Sir Robin

Sir Robin
#N Sir Robin #O Adam P. Goucher, Tom Rokicki; 2018 #C The first elementary knightship to be found in Conway's Game of Life. #C http://conwaylife.com/wiki/282P6H2V1 x = 31, y = 79, rule = B3/S23 4b2o$4bo2bo$4bo3bo$6b3o$2b2o6b4o$2bob2o4b4o$bo4bo6b3o$2b4o4b2o3bo$o9b 2o$bo3bo$6b3o2b2o2bo$2b2o7bo4bo$13bob2o$10b2o6bo$11b2ob3obo$10b2o3bo2b o$10bobo2b2o$10bo2bobobo$10b3o6bo$11bobobo3bo$14b2obobo$11bo6b3o2$11bo 9bo$11bo3bo6bo$12bo5b5o$12b3o$16b2o$13b3o2bo$11bob3obo$10bo3bo2bo$11bo 4b2ob3o$13b4obo4b2o$13bob4o4b2o$19bo$20bo2b2o$20b2o$21b5o$25b2o$19b3o 6bo$20bobo3bobo$19bo3bo3bo$19bo3b2o$18bo6bob3o$19b2o3bo3b2o$20b4o2bo2b o$22b2o3bo$21bo$21b2obo$20bo$19b5o$19bo4bo$18b3ob3o$18bob5o$18bo$20bo$ 16bo4b4o$20b4ob2o$17b3o4bo$24bobo$28bo$24bo2b2o$25b3o$22b2o$21b3o5bo$ 24b2o2bobo$21bo2b3obobo$22b2obo2bo$24bobo2b2o$26b2o$22b3o4bo$22b3o4bo$ 23b2o3b3o$24b2ob2o$25b2o$25bo2$24b2o$26bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ TRACKLOOP 6 -1/6 -1/3 THUMBSIZE 2 HEIGHT 480 ZOOM 4 GPS 12 ]]
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Pattern type	Spaceship
Number of cells	282
Bounding box	31 × 79
Direction	Oblique
Slope	2
Period	6
Mod	6
Speed	(2,1)c/6 | (2,1)c/6
Heat	271
Discovered by	Adam P. Goucher Tomas Rokicki
Year of discovery	2018
Rules Outer-totalistic rules B3/S23 only # of rules 20 = 1 Isotropic rules B3/S23 – B3/S234ce
Pattern files RLE sirrobin.rle
Identifiers apgcode xq6_yyocxukcy6gocs20h0a38bac2qq73uszyjo4w8y0e4mo0vu0o606s6444u08clav0h03g440qq1333333x11zy9ecec2ik032i210sw3f0hy011w70401011033547442zy0emj896he1e1kif6q2gc50ew9qb30dzgo403gg066m32w11z34407q441n6zy311

Sir Robin (also known by its systematic name 282P6H2V1, and alternatively called seahorse) is a (2,1)c/6 spaceship found by Adam P. Goucher on March 6, 2018 using his ikpx search program. It is based on a partial found by Tomas Rokicki, which makes up about 62% of the ship, and which was itself an independent rediscovery of roughly half of a partial found by Josh Ball in April 2017. Sir Robin is the first elementary knightship in Conway's Game of Life. Sir Robin can also be considered the "Minstrel 0".

A scientific paper describing the method used to find the ship is forthcoming.

Partials

Josh Ball's original partial from April 2017 is shown below:

#O Josh Ball, April 2017 #C Knightship partial, later independently rediscovered in extended form by Tom Rokicki #C and developed into a true elementary knightship, Sir Robin, by Adam P. Goucher. #C http://conwaylife.com/wiki/Partial_result #C http://conwaylife.com/wiki/Sir_Robin x = 26, y = 31, rule = B3/S23 4b3o$3bo2b2o$3bo4bo2$3b3o3b2ob3o$b2obobo4bob2o$3bo2bo4bo2b2o$o2bo8bo$o 4bo2b2o2bo2bo$bob3o2b2o3b2o$3b2obob2obo3bo$9b2ob3o$9bo5bo$12b3o2b3o$ 15bob2o$10b2obo3b3o$10b2o2bo2b2o$12b4o3bo$13b2obo2bo$11b2obobobo$14bo$ 11bo7b2o$12b2o5b2o$14b2obo$16b3o2bobo$16b2o3bo$17bo$18b5obo$19b2o2b3o$ 19b2o4bo$23b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 16 THUMBSIZE 2 WIDTH 640 HEIGHT 560 GPS 6 ]]

(click above to open LifeViewer) RLE: here Plaintext: here

Synthesis

No glider synthesis for Sir Robin exists as of March 10, 2018; finding a synthesis is considered a challenging task at best, due to the large size of the ship, and the amount of space dust it contains.

