## New small c/4 orthogonal ship

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.

### New small c/4 orthogonal ship

I found this c/4 orthogonal ship with WLS. Minimum population of 37 on cells, which I believe makes this the smallest ship of this velocity.

`x = 19, y = 12bo\$bo8bo\$obo5bo3bo\$8bo3boo\$5boboo5boo\$b6obbo6bo\$bboo6bo3b3o\$10bo3boboo\$13bo\$18bo\$17bo\$17bo!`
-Josh Ball.

velcrorex

Posts: 339
Joined: November 1st, 2009, 1:33 pm

### Re: New small c/4 orthogonal ship

Wow! This significantly beats a nearly 16-year-old record! Nice work.
-Matthias Merzenich
Sokwe
Moderator

Posts: 1479
Joined: July 9th, 2009, 2:44 pm

### Re: New small c/4 orthogonal ship

This leads to another small c/4 ship with a minimum population of 43:
`x = 19, y = 12, rule = B3/S233o\$bo8bo\$8bo3bo\$3b2o3bo3b2o\$2b2obob2o5b2o\$2b2ob2o2bo6bo\$3bo6bo3b3o\$4b2o4bo3bob2o\$5bo7bo\$18bo\$5b2o10bo\$17bo!`

Here are some related, relatively-small spaceships:
`x = 147, y = 106, rule = B3/S2363b3o\$77b2o7b3o\$63bobo11b2obo\$71b5obo2b2o3bo2bo\$66b2o2bo4b2o6bo2bo\$66bobo4bo3b2o3b6o\$67b2o4bo2b3o\$66bo5bo3bo5b2o\$69bo2\$67b3o15\$6bo30bo61bo29bo\$6bo8bo21bo8bo20bo31bo8bo20bo8bo\$5bobo5bo3bo18bobo5bo3bo18bo8bo21bobo5bo3bo17bobo5bo3bo\$13bo3b2o25bo3b2o16bobo5bo3bo27bo3b2o24bo3b2o\$10bob2o5b2o20bob2o5b2o22bo3b2o23bob2o5b2o19bob2o5b2o\$6b6o2bo6bo15b6o2bo6bo18bob2o5b2o17b6o2bo6bo14b6o2bo6bo\$3o4b2o6bo3b3o16b2o6bo3b3o14b6o2bo6bo17b2o6bo3b3o15b2o6bo3b3o\$bo13bo3bob2o23bo3bob2o14b2o6bo3b3o25bo3bob2o22bo3bob2o\$3b2o13bo16b2o12bo26bo3bob2o16b2o9bo18b2o9bo\$4bobo16bo11bobo16bo10b2o12bo19bobo14bo12bobo14bo\$22bo13b3o14bo11bobo16bo13b3o14bo12b3o14bo\$4b3o15bo13b2o15bo12b3o14bo15b2o14bo13b2o14bo\$4bo31b2o28b2o15bo15b2o28b2o\$2bobo28b3o30b2o33b3o27b3o\$b2o60b3o\$2b4o\$33b2o67b2o28b2o\$33b2o28b2o37b2o28b2o\$32b2o29b2o36b2o30b2o\$64b2o16\$78bo\$76bo3bo\$76bo3b2o\$75b2o5b2o\$70b3o4bo6bo\$73b2o3bo3b3o\$71bo6bo3bob2o\$70bo10bo\$68bobo15bo\$67bob2o14bo\$67b2o16bo\$68bo\$68bo\$66b2obob2o\$67b2o2b2o\$67bo3bo\$66b3ob2o2\$68b4o\$68bo2bo\$68bo2bo15\$65bo18bo\$63bo3bo14bo3bo\$62b2o3bo14bo3b2o\$60b2o5b2o12b2o5b2o\$59bo6bo4b3o2b3o4bo6bo\$59b3o3bo3b2o8b2o3bo3b3o\$58b2obo3bo6bo4bo6bo3bob2o\$62bo24bo\$57bo13bob4obo13bo\$58bo12bo2b2o2bo12bo\$58bo32bo!`
-Matthias Merzenich
Sokwe
Moderator

