LifeWiki:Spaceship Search Status Page

From LifeWiki
(Redirected from User:Codeholic/Sandbox)
Jump to navigation Jump to search

Conventions

The tables below give the minimum orthogonal width and height of the envelope of a spaceship of the specified type. This is found by simulating a period-p spaceship for p iterations, with the initial phase chosen to minimise the width or height.

For types where the minimum is known, references point to the proof of minimality rather than the discovery of the ship possessing it. A stamp collection of minimum-width ships is given below the table.

Symmetry considered is in the line parallel to a spaceship's direction of motion.

Known spaceships by width

The width in the following table is the width of the envelope of the pattern after it has been run through every phase in its period and minimized over all starting phases. Further, the width is the direction perpendicular to the orthogonal direction of greatest displacement. For example, for a (2,1)c/6 ship the width is the dimension perpendicular to the direction in which the ship is displaced by 2 cells.

Note that symmetric diagonal spaceships always have an odd diagonal width (measured by half-diagonals), but since this table records the orthogonal width of the ship, the minimum width for such a ship might not be odd. The same applies to glide symmetric diagonal ships, although these ships can have odd or even width depending on whether their diagonal placement is even or odd respectively.

Velocity Asymmetric Odd-symmetric Even-symmetric Gutter Odd glide-symmetric Even glide-symmetric
(1,0)c/2 21 21 28 21 - -
(1,0)c/3 12 15 12 17 - -
(1,0)c/4 10 13 16 17 - -
(1,1)c/4 3 7[n 1] - 7[n 1] - 3
strict 18[1] 19[1]
(2,0)c/4 5 11 12[n 1] 11 5 12[n 1]
strict 20[2] 16[1]
(1,0)c/5 11 19 18 19 - -
(1,1)c/5 13[3] w ≤ 24 - w ≤ 24 - -
(2,0)c/5 10 15 18 15 - -
(1,0)c/6 12[4] 19 18 21 - -
(1,1)c/6 10 < w ≤ 35 10 < w ≤ 36 - 10 < w - 10 < w ≤ 35
(2,0)c/6 12[5] 17[2] 18[2][6] 19[2] 17 18[6]
(2,1)c/6 15[3] < w ≤ 31 - - - - -
(3,0)c/6 21[7] 21 28 21 - -
(1,0)c/7 10[8][9] 19[9] 22[10][n 1] 21[8][9][n 1] - -
(1,1)c/7 9 < w ≤ 27 9 < w ≤ 27 - 9 < w - -
(2,0)c/7 11[11][12] 23[2] 18 23[12] < w ≤ 33 - -
(2,1)c/7 11[13] - - - - -
(3,0)c/7 14[14] 29[15] 28[14] 31[14][16] - -
(1,0)c/8 10[17] 19[18] 20[19] 21[17] - -
(1,1)c/8 7 < w ≤ 21 7 < w - 7 < w - 7 < w ≤ 21
(2,0)c/8 9[2] 15[2][20] 18[2][20] 17[2][20] 13 14
(2,1)c/8 8 - - - - -
(2,2)c/8 8 < w ≤ 24 8 - 8 8 -
(3,0)c/8 11[13] 21[13] 22[21] 23[13] - -
(3,1)c/8 12[13] - - - - -
(4,0)c/8 11[2] 17[2] 20[2] 19[2] 17 20[2]
(1,0)c/9 8[22] 15[22] 16[22] 15[23] - -