Reactions

Martin Grant constructed a Sir Robin eater with a repeat time of 557 on March 8, 2018:

#N Sir Robin eater #O Martin Grant; March 2018 #C Eater for Sir Robin (but not his minstrels), repeat time 557. #C http://conwaylife.com/wiki/Sir_Robin #C http://www.conwaylife.com/forums/viewtopic.php?p=57499#p57499 x = 176, y = 354, rule = B3/S23 67b2o$67bobo$69bo4b2o$44b2o19b4ob2o2bo2bo$44bobo18bo2bobobobob2o$46bo 4b2o15bobobobo$42b4ob2o2bo2bo14b2obobo$42bo2bobobobob2o18bo$45bobobobo $46b2obobo7b2o$50bo9bo7b2o$60bobo5b2o$36b2o23b2o$37bo7b2o$37bobo5b2o$ 38b2o$27b2o$26bo2bo3b2o$26bobo3bobo$27bob4obob2o33b2o22bo$29bo4bo2bo 33bo3bo17b3o$28bo3b2obo36b4o16bo$27bo3bobob2o11b2o42b2o$27b2o3bo15bo 21b4o$49b3o17bo3bo$21b2o28bo17b2o29b2o$22bo78bo$22bobo76bob2o$23b2o52b 2o14b2o4b3o2bo$78bo14b2o3bo3b2o$78bob2o16b4o$70b2o4b3o2bo2b2o15bo$70b 2o3bo3bobobobo12b3o$75b4o2bobo13bo$61b2o15bobo2bo14b5o$60bobo12b3o2bob o19bo$60bo13bo5b2o18bo$59b2o14b5o20b2o$79bo$77bo$77b2o9$63bo$63b3o$66b o$65b2o2$24b2o$23bobo$23bo$22b2o2$75b2o$68b2o5bobo$58b2o8b2o7bo$58bo 18b2o$56bobo$56b2o6bo$63bobob2o$63bobobobo$60b2obobobobo2bo$60bo2bo2b 2ob4o$62b2o4bo$68bobo$69b2o4$9bo$9b3o$12bo$11b2o14b2o$26bobo$26bo$3b2o 20b2o$3bo$2obo$o2b3o4b2o$b2o3bo3b2o$3b4o$3bo15b2o$4b3o12bobo$7bo13bo 34b2o$2b5o14b2o33bo2bo$2bo53bo3bo$4bo53b3o$3b2o28b2o19b2o6b4o$33b2o19b ob2o4b4o$53bo4bo6b3o$54b4o4b2o3bo$52bo9b2o$53bo3bo$35bo22b3o2b2o2bo$ 33b3o18b2o7bo4bo$32bo32bob2o$32b2o28b2o6bo$63b2ob3obo$62b2o3bo2bo$62bo bo2b2o$62bo2bobobo$62b3o6bo$63bobobo3bo$22b2o42b2obobo$21bobo5b2o32bo 6b3o$21bo7b2o$20b2o41bo9bo$63bo3bo6bo$34bo29bo5b5o$30b2obobo28b3o$29bo bobobo32b2o$26bo2bobobobob2o26b3o2bo$26b4ob2o2bo2bo24bob3obo$30bo4b2o 25bo3bo2bo$28bobo32bo4b2ob3o$28b2o35b4obo4b2o$65bob4o4b2o$71bo$72bo2b 2o$72b2o$73b5o$77b2o$71b3o6bo$72bobo3bobo$71bo3bo3bo$71bo3b2o$70bo6bob 3o$71b2o3bo3b2o$72b4o2bo2bo$74b2o3bo$73bo$73b2obo$72bo$71b5o$71bo4bo$ 70b3ob3o$70bob5o$70bo$72bo$68bo4b4o$72b4ob2o$69b3o4bo$76bobo$80bo$76bo 2b2o$77b3o$74b2o$73b3o5bo$76b2o2bobo$73bo2b3obobo$74b2obo2bo$76bobo2b 2o$78b2o$74b3o4bo$74b3o4bo$75b2o3b3o$76b2ob2o$77b2o$77bo2$76b2o$78bo 108$149b2o$148b2o$150b2obo$148bo3b3ob2o$147b6ob2o2bo$146b2ob2o4bo$146b o4bo6bobo$146b5o4b3o2bo$146b3obo4b2o$151b2o2bobo$147bo3b2o3b2o$152bo3b o2bobo$155b3o2b3o$155b2obo$157bob3ob2o$155bo2bo$154b2obo2bobo$154b2o2b 3o$155bo2bo2bobo$155b2obob2o2b2o$157bob3o$163b3o$164b2o2$156b2o6bo2bo$ 156b2obo4b4o$157b2o3b5o$157bo3b2o$157b2o4bo$157bo4b2o$155b5o2bo2bo$ 158bo5b2o$157b2o6bob3o$158bo4b2o3b2o$161b4o$164b3o$165bo4bo$165b7o$ 168bob2o$164b3o3b2o$167bo5bo$164b2ob3o2bo$163b2o3b2ob2o$163bobo2bobobo bo$164b2ob5o3bo$164b2o3bo2bobo$165bo2bo$166bo$165b3o$164bo$164bob3o$ 169bo$163bo6bo$162b2obo3bo$165bob2o$166b3o$169b2o$162b4o4bo$163b5obobo $163bo6bo$170bo2bo$170bo2bo$168b6o$166bob2obo$166bo7bo$166bo4b3obo$ 167bo3bobo$167b2o4bobo$168b2obob2o$169bob5o$167bob2o2bo$170bo$167bo4bo 2bo$168bo3b2o$172bo$170b2o$169b2o$170bo$170bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]