Posts: 1479
Joined: July 9th, 2009, 2:44 pm

### Re: New small c/4 orthogonal ship

Here are some new, small ships (including two with 45 cells and one with 46 cells):
`x = 198, y = 54, rule = B3/S2381b2o\$80bo\$80b2o\$80b2o80bo\$75b4obo74bobob2obo\$72bob3o76bo3bobo\$71b2o7b2o70bo\$151bo3b2o\$71bob2obo74bob2o\$71b2o3bo75bo\$16bobobo55bo73bo\$14bo3bob2obo47b2o76bobo\$13bo9bo47bo74bo2bobo44bo\$12bo3b2o53b3o71bobo47bobo\$12bob2o56b2o3bo66bo2bo47bobo\$b2ob2o7bo64bo66bo49bo\$3o8bo63b2o59bo2b2o5b2o\$b2obo2bo2bobo37bo23bob2o58b2o2bo5bo48bobo\$10bobo36bobo22b2o60bo3b3o2b2o\$5b2obo40bobo18bobo35bobo29b2obo3bo45b3o\$7b2o40bo20bo36bo2bo30bo4bo45bo\$7b3o60bobo33bo3bo31b2o47b2obo\$9bo2b2o35bobo53b2o36bo3bo47bo\$11bo92bo39bo2bo47bo\$47b3o53b2obo2b2o34bobo42bobo\$46bo52bo3b3o2b3o76bob2o\$45b2obo50b2o2bo81b2ob2o\$35bob2o10bo49bo2b2o10bo70b2ob2o\$33b2o3bo10bo60b4o2bo71bo\$35bobo6bobo37bo25b2obo2bo59bob2o6bobo\$39b3ob2o38bobo26b4o60bo3b2o\$39b2ob2o39bobo90bob2o6bobo\$41bobo39bo32b2o3bo59b3ob2obo\$23bo18b3o70bo3bo2b2o31bobobo22bob2o\$16bobob2obo18b4o37bobo27bo4b2o33bo3bob2obo\$14bo3bobo24bo67bo3bo34bo9bo20bobo\$13bo67b3o29bobo35bo3b2o28b2obo\$12bo3b2o62bo70bob2o33bo\$12bob2o63b2obo69bo\$b2ob2o7bo69bo66bo\$3o8bo71bo65bobo\$b2obo2bo2bobo65bo67bo2bobo\$10bobo64b2obo64bobo\$5b2obo58bob2o73bo2bo\$7b2o56b2o3bo74bo\$7b3o57bobo6bobo57bo2b2o5b2o\$9bo2b2o57b3ob2o59b2o2bo5bo\$11bo59b2ob2o60bo3b3o2b2o\$73bobo64b2obo3bo\$74b3o64bo4bo\$74b4o64b2o\$77bo65bo3bo\$144bo2bo\$145bobo!`

