259bobo 42bo$b3obo11bo6bo11bob3o292bo$2o2bo3bo5bo12bo5bo3bo2b2o21bo$b2o2bob2o 5b2o10b2o5b2obo2b2o21bobo$2bo7b3o16b3o7bo23bo44bo$10b3o16b3o$9bobobo 14bobobo75bo244bo$10bobo16bobo9bo65b3o242bobo$11bo18bo9bobo310bo$10bob o16bobo9bo322bo$11bo18bo325bo6bobo$355bobo6bo$356bo$329b2o$32bo78b2o 215bobo$31bobo77bobo202bo12bo5bo$32bo79bo202bobo16bobo3bo$316bo18bo3bo bo$340b2o$52bo$51bobo$52bo32bo266bo$47b2o35bobo227b2o35bobo$47bobo35bo 228bobo22bo12bo$48bo266bo22bobo$103bo234b2o$102bobo$103bo$113bo185bo$ 112bobo183bobo$38b2o73bo185bo$37bobo$25bo12bo53bo$24bobo53bo10bobo$25b o53bobo10bo$80bo$316bo$39bo275bobo$38bobo275bo$39bo305bo$344bobo$58bo 286bo$53bo3bobo$52bobo3bo$29b2o21b2o$28bobo$29bo44bo$73bobo$74bo3$56bo $55bobo$56bo128bo$184bobo$38bo146bo$37bobo$38bo$28bo76bo$27bobo74bobo$ 28bo48b2o26bo$77bobo$49bo28bo121b2o$48bobo109bo38bobo$49bo42bo64bob2o 39bo$84bo6bobo66bo$83bobo6bo110bo$84bo94b2o21bobo$179bobo21bo$180bo3$ 181bo15bo$180bobo13bobo$181bo15bo! #C [[ COLOR ALIVE 255 255 255 ]] #C [[ COLOR ALIVERAMP Aqua ]] #C [[ COLOR DEAD 0 128 64 ]] #C [[ COLOR DEADRAMP 64 128 0 ]] #C [[ THUMBNAIL WIDTH 800 HEIGHT 800 ZOOM 2 ]]

Linear sawtooth

As noted by toroidalet, a period-p stream of T-ship can be burnt with the 180-degree kickback reaction at a speed of ((p-2)/4)c/(p/2+1). When the period is 66, the burning speed matches the speed of 16c/34o spaceship, allowing for the construction of a linear sawtooth.[10] GUYTU6J found the following variant with a minimum population of 188 cells, which appears at generations 0, 1122, 39270, 1336302, ... , that is, any natural number of the form 34n+1-34. At generations of the form (34n+1-34)/2, the population is 40*(34n-1)/33+277.

x=70, y = 51, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c 8bo49bo$7bobo47b3o$8bo48bo$56bo$bo27bo25b3o3b2o$obo25bobo29bo$bo27bo 30bo$19bo41b2o$18bobo$5b3o11bo47b3o$4bo2bo61bo$bo2bo3bo56bo3bo$obobo3b o43bo2bo2bo2b2obo$bo3bo2bo43b2obob2obob3o3bo$52bo2bo2bo2b2obo$65bo3bo$ 69bo$67b3o2$26b2obo29bo$23b2obobo$23b2ob3o5$59bo2$67b3o$4b3ob2o59bo$4b obob2o55bo3bo$3bob2o45bo2bo2bo2b2obo$52b2obob2obob3o3bo$52bo2bo2bo2b2o bo$65bo3bo$69bo$67b3o$24bo2bo3bo$24bo3bobobo8bo2bo16b2o$24bo3bo2bo28bo $25bo2bo31bo$13bo11b3o27b3o3b2o$12bobo41bo$13bo43bo$3bo53b3o$2bobo53bo $3bo$42bo$24bo16bobo$23bobo16bo$24bo! #C [[ COLOR ALIVE 255 255 255 ]] #C [[ COLOR ALIVERAMP Aqua ]] #C [[ COLOR DEAD 0 128 64 ]] #C [[ COLOR DEADRAMP 64 128 0 ]] #C [[ THUMBNAIL WIDTH 800 HEIGHT 600 ZOOM 8 ]]

References

  1. GUYTU6J (September 14, 2020). Re: Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c) (discussion thread) at the ConwayLife.com forums
  2. GUYTU6J (January 3, 2021). Re: Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c) (discussion thread) at the ConwayLife.com forums
  3. GUYTU6J (January 7, 2021). Re: Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c) (discussion thread) at the ConwayLife.com forums
  4. GUYTU6J (February 19, 2021). Re: Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c) (discussion thread) at the ConwayLife.com forums
  5. 5.0 5.1 GUYTU6J (January 18, 2021). Re: Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c) (discussion thread) at the ConwayLife.com forums
  6. GUYTU6J (January 12, 2021). Re: Thread for basic non-CGOL questions (discussion thread) at the ConwayLife.com forums
  7. GUYTU6J (February 9, 2021). Re: Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c) (discussion thread) at the ConwayLife.com forums
  8. GUYTU6J (February 17, 2021). Re: Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c) (discussion thread) at the ConwayLife.com forums
  9. GUYTU6J (February 13, 2021). Re: Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c) (discussion thread) at the ConwayLife.com forums
  10. toroidalet (February 15, 2021). Re: Glimmering Garden (B3-jknr4ity5ijk6i8/S23-a4city6c7c) (discussion thread) at the ConwayLife.com forums