(1,1)c/9 6 6 - 6 - -
(2,0)c/9 8[24] 15[25] 16[23] 17[24] - -
(2,1)c/9 7 - - - - -
(2,2)c/9 7 7 - 7 - -
(3,0)c/9 11[26] 17[2] 16[5] 17[2] - -
(3,1)c/9 8 - - - - -
(4,0)c/9 11[14] 21[14] 22[27] 23[14] - -
(1,0)c/10 6[28] 11[28] 10 13[28] - -
(1,1)c/10 7 7 - 7 - 7
(2,0)c/10 6 < w ≤ 11 11 < w ≤ 19 12 < w ≤ 20 13 < w ≤ 19 13[27] < w ≤ 19 14[27] < w ≤ 20
(2,1)c/10 6 - - - - -
(2,2)c/10 6 6 - 6 6 -
(3,0)c/10 9[29] 17[30] 18[29] 17[31] - -
(3,1)c/10 7 - - - - -
(3,2)c/10 8 - - - - -
(4,0)c/10 10[5] 15[2] 22[32] 21[2] 15[33] 16[33]
(4,1)c/10 8 - - - - -
(5,0)c/10 11[5] 19[2] 22[5] 19[2] - -
(1,0)c/11 6[34] 11[35] 12[35] 11[34] - -
(1,1)c/11 ? ? - ? - -
(2,0)c/11 6[28] 11[28] 12[28] 13[28] - -
(2,1)c/11 ? - - - - -
(2,2)c/11 ? ? - ? - -
(3,0)c/11 6 11 12 13 - -
(3,1)c/11 ? - - - - -
(3,2)c/11 ? - - - - -
(4,0)c/11 9[36] 17[36] 18[36] 19[36] - -
(4,1)c/11 ? - - - - -
(5,0)c/11 10[36] 19[36] 20[36] 21[36] - -
(2,0)c/12 w ≤ 63 ? ? ? 9[37] ?
x = 1122, y = 633, rule = B3/S23 39b3ob3o193b3ob3o209b3o2b4o2b3o220b3ob3o215b3o153b3o4b3o$38bo2bobo2bo 191bo2bobo2bo207bo3bob4obo3bo218bo2bobo2bo213bo2bo153bo2bo3bo2bo$37bo 3bobo3bo189bo3bobo3bo205bo6bo2bo6bo216bo3bobo3bo215bo153bo6bo$37bo9bo 189bo9bo205bo3b2o6b2o3bo216bo9bo215bo153bo6bo$39bo5bo193bo5bo209bo12bo 220bo5bo214bobo155bobo4bobo$36bobo7bobo187bobo7bobo203bobo14bobo214bob o7bobo$35b2obob2ob2obob2o185b2obob2ob2obob2o201b2obob2o8b2obob2o212b2o bob2ob2obob2o$34bobobo2bobo2bobobo183bobobo2bobo2bobobo199bobobob2o8b 2obobobo210bobobo2bobo2bobobo$33b2obo4bobo4bob2o181b2obo4bobo4bob2o 197b2o3bo2bo8bo2bo3b2o208b2obo4bobo4bob2o$32bo3bob2obobob2obo3bo179bo 3bob2obobob2obo3bo195bo3bobo2b2o6b2o2bobo3bo206bo3bob2obobob2obo3bo$ 36bo4bobo4bo187bo4bobo4bo202bo20bo213bo4bobo4bo$32b2o3bo2bo3bo2bo3b2o 179b2o3bo2bo3bo2bo3b2o195b2o24b2o206b2o3bo2bo3bo2bo3b2o9$912bo158b2o$ 911bobo153b2obo2bob2o$910bo3bo152b2o6b2o$911b3o153bobo4bobo$1069b2o2b 2o$909b2o3b2o152b2ob2ob2o$906b2o3bobo3b2o151bo2bo$906b2o3bobo3b2o149bo 6bo$904b2o5bobo5b2o147bo6bo$908b2obobob2o$41b2o199bo218b2o222b3o9b3o 204bo6bobo6bo147b8o$37b2obo2bob2o194bobo213b2obo2bob2o217bobob2o5b2obo bo206b2o2bobo2b2o149b2o6b2o$37b2o6b2o193bo3bo212b2o6b2o217bobobo7bobob o204bo2bobo3bobo2bo$37bobo4bobo194b3o213bobo4bobo218bob2ob2ob2ob2obo 205b2o11b2o151b2o$39b2o2b2o414b2o2b2o224bobobobo209b2o11b2o150bo2bo$ 38b2ob2ob2o193b2o3b2o212b2ob2ob2o221bobobobobobo210bo7bo$40bo2bo193bo 3bobo3bo212bo2bo222b2obobobobob2o209b3o3b3o153bo2bo$38bo6bo190b2o3bobo 3b2o209bo6bo220b3o2bobo2b3o211bo3bo151b3ob4ob3o$38bo6bo189bo5bobo5bo 208bo6bo220b2o2bo3bo2b2o208b2obo3bob2o147bo12bo$236bob2obobob2obo436bo 4b2ob2o4bo209b2o3b2o150bob2o4b2obo$38b8o412b8o219bo13bo209bobobobo154b 