For reference, here are all of the known c/4 orthogonal spaceships with fewer than 60 cells:
`x = 334, y = 204, rule = B3/S23305bo\$298bobob2obo\$296bo3bobo\$295bo\$294bo3b2o\$294bob2o\$295bo\$293bo\$292bobo\$289bo2bobo\$288bobo\$287bo2bo\$288bo\$279bo2b2o5b2o\$279b2o2bo5bo\$279bo3b3o2b2o\$283b2obo3bo\$284bo4bo\$285b2o\$286bo3bo\$287bo2bo\$288bobo9\$298bobobo\$296bo3bob2obo\$295bo9bo\$294bo3b2o\$294bob2o\$295bo\$293bo\$292bobo\$289bo2bobo\$288bobo\$287bo2bo\$288bo\$279bo2b2o5b2o\$279b2o2bo5bo\$279bo3b3o2b2o\$283b2obo3bo\$284bo4bo\$285b2o\$286bo3bo\$287bo2bo\$288bobo10\$293bo\$291bo2b2o\$289b3o\$288bobo\$288bob2o\$287bo4bo\$286b2o2\$285bo4b2o\$180bo3bo104bo\$179bob2obo101b3o\$179bobo106bo\$180bo108bo12bo\$178b2o57bo50b2o7bo2b3o\$178b2o55b2o52bo7bo2b2o\$182bob2o51bo51b2ob2o3bo\$156b2o23b2o56bobo44bo2b2obob3o\$155bo82bo2bo42b2o3bo3b4o\$85b3o67b2o24b2obo53bo2bo44bo7bo\$83b2o3bo66b2o24b2obo53bobo\$81bo68b4obo27bo56bo\$79b2o3bo3bo58bob3o28bo2b2o16bo36b2o\$81bo2bo3bo57b2o7b2o24b3o15b2o17bobo17b2o\$59bobobo19b2o116bo10b2o2b2o2bo21bob2o\$57bo3bob2obo17bo3bo57bob2obo28bo22b5o3b3o6bo20b2o\$56bo9bo17bo3bo57b2o3bo28b2o22bo4bo4bobo\$55bo3b2o23b3o64bo27bo2b2o20bo4bob3o2bo24b2obo\$55bob2o47b2o38b2o33bobo20bo4bo6b2o23b2obo\$44b2ob2o7bo27b3o18b3o20bo17bo30b2o3bo20b2obo3b3o3b3o24bo\$43b3o8bo29bo3bo17bo20bo18b3o29b3o24bo4b3o27bo2b2o19bobo65bo\$44b2obo2bo2bobo28bo3bo18b2ob2o15b2o18b2o3bo26b2o26b2o2b2o28b3o20bo3bo24bo37bobo\$53bobo27b2o27bo5bo6bo27bo28bo25b2o54bo2b2o22bo2b2o35bobo\$9bo20bo17b2obo29bo2bo3bo18b2o7bobob3o6bo20b2o28bobo57bo25bobo20b3o39bo\$7bo2b2o16bo2b2o17b2o27b2o3bo3bo19bo6bobo4b3ob2obo19bob2o28bo58b2o26bo19bobo\$5b3o18b3o21b3o28bo27bo2bo9b2o25b2o88bo2b2o23b2obo17bob2o39bobo\$4bobo18bobo24bo2b2o26b2o3bo21bobobob2o27bobo93bobo24bobo16bo4bo\$4bob2o17bob2o25bo30b3o21b2o3bo30bo91b2o3bo23bo19b2o41b3o\$3bo4bo15bo4bo81bo33bobo90b3o24b2o61bo\$2b2o19b2o214b2o44bo4b2o35b2obo\$242bo21b2o2b2o19bo41bo\$bo4b2o14bo4b2o211bobo21b3ob2o16b3o42bo\$5bo20bo214bo25bob2o17bo37bobo\$2b3o18b3o240b2o21bo33bob2o\$4bo20bo182bo57bo21b2o7bo2b2o19b2ob2o\$5bo20bo4bo139bobo32b2o3bo54bob2o19bo7bo2b3o18b2ob2o\$4b2o19b2ob2obo127bo11bo36bo2b2o53bo3bo18b2ob2o3bo4bo21bo\$5bo18bo3bo37bo26bo64bobo10bobo2bo2bo31b2o53bo19bo2b2obob3o15bob2o6bobo\$5b2o17b4o31bobob2obo25bobo11b2o50bobo13bo36bo55bo16b2o3bo3b4o15bo3b2o\$2bo2b2o14bo3b2o30bo3bobo28bobo10b3o50bo16bob2obo29b2o59bobo12bo7bo17bob2o6bobo\$2o3bo15b2o33bo35bo13bo15b2o52b3obo30bo56b2o3bo43b3ob2obo\$2bo18bo33bo3b2o46b2ob2o10b3ob2obo28bobo14bo4bo2bob2o23bo56bobo3bo44bob2o\$55bob2o33bobo17bo5bob3o6bo42bo3b2o3bob4o21b3o56b2obo\$44b2ob2o7bo50b2o7bobo6bo30b3o13b2o2bo2bob2o4bo23bo31bobo17bobo53bobo\$43b3o8bo35b3o15bo6bobo9b2o26bo16bo8b2o4bo2b2o15bo3b2o30bo3bo15bo57b2obo\$44b2obo2bo2bobo33bo19bo2bo14bo26b2obo19b2o3b2o3bo2b3o18b2o30bo4b2o13bobo58bo\$53bobo32b2obo18bobobob2o10bo29bo33bo15b2obo33bo3bo2b2o\$48b2obo26bob2o10bo16b2o3bo43bo49b2ob2o33b2o3bo\$50b2o24b2o3bo10bo18bo41bo55bo3bo\$50b3o25bobo6bobo62b2obo50b2obobo30b4o\$52bo2b2o25b3ob2o54bob2o61bo3bo28b2obo2bo47bo\$54bo27b2ob2o53b2o3bo61bo32b4o2bo45bo2b2o\$84bobo55bobo6bobo54bobo18bo2b2o10bo45b3o\$85b3o58b3ob2o59bo17b2o2bo55bobo\$85b4o57b2ob2o59b3o16bo3b3o2b3o48bob2o\$88bo59bobo20bobo59b2obo2b2o47bo4bo\$149b3o19bo38bo23bo52b2o\$149b4o18bobo2bo2bo27bo2bo24b2o\$152bo21bo32b2o2b2o23bo3bo45bo4b2o\$175bob2obo26bo29bo2bo49bo\$176b3obo57bobo46b3o\$175bo4bo2bob2o102bo\$172bo3b2o3bob4o103bo\$172b2o2bo2bob2o4bo4bo96b2o\$172bo8b2o4bo2b3o97bo\$177b2o3b2o3bo2b2o98b2o\$287bo2b2o3bo\$285b2o3bo3b4o\$287bo5bob3o\$293b2o3bo4bo\$298bo2b3o\$298bo2b2o9\$293bo\$291bo2b2o\$289b3o\$288bobo\$288bob2o\$287bo4bo\$286b2o2\$285bo4b2o\$289bo\$286b3o\$288bo\$289bo\$288b2o\$289bo\$289b2o\$286bo2b2o3bo\$284b2o3bo3b4o\$286bo5bob3o\$292b2o3bo\$297bo2b2o\$297bo2b3o\$302bo9\$293bo\$291bo2b2o\$289b3o\$288bobo\$288bob2o\$287bo4bo\$286b2o2\$285bo4b2o\$289bo\$286b3o\$288bo\$289bo\$288b2o\$289bo\$289b2o\$286bo2b2o\$284b2o3bo3bobo\$286bo8bo3bo\$292b2ob3obo\$292bo6bo\$290bo6b3o\$290b2o6bo\$290bo!`

Edit: A new 58-cell ship:
`x = 16, y = 23, rule = B3/S2313bo\$11bo2b2o\$9b3o2\$10b2o\$5b4o2bo\$2bob3o3b3o\$b2o7b4o\$13bo\$bob2obo\$b2o3bo\$6bo\$b2o\$bo\$b3o\$2b2o3bo\$8bo\$5b2o\$4bob2o\$4b2o\$obo\$o\$obo!`
-Matthias Merzenich
Sokwe
Moderator

Posts: 1479
Joined: July 9th, 2009, 2:44 pm

### Re: New small c/4 orthogonal ship

I came up with a slick idea for a constraint propagation algorithm for spaceship searches. So I gutted my 20 year old search program "knight" and started writing "knight2" three weeks ago. I used c/4 searches as my initial debug test.