(click above to open LifeViewer) RLE: here Plaintext: here

Tagalongs

Tagalongs of Sir Robin are dubbed minstrels. There are eight known ways in which Sir Robin can be extended by attaching minstrels:

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636bo27bo3bo120bob2o$633b2obo30b2o121b2ob2o$635b2obo26b2o123b2o2bo$ 635bo2bo151bo$637b3o147b2o2bo2bo$634b3o149b2o3bo2bo$633bobo150b2o5b3o$ 633bo153b3obo2b2o$788bo$634bo2bo150bo2b3o$634b3o152bo2bo$637b2o$632b3o b2o155b2o$635b3o155b2o$631bo3b2o155b2obo$632bobo$792b2o2b2o$792bobo$ 792bo2b2o$796bo$793b2obo$795bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 880 HEIGHT 560 ZOOM 2 THUMBSIZE 2 AUTOSTART ]]

In order to expand and view annotations: (click above to open LifeViewer) RLE: here Plaintext: here

The complete spaceships are named Minstrel 0 (Sir Robin) through to Minstrel 8, in order of discovery. The indecomposable tagalongs are given the following names:

• Errant minstrel := Minstrel 1 - Minstrel 0
• Lightweight minstrel := Minstrel 2 - Minstrel 0
• Heavyweight minstrel := Minstrel 3 - Minstrel 0
• Wandering minstrel := Minstrel 5 - Minstrel 3
• Ragged minstrel := Minstrel 6 - Minstrel 2

History

The first tagalong, Minstrel 1, was discovered by Adam P. Goucher on July 15, 2018, after resuming the original ikpx search.

Dave Greene modified Martin Grant's Sir Robin eater to act as a Minstrel 1 detector the same day, which removes the errant minstrel to yield the original Sir Robin.

On July 19, 2018, Adam P. Goucher found a second and third minstrel, dubbed Minstrel 2 and Minstrel 3, that follow Sir Robin more closely. The lightweight and heavyweight minstrels are not true tagalongs because they change the evolution of the Sir Robin itself.