4o$37b2o6b2o410b2o6b2o600bo2b4o2bo$909bo2bo2bo152b2ob2ob2o$910b2ob2o 152bob6obo$909b2o3b2o151bo8bo$906b2obo5bob2o$906b2o3b3o3b2o146bo5b2o5b o$906bob9obo145b2o3b2o2b2ob4o$910b2ob2o148bo2b4o4bobo3bo$910bo3bo152bo bo3b2obo$908bo2bobo2bo149b3o6b2o$909bobobobo150bo8b2o$911bobo$906bo3bo 3bo3bo$905b3o2bobobo2b3o$904bo3bobo3bobo3bo$905bobo2bob2o2bo2bo$909b5o 2b2o$912bo3bo$913bobo$5b2o38bo29b3o162bo3bo33b3o3b3o171bo6bo31b3o4b3o 182b3ob3o32b3o3b3o175bobo$4b2o39bo29bo2bo161bo3bo33bo2bobo2bo171bo6bo 30bo2bo4bo2bo182bo3bo33bo2bobo2bo$6bo37bobo28bo163bobobobo31bo3bobo3bo 169bobo4bobo32bo4bo222bo3bobo3bo$75bo203bobobobo213bo4bo182b2o7b2o31bo bobobo$43bo32bobo160bobobobo33bo5bo210bobo6bobo179b5ob5o31bo5bo$41b3o 197bobo35b2o3b2o172bo6bo218b2o3bobobobo3b2o28b2o3b2o$40bo2bo194bobo3bo bo33b2ob2o172b3ob2ob3o218b4o2bobo2b4o30b2ob2o$37b3o3bo194bobo3bobo33b 2ob2o172b3ob2ob3o223bo3bo35b2ob2o$40b3o195bo2b3o2bo32bo5bo170bo2bo4bo 2bo261bo5bo$40b2o2b2o410b2o3b2o3b2o221b2o3b2o$37bobo2bo3bo190b2o7b2o 207b2obob4obob2o217b3o7b3o405b3o10b3o$40b2o4bo190bo9bo210bobo2bobo220b 2o9b2o405bo2bo8bo2bo$39bobob2o193bo7bo210b3o4b3o222b2o3b2o408bo14bo$ 39bo197b2ob5ob2o210bo6bo224bo3bo409bo3bo6bo3bo$39b3o196bo2bobo2bo208bo bo8bobo220b2o3b2o408bo3bo6bo3bo$38bo2bo197bobobobo209bobo3b2o3bobo218b o2bo3bo2bo407bo3bo4bo3bo$38bo2bo416b3o2b3o221bo2bo3bo2bo412bo2bo$240b 2ob2o210bo4bo2bo4bo217bo11bo412b2o$39b2ob2o196bo3bo210bo4bo2bo4bo219b 2o5b2o411bobo2bobo$38bo2b3o195b2o3b2o210bo10bo640bo6bo$39bo199b2o3b2o 212b2o4b2o222b2o5b2o213bo3bo32bo5bo155b2o2b2o$41b2o416bob2obo224bo5bo 214bo3bo31b3o3b3o152b2o6b2o$38b2obob2o414b6o444bobobobo29b2obo3bob2o 150b3obo2bob3o$41bo2bo413bo6bo223b2o3b2o249bob2o3b2obo149b2o2bo4bo2b2o $43b2o413bo2b2o2bo443bobobobo27b2o2b7o2b2o146bo2bo8bo2bo$40bo2bo414bo 6bo445bobo32bob5obo149bo2b2o6b2o2bo$42bo416b2o2b2o443bobo3bobo28bo4bo 4bo146bo3bo10bo3bo$39b2o3bo414b2o2b2o443bobo3bobo185bo3b3o6b3o3bo$43b 2o863bo2b3o2bo25b3o11b3o145bo14bo$41b2obo900b2o7b2o146bo2bo12bo2bo$ 907b2o7b2o24b3o11b3o143bob2o12b2obo$43b3o861bo9bo24b2ob2o7b2ob2o144b3o 12b3o$42b4o862bo7bo27bo5bo5bo$41bo2bo862b2ob5ob2o27bo3b3o3bo$43bo864bo 2bobo2bo31b5o150b2o14b2o$43bo865bobobobo28bo11bo146bo16bo$40b2o903b4o 3b4o146bobo14bobo$40b3o867b2ob2o33b2ob2o153bo4b2o4bo$41bo868bo3bo34b3o 154b2ob2o2b2ob2o$42bo866b2o3b2o31b2obob2o150b4o8b4o$42b2o198bo36bo5bo 623b2o3b2o29b2obobobob2o147b2o2b2obo2bob2o2b2o$242bo35b3o3b3o658b2ob2o b2ob2o146bo18bo$43bo198bo34bo2bo3bo2bo621b2o3b2o28bo2bo5bo2bo148b2o2bo 4bo2b2o$41b2o195bo3bo3bo29b3o7b3o619bo2bobo2bo26b2o3bo3bo3b2o144b2o16b 2o$235bobob2obob2obobo27bobo5bobo623bobo30bo11bo149b2o8b2o$234b2obobob 