I have found the following small c/4 ships of pip counts 41, 48, 55, and 56:

`x = 94, y = 25, rule = B3/S2332bo\$32b2o\$32bo58bo\$34bo54bo2b2o\$34bo19b2o31b3o\$11bo21b2o18b3o5bobo4b2o16bobo\$9b2o43bo6bo7bo2bo13bob2o\$11bo2b2o19bo19bo5bo2b3o5bo12bo4bo\$13b2o19bobo19b2o5bo5bo2bo11b2o\$14bo18b4o18b3o10b2o\$7b3o4bo14b2o2bo18bo2b2o4b2o20bo4b2o\$10b2o2bo14b2obobo17b2o4b2o27bo\$5b2o4bo2bo14b2o2bo18bo3b2obo2bo21b3o\$o3bo6b3o14b2o26b3o27bo\$2o7bo17bo28b2ob2obobo22bo\$o2b2o4b2obobo12bo5bo26bo3bo21b2ob2o\$5b3o4bobo13bob3o27bo24b2o2bo\$14bo18bo51b2o3bo\$30b4o50bobo3b2o\$30bo2bo50b2o4b2o\$33bo51b3obo\$32bo53b2ob3o\$32bobo49bo\$32bobo49bo\$33bo50bobo!`

I added the four ships I found and the 58 cell ship mentioned in the previous post to the collection of known c/4 spaceships of less than 60 points:

`x = 392, y = 204, rule = B3/S23340bo\$333bobob2obo\$331bo3bobo\$330bo\$329bo3b2o\$329bob2o\$330bo\$328bo\$327bobo\$324bo2bobo\$323bobo\$322bo2bo\$323bo\$314bo2b2o5b2o\$314b2o2bo5bo\$314bo3b3o2b2o\$318b2obo3bo\$319bo4bo\$320b2o\$321bo3bo\$322bo2bo\$323bobo9\$333bobobo\$331bo3bob2obo\$330bo9bo\$329bo3b2o\$329bob2o\$330bo\$328bo\$327bobo\$324bo2bobo\$323bobo\$322bo2bo\$323bo\$314bo2b2o5b2o\$314b2o2bo5bo\$314bo3b3o2b2o\$318b2obo3bo\$319bo4bo\$320b2o\$321bo3bo\$322bo2bo\$323bobo10\$328bo\$326bo2b2o\$324b3o\$323bobo\$268b2o53bob2o\$267b3o5bobo4b2o38bo4bo\$268bo6bo7bo2bo17bo16b2o\$269bo5bo2b3o5bo15bo2b2o\$270b2o5bo5bo2bo13b3o17bo4b2o\$215bo3bo49b3o10b2o15bobo22bo\$214bob2obo46bo2b2o4b2o22bob2o18b3o\$214bobo49b2o4b2o24bo4bo19bo\$215bo50bo3b2obo2bo20b2o25bo12bo\$213b2o55b3o50b2o7bo2b3o\$213b2o55b2ob2obobo17bo4b2o21bo7bo2b2o\$217bob2o53bo3bo21bo23b2ob2o3bo\$191b2o23b2o56bo22b3o21bo2b2obob3o\$106b3o81bo108bo19b2o3bo3b4o\$104b2o3bo80b2o24b2obo80bo20bo7bo\$102bo87b2o24b2obo79b2ob2o\$100b2o3bo3bo75b4obo27bo79b2o2bo\$102bo2bo3bo72bob3o28bo2b2o16bo61b2o3bo\$80bobobo19b2o75b2o7b2o24b3o15b2o17bobo41bobo3b2o\$78bo3bob2obo17bo3bo126bo10b2o2b2o2bo41b2o4b2o\$77bo9bo17bo3bo71bob2obo28bo22b5o3b3o6bo42b3obo\$76bo3b2o23b3o73b2o3bo28b2o22bo4bo4bobo47b2ob3o85bo\$76bob2o47b2o57bo27bo2b2o20bo4bob3o2bo20bo24bo63bo27bobo\$65b2ob2o7bo27b3o18b3o20bo31b2o33bobo20bo4bo6b2o17b2o25bo61bo2b2o25bobo\$64b3o8bo29bo3bo17bo20bo17bo14bo30b2o3bo20b2obo3b3o3b3o18bo24bobo57b3o29bo\$65b2obo2bo2bobo28bo3bo18b2ob2o15b2o16b2o13b3o29b3o24bo4b3o26bobo\$74bobo27b2o27bo5bo6bo19bo15b2o3bo26b2o26b2o2b2o25bo2bo51bo29b2o29bobo\$51bo17b2obo29bo2bo3bo18b2o7bobob3o6bo17bo19bo28bo25b2o28bo2bo49bo2b2o22b4o2bo\$9bo39bo2b2o17b2o27b2o3bo3bo19bo6bobo4b3ob2obo17bo16b2o28bobo55bobo48b3o23bob3o3b3o26b3o\$7bo2b2o17bo17b3o21b3o28bo27bo2bo9b2o22b2o15bob2o28bo58bo47bobo23b2o7b4o24bo\$5b3o19b2o17bobo24bo2b2o26b2o3bo21bobobob2o45b2o87b2o48bob2o34bo23b2obo\$4bobo22bo2b2o12bob2o25bo30b3o21b2o3bo33bo10bobo90b2o47bo4bo21bob2obo34bo\$4bob2o23b2o12bo4bo81bo35bobo9bo96bob2o40b2o26b2o3bo34bo\$3bo4bo23bo11b2o121b4o9bobo93b2o76bo29bobo\$2b2o21b3o4bo130b2o2bo152bo4b2o22b2o30bob2o\$28b2o2bo10bo4b2o113b2obobo107b2obo44bo24bo29b2ob2o\$bo4b2o15b2o4bo2bo14bo115b2o2bo108b2obo41b3o25b3o27b2ob2o\$5bo12bo3bo6b3o12b3o115b2o114bo44bo26b2o3bo26bo\$2b3o13b2o7bo18bo114bo113bo2b2o44bo31bo13bob2o6bobo\$4bo13bo2b2o4b2obobo14bo4bo108bo5bo75bo32b3o44b2o7bo2b2o16b2o15bo3b2o\$5bo17b3o4bobo13b2ob2obo109bob3o39bobo32b2o3bo77bo7bo2b3o14bob2o14bob2o6bobo\$4b2o26bo12bo3bo37bo26bo52bo26bo11bo36bo2b2o27bo48b2ob2o3bo4bo14b2o21b3ob2obo\$5bo39b4o31bobob2obo25bobo11b2o35b4o25bobo10bobo2bo2bo31b2o27b2o21bobo20bo2b2obob3o16bobo25bob2o\$5b2o35bo3b2o30bo3bobo28bobo10b3o35bo2bo25bobo13bo36bo27bo2b2o19bo3bo16b2o3bo3b4o16bo\$2bo2b2o35b2o33bo35bo13bo15b2o22bo25bo16bob2obo29b2o29bobo19bo2b2o18bo7bo18bobo26bobo\$2o3bo36bo33bo3b2o46b2ob2o10b3ob2obo15bo44b3obo30bo25b2o3bo22bobo76b2obo\$2bo73bob2o33bobo17bo5bob3o6bo15bobo24bobo14bo4bo2bob2o23bo27b3o26bo79bo\$65b2ob2o7bo50b2o7bobo6bo19bobo38bo3b2o3bob4o21b3o28b2o25b2obo\$64b3o8bo35b3o15bo6bobo9b2o17bo23b3o13b2o2bo2bob2o4bo23bo30bo24bobo\$65b2obo2bo2bobo33bo19bo2bo14bo41bo16bo8b2o4bo2b2o15bo3b2o27bobo22bo\$74bobo32b2obo18bobobob2o10bo39b2obo19b2o3b2o3bo2b3o18b2o28bo22b2o\$69b2obo26bob2o10bo16b2o3bo57bo33bo15b2obo\$71b2o24b2o3bo10bo18bo60bo49b2ob2o50b2o2b2o\$71b3o25bobo6bobo77bo55bo3bo49b3ob2o\$73bo2b2o25b3ob2o78b2obo50b2obobo54bob2o\$75bo27b2ob2o69bob2o61bo3bo53b2o27bo\$105bobo67b2o3bo61bo57bo26bo2b2o\$106b3o68bobo6bobo54bobo54bob2o21b3o\$106b4o71b3ob2o59bo53bo3bo19bobo\$109bo71b2ob2o59b3o52bo23bob2o\$183bobo20bobo92bo21bo4bo\$184b3o19bo38bo32bobo24bobo14b2o\$184b4o18bobo2bo2bo27bo2bo32bo3bo19b2o3bo\$187bo21bo32b2o2b2o30bo4b2o16bobo3bo13bo4b2o\$210bob2obo26bo37bo3bo2b2o12b2obo20bo\$211b3obo65b2o3bo10bobo22b3o\$210bo4bo2bob2o75bo26bo\$207bo3b2o3bob4o55b4o16bobo25bo\$207b2o2bo2bob2o4bo4bo47b2obo2bo42b2o\$207bo8b2o4bo2b3o47b4o2bo43bo\$212b2o3b2o3bo2b2o37bo2b2o10bo45b2o\$264b2o2bo53bo2b2o3bo\$264bo3b3o2b3o44b2o3bo3b4o\$268b2obo2b2o46bo5bob3o\$269bo58b2o3bo4bo\$270b2o61bo2b3o\$271bo3bo57bo2b2o\$272bo2bo\$273bobo7\$328bo\$326bo2b2o\$324b3o\$323bobo\$323bob2o\$322bo4bo\$321b2o2\$320bo4b2o\$324bo\$321b3o\$323bo\$324bo\$323b2o\$324bo\$324b2o\$321bo2b2o3bo\$319b2o3bo3b4o\$321bo5bob3o\$327b2o3bo\$332bo2b2o\$332bo2b3o\$337bo9\$328bo\$326bo2b2o\$324b3o\$323bobo\$323bob2o\$322bo4bo\$321b2o2\$320bo4b2o\$324bo\$321b3o\$323bo\$324bo\$323b2o\$324bo\$324b2o\$321bo2b2o\$319b2o3bo3bobo\$321bo8bo3bo\$327b2ob3obo\$327bo6bo\$325bo6b3o\$325b2o6bo\$325bo!`
moebius

Posts: 26
Joined: December 10th, 2015, 9:07 am

### Re: New small c/4 orthogonal ship

Wow. Umm... so you're Tim Coe? Wow...
Didn't expect new posts from a new member to be pretty exciting ones from one of the Life Enthusiasts from long ago! Welcome to the Conwaylife forums!!!