On July 20, 2018, Goldtiger997 built a stable circuit that can accept any of Minstrel 0 through to Minstrel 3, emitting a glider in one of four directions (depending on the input spaceship) along with an unadorned Sir Robin travelling along the original path. When the original input is a Sir Robin, this circuit is a Heisenburp; otherwise, it is a downconverter. The circuit was later optimised by including a bend in the 2c/3 signal wire, among other bounding-box reductions.

On Christmas Day in 2018, Entity Valkyrie discovered that the heavyweight and errant can be composed, yielding Minstrel 4. Two days later, Goldtiger997 updated the previous minstrel remover/detector to accept any of the known tagalongs including the composite Minstrel 4.

On December 31, 2018, Adam P. Goucher resumed the ikpx search and another Minstrel 3 tagalong was found, dubbed Minstrel 5. Again, Goldtiger997's minstrel remover/detector was updated to accept the newest spaceship.

The following month a further tagalong, Minstrel 6, was discovered by the ikpx search program. Dave Greene assembled existing components to discover two new spaceships, Minstrels 7 and 8.

Minstrel arithmetic

By pure coincidence, the relationships between these spaceships can be encapsulated by 'minstrel arithmetic': the observation that integer 'weights' can be assigned to Sir Robin and its indecomposable tagalongs such that the sum of the weights of the components of Minstrel n is exactly n:

• Sir Robin: 0
• Errant minstrel: 1
• Lightweight minstrel: 2
• Heavyweight minstrel: 3
• Wandering minstrel: 2
• Ragged minstrel: 4

In particular, we have:

• Minstrel 0 = 0 (Sir Robin)
• Minstrel 1 = 0 + 1 (Sir Robin + errant minstrel)
• Minstrel 2 = 0 + 2 (Sir Robin + lightweight minstrel)
• Minstrel 3 = 0 + 3 (Sir Robin + heavyweight minstrel)
• Minstrel 4 = 0 + 3 + 1 (Sir Robin + heavyweight minstrel + errant minstrel)
• Minstrel 5 = 0 + 3 + 2 (Sir Robin + heavyweight minstrel + wandering minstrel)
• Minstrel 6 = 0 + 2 + 4 (Sir Robin + lightweight minstrel + ragged minstrel)
• Minstrel 7 = 0 + 2 + 4 + 1 (Sir Robin + lightweight minstrel + ragged minstrel + errant minstrel)
• Minstrel 8 = 0 + 2 + 4 + 2 (Sir Robin + lightweight minstrel + ragged minstrel + wandering minstrel)

Other spaceships

The lightweight minstrel is also capable of supporting both ends of knightwave, as noted by Matthias Merzenich. The heavyweight minstrel can support the left end in the same manner.

[[:RLE:Knightwavepartialsupport]] #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ TRACKLOOP 6 -1/6 -1/3 THUMBSIZE 2 WIDTH 600 HEIGHT 800 ZOOM 4 GPS 6 AUTOSTART ]]

Knightwave supported between Minstrel 7 (upper right) and Minstrel 5 (lower left) (click above to open LifeViewer) RLE: here Plaintext: here

Currently, the grammar of known (2,1)c/6 spaceships can be completely classified. In particular, every known (2,1)c/6 spaceship is either:

• Minstrel n (for some n between 0 and 8), or
• A horizontal sequence of two or more spaceships, each of the above form, with adjacent spaceships joined by a horizontal segment of knightwave containing any sufficiently large number of repeating components (where 'sufficiently large' is such that the two knightships do not interact). The leftmost spaceship in the sequence must contain either a lightweight or heavyweight minstrel, and the remaining spaceships must all contain lightweight minstrels.

External links

• Sir Robin at the Life Lexicon

Articles and announcements

• A rather satisfying winter: cp4space article describing the events leading to the discovery
• b3s23life article announcing the discovery itself
• Elementary Knightship found in Conway's Game of Life on Hacker News
• An elementary knightship has been found in Conway's Game of Life on Reddit

Object catalogues

• Sir Robin at Adam P. Goucher's Catagolue (extended)

Forum threads

• Elementary knightship (discussion thread) at the ConwayLife.com forums

• Synthesizing the elementary knightship (discussion thread) at the ConwayLife.com forums

• What are the odds that Sir Robin will appear naturally? (discussion thread) at the ConwayLife.com forums

Tools

• ikpx on Gitlab