Although I'm not a good programmer, I'm curious about how your program works.
Especially, is it an exhaustive search? On the other thread I think you said that a failure is reported at most in two weeks, but a successful search can carry on for months. This looks something like a non-exhaustive search, but on the other hand, referring to LifeWiki negative results seem to tell us that the search is exhaustive. Which is correct?

PS. You have your own page in LifeWiki! (And some of the patterns are older than me )
David Eppstein wrote:Life evolution rule is hardcoded as a sequence of bit-parallel integer operations, multiple times throughout 25 pages of uncommented C (so not really possible to change without rewriting the whole program).
Best wishes to you, Scorbie

Scorbie

Posts: 1380
Joined: December 7th, 2013, 1:05 am

### Re: New small c/4 orthogonal ship

moebius wrote:I came up with a slick idea for a constraint propagation algorithm for spaceship searches.

I would very much like to hear more details.

moebius wrote:I have found the following small c/4 ships of pop counts 41, 48, 55, and 56

The 41-cell ship was discovered by Josh Ball a few years back, but the others are new. One of the components in the 55-cell ship can be replaced with a smaller component to get a new 48-cell ship:
`x = 15, y = 16, rule = B3/S2310bo\$8b2o\$10bo\$3bo8bobo\$3b2o6bo2bo\$3bo7bo2bo\$5bo5bobo\$5bo7bo\$4b2o\$2bo2bo2bobo\$2o6bob2o\$2bo5b4o\$4b4o\$9bo3bo\$9b5o\$10b2o!`

Here is the current collection of all known c/4 orthogonal ships up to 70 cells (including your new ships):
`x = 834, y = 515, rule = B3/S23162bobo\$162bo3bo19bo\$162bo2b2o17bo2b2o\$30bo133bobo15b3o\$28bo2b2o133bo14bobo\$26b3o136b2obo12bob2o\$25bobo138bobo11bo4bo\$25bob2o135bo14b2o\$obobo3bobobo11bo4bo110bobobo3bobobo10b2o\$23b2o153bo4b2o\$4bo7bo127bo7bo13b2o2b2o14bo\$22bo4b2o133b3ob2o11b3o\$obobo7bo13bo113bobobo3bobobo12bob2o12bo\$23b3o138b2o16bo\$4bo7bo12bo118bo3bo3bo11bo16b2ob2o\$26bo137bob2o12b2o2bo\$obobo7bo12b2o113bobobo3bobobo11bo3bo11b2o3bo\$26bo137bo14bobo3b2o\$26b2o137bo13b2o4b2o\$23bo2b2o141bobo8b3obo\$21b2o3bo139b2o3bo9b2ob3o\$23bo141bobo3bo7bo\$165b2obo10bo\$161bobo15bobo\$161bo\$161bobo7\$35bo\$26b3o4bobo\$o3bo4bo11bo2b2o4b2obobo\$21b2o7bo\$o3bo4bo11bo3bo6b3o152bo\$26b2o4bo2bo144bobob2obo25bobobo18bo24bo24bo24bo24bo\$obobo4bo21b2o2bo142bo3bobo26bo3bob2obo13bo2b2o20bo2b2o20bo2b2o20bo2b2o20bo2b2o\$28b3o4bo141bo32bo9bo11b3o22b3o22b3o22b3o22b3o\$4bo4bo25bo140bo3b2o27bo3b2o16bobo22bobo22bobo22bobo22bobo\$34b2o140bob2o29bob2o18bob2o21bob2o21bob2o21bob2o21bob2o\$4bo4bo22bo2b2o103bobobo3bobobo24bo32bo19bo4bo19bo4bo19bo4bo19bo4bo19bo4bo\$30b2o143bo32bo20b2o23b2o23b2o23b2o23b2o\$32bo107bo11bo21bobo30bobo\$171bo2bobo27bo2bobo18bo4b2o18bo4b2o18bo4b2o18bo4b2o18bo4b2o\$140bobobo7bo17bobo30bobo26bo24bo24bo24bo24bo\$169bo2bo29bo2bo23b3o22b3o22b3o22b3o22b3o\$144bo7bo17bo32bo27bo24bo24bo24bo24bo\$161bo2b2o5b2o21bo2b2o5b2o26bo12bo11bo24bo24bo24bo\$140bobobo7bo8b2o2bo5bo22b2o2bo5bo26b2o7bo2b3o10b2o7bo2b2o11b2o23b2o23b2o\$161bo3b3o2b2o22bo3b3o2b2o27bo7bo2b2o12bo7bo2b3o11bo24bo24bo\$165b2obo3bo25b2obo3bo26b2ob2o3bo16b2ob2o3bo4bo11b2o23b2o23b2o\$166bo4bo27bo4bo24bo2b2obob3o14bo2b2obob3o14bo2b2o3bo16bo2b2o3bo16bo2b2o\$167b2o31b2o25b2o3bo3b4o12b2o3bo3b4o12b2o3bo3b4o12b2o3bo3b4o12b2o3bo3bobo\$30bo137bo3bo28bo3bo23bo7bo16bo7bo16bo5bob3o14bo5bob3o14bo8bo3bo\$28bo2b2o136bo2bo29bo2bo79b2o3bo4bo14b2o3bo19b2ob3obo\$26b3o141bobo30bobo84bo2b3o19bo2b2o15bo6bo\$25bobo262bo2b2o20bo2b3o12bo6b3o\$25bob2o291bo12b2o6bo\$o3bo3bobobo11bo4bo303bo\$23b2o\$o3bo7bo\$22bo4b2o\$obobo3bobobo13bo\$23b3o\$4bo7bo12bo\$26bo4bo\$4bo3bobobo12b2ob2obo\$24bo3bo145bo\$24b4o144bo2b2o\$21bo3b2o143b3o\$21b2o\$21bo149b2o\$166b4o2bo24bo35bo35bo35bo35bo34bo13bo\$163bob3o3b3o14b3o4bobo26b3o4bobo26b3o4bobo26b3o4bobo26b3o4bobo5b2obobo14b3o4bobo5b2obob2obo\$140bobobo3bobobo9b2o7b4o8bo2b2o4b2obobo21bo2b2o4b2obobo21bo2b2o4b2obobo21bo2b2o4b2obobo14bo6bo2b2o4b2obobo3bo4bob2obo6bo2b2o4b2obobo3bo4bobo\$174bo8b2o7bo26b2o7bo26b2o7bo11b2obobo9b2o7bo11b2obob2obo6b2o7bo7bo10bo6b2o7bo7bo\$140bo7bo3bo9bob2obo15bo3bo6b3o22bo3bo6b3o22bo3bo6b3o5bo4bob2obo6bo3bo6b3o5bo4bobo9bo3bo6b3o3bo3b2o12bo3bo6b3o3bo3b2o\$162b2o3bo20b2o4bo2bo26b2o4bo2bo26b2o4bo2bo3bo10bo11b2o4bo2bo3bo22b2o4bo2bo3b3o19b2o4bo2bo3b3o\$140bobobo3bobobo14bo25b2o2bo31b2o2bo31b2o2bo3bo3b2o22b2o2bo3bo3b2o22b2o2bo30b2o2bo\$162b2o26b3o4bo4b3o21b3o4bo4b3o21b3o4bo4b3o21b3o4bo4b3o21b3o4bo27b3o4bo\$144bo3bo3bo9bo34bo3bo3b2o26bo3bo3b2o26bo35bo35bo34bo\$162b3o31b2o3bo10bo19b2o3bo30b2o34b2o34b2o33b2o\$140bobobo3bobobo10b2o3bo25bo2b2o3bo4bob2obo17bo2b2o3bo4bobo20bo2b2o31bo2b2o31bo2b2o30bo2b2o\$74bo94bo22b2o10b2obobo18b2o10b2obob2obo15b2o34b2o34b2o33b2o\$37bobobo25bobob2obo91b2o26bo35bo17bo17bo35bo35bo34bo\$35bo3bob2obo20bo3bobo93bob2o\$o3bo3bobobo21bo9bo19bo100b2o\$33bo3b2o24bo3b2o92bobo\$o3bo3bo24bob2o26bob2o94bo\$22b2ob2o7bo17b2ob2o7bo96bobo\$obobo3bobobo8b3o8bo18b3o8bo\$22b2obo2bo2bobo18b2obo2bo2bobo\$4bo7bo18bobo27bobo\$26b2obo26b2obo\$4bo3bobobo15b2o28b2o\$28b3o27b3o\$30bo2b2o25bo2b2o\$32bo29bo3\$181bo\$180bobo\$180bobo\$180bo2\$180bobo2\$178b3o\$140bobobo3bobobo24bo\$176b2obo\$140bo7bo3bo27bo\$27b3o23bo126bo\$25b2o3bo21bobo85bobobo3bobobo22bobo\$23bo27b2o119bob2o\$21b2o3bo3bo22bo90bo7bo17b2ob2o\$23bo2bo3bo22bo116b2ob2o\$o3bo3bobobo12b2o113bobobo3bobobo20bo\$26bo3bo21b2o107bob2o6bobo\$o3bo3bo17bo3bo19b2o109bo3b2o\$26b3o19b2o2bo108bob2o6bobo\$obobo3bobobo35b3o115b3ob2obo\$26b3o8bo2b2o9b2o114bob2o\$4bo3bo3bo13bo3bo6b2o2bo\$26bo3bo6bo3b3o2b3o119bobo\$4bo3bobobo12b2o14b2obo2b2o121b2obo\$23bo2bo3bo11bo130bo\$21b2o3bo3bo12b2o\$23bo20bo3bo\$25b2o3bo14bo2bo\$27b3o16bobo7\$164bobo29bobo\$162b2o3b2o27bo3bo\$162bobo31bo4b2o\$164bo33bo3bo2b2o\$161bo37b2o3bo\$161b2o3bo\$140bobobo4bo19b2o24b4o\$164b2o3bo23b2obo2bo\$140bo8bo15bobo4b2o19b4o2bo\$22b2o29b2o110b7obo23bo\$o3bo3bobobo8b3o20bo7b3o85bobobo4bo14bo\$22bo20bo9bo15b2o94b7obo17b3o\$o3bo7bo10b2ob2o15b2o9b2ob2o10b3ob2obo63bo3bo4bo15bobo4b2o17b3o\$28bo5bo6bo17bo5bob3o6bo87b2o3bo10bo2b2o\$obobo7bo10b2o7bobob3o6bo8b2o7bobo6bo67bobobo4bo19b2o9b2o2bo\$24bo6bobo4b3ob2obo9bo6bobo9b2o85b2o3bo13bo3b3o2b3o\$4bo7bo12bo2bo9b2o16bo2bo14bo86bo22b2obo2b2o\$26bobobob2o23bobobob2o10bo88bo20bo\$4bo7bo12b2o3bo25b2o3bo100bobo21b2o\$27bo30bo103b2o3b2o18bo3bo\$164bobo21bo2bo\$189bobo11\$26bo146bo\$26b2o143b2o96b2o31b2o\$26bo146bo94bo32bo5bo\$28bo146bobo15bo3b2o27bo3b2o35b2ob3o27b2ob3o2b2o\$28bo145bo2bo13bo2b2obobo24bo2b2obobo31b7obo2b2o20b7obo105b2o34b2o\$27b2o18bo126bo2bo11b3o6bo3bo19b3o6bo3bo5bo22bo3bo5bo22bo3bo108bobo4bo28bobo\$45b2o127bobo11bobo7b7obo14bobo7b7obo2b2o15bo3bobo26bo3bobo35bo35bo36bo2bob2obobo25bo2bob2obobo\$29bo17bo12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9b2o2bo\$4bo3bo3bo11b6o23b6o23bo3bo10b2o2bo\$28b2o2bobo22b2o2bobo18bobo13b2o\$4bo3bobobo9bo2b2o5b2ob2o14bo2b2o5b2ob2o16bo3b2o\$20b2o3bob2ob2o17b2o3bob2ob2o10bo11bo16bo\$22bo3b2o3bo5bobo11bo3b2o3bo5bob2obo11bo16b3obo\$27bo6b2obob2obo13bo6b2obobo12bo17bo2bo\$31b2o9bo17b2o17b3o16b2o4bo\$82bo14bo6bo\$78bo4b2o12b2o4bo\$103bo\$79b2o18b3o\$80bo4bo12bo4b2o\$81bob2o12b3o\$81bobo14b2o\$82b3o\$84bo2b2o\$86bo!`

Also, here is the collection of all known c/3 ships up to 50 cells:
`x = 761, y = 462, rule = 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Nicolay Beluchenko collected all of the known c/4 diagonal spaceships up to 70 bits here.

Finally, a collection of most of the known 2c/5 orthogonal ships up to 90 cells can be found here. The only ships that are missing are the ones from this post.

Edit: I added the following ship to the c/4 orthogonal collection above (based on one of the new ships):
`x = 10, y = 30, rule = B3/S232bo\$2o3bo\$2bo2b2o\$5b2o\$5bo\$4b2o\$5bo\$2b3o\$2b2o\$bobo\$bob4o\$bobo\$6b2o\$3b3o\$2b2obo\$2b2o2bo\$2b2o2bo\$3b2o2\$5bo\$5b3obo\$4bo2bo\$3b2o4bo\$2bo6bo\$2b2o4bo\$8bo\$4b3o\$3bo4b2o\$2b3o\$3b2o!`
-Matthias Merzenich
Sokwe
Moderator

Posts: 1479
Joined: July 9th, 2009, 2:44 pm

### Re: New small c/4 orthogonal ship

Scorbie,

Yes, I am Tim Coe.

If I do a run of "knight2" and nothing is found, no spaceships exist under those run parameters (barring bugs of course).

If a spaceship is found I always do some tree trimming. This will always preclude finding some other spaceships. This is a real problem when searching for 2c/6 ships, as many c/3 ships are found and the associated tree trimming has a tendency to mask and make undiscoverable some 2c/6 ships. I am considering algorithms to make my searches exhaustive when ships are found, but doing so will be a significant amount of programming.

David Eppstein's analysis of my programming style still applies. Now though, the ship movement and ship period are implicit in the hookup of the constraint propagation network and I have my program lie to itself as to what the actual period is when running c/5 searches.

Sokwe,

I will be describing my search approach as time goes on. I will also post the actual code.

Josh Ball certainly found quite the number of tags for the 41-cell ship.

I have found a number of c/4 ships in the 60 to 70 cell range and will eventually post an updated table.

Have a happy day,

-Tim Coe
moebius

Posts: 26
Joined: December 10th, 2015, 9:07 am