3obobob2o28b2o3b2o622bo2bobo2bo31b2ob2o153b3o6b3o$233bo3bo9bo3bo23bo4b o3bo4bo617b2ob2ob2ob2o28b3o2bo155b3o4b3o$233bobobob2o3b2obobobo28bo3bo 622b4obob4o29b3ob3o155bo4bo$237b2obo3bob2o27b2o3bo3bo3b2o621b3o32b2o2b 4o153bo2bo2bo2bo$234b2obo9bob2o26bo2bo3bo2bo624bo195bobo2bobo$237b2o2b obo2b2o31bo5bo175b2o32bo12bo177bo11bo30bo5bo210b2o157b2obo6bob2o$237bo bobobobobo213b2o31bobo10bobo174b2obobo5bobob2o27b3o3b3o175bo33b2o5bo 152bo2bo4bo2b2o$239bobobobo213bob2obo28b2ob2o8b2ob2o176bob2o3b2obo29bo 2bo3bo2bo173b4o31b2o3b2obo149bobo3bo3bo3b2o$239bobobobo211b3o4b3o26b2o 14b2o173b2obo3bobo3bob2o25b3o7b3o170b2o3b2o29b2o4bo2b2o147b2o5bo$239bo bobobo208b2o12b2o25bo12bo175b3o2bobobobo2b3o26bobo5bobo171b2o3b2o30bo 2b3o2b2o148bo4bo$236b2obobobobob2o205b2o2bob4obo2b2o25b4o6b4o180bobobo bo33b2o3b2o172bob3o2bo31bo5b3o148b2obo$235bobobobobobobobo208bobo2bobo 29bo2b2o4b2o2bo177bo2bobobobo2bo26bo4bo3bo4bo167bo2b2o2bo30bo5bo2b2o$ 236bo2bobobobo2bo247b2o2bo2bo2b2o179bobobobobobo32bo3bo173bo2bo2bo29bo bo4bo2b2o$238bo2bobo2bo210b2o6b2o30b2ob4ob2o180b3obobob3o27b2o3bo3bo3b 2o169b2o33b5o5b3o$454b6o4b6o28bobo2bobo179bo2b3o3b3o2bo27bo2bo3bo2bo 173bo33b2o$2b3o35bo38bo374bobo10bobo29bo4bo185b2ob2o34bo5bo175bo2bo29b o$bo37b5o34bobo157b3o3b3o207bob2o8b2obo215b2o11b2o211bo32b3o2b3o$o5bo 31bo3bobo32b2ob2o153bo3b2o3b2o3bo204bob2o8b2obo28bo6bo179b2o11b2o211b 2o35bo2bo4bo$o5bo31bobobobo32bo2b2o152b3o4bobo4b3o202b2ob2o8b2ob2o25b 2ob2o2b2ob2o178b3o7b3o212b2o32b3o4b2o2bo$b2obo34b2ob2o32b3o159bo2bobo 2bo206b2obo10bob2o26bo8bo177b2o2bo7bo2b2o207bo7bo26bo2b2o6bobo$3o2bob 2o31b3o31b2o4b2o155bobobobobobo206bobo10bobo27b2o6b2o177bobobo7bobobo 206b3o6bobo28bobo5b2o$bo5bo66b4o157bo5bobo5bo206bo2b2o2b2o2bo439bobo5b o2bo23bo7bo5bo$8bo31b3o29bo5b2o155bo5bobo5bo205bo4bo2bo4bo217bo11bo 212b2o2b3o33bo$b2o38bob2o29b3obo157b5o3b5o212b2o222bobob2o3b2obobo206b 2o4bo3bo35bobo$3o33b3o3b2o33bo382bo2bo225b2o3b2o210b2o5b2o29b2o$o3b2o 30b3o36bobo613bobo213bo2bo$3o34bob3o31bobo380b4o4b4o218bobob2ob2obobo 211bobo$2o7b2o28bo32bobo378b3o2b2ob2ob2o2b3o217b2obobob2o$bo5bo3bo27b 3o35bo377bo5b2o5bo220bobobobo$b2obob2o2bo26bo38bobo374b2obob3o2b3obob 2o214b3obobobobob3o$bo4bo29bo2bo35bo379b3o3b2o3b3o215bo6bobo6bo$2bo4bo 2bo25b7o32bo379bo12bo218bo3bobo3bo$7bobo27bo2b3o33bobo378b2o2b2o2b2o 223b2ob2o$6bob2o27bo5bo34b2o377b10o217bo2b2o2bobo2b2o2bo$6bobo29bobob 2o31b2ob2o377bob2o2b2obo217bo2bob2o3b2obo2bo$7b2o35bo414bo4bo220b2o11b 2o$8bo28b2o5bo29bo385bo2bo$8bo27bobobob2obo28bobo381bobo2bobo219bobo9b obo$7bo29bo3bobo31bo381b2ob4ob2o218bo2bo7bo2bo$8b2o35bo28b2o381b2ob4ob 2o218bo3bo5bo3bo$40bo3bo29b2o382bo6bo221bo2bo3bo2bo$38b3o35bo380b3o4b 3o220b2o7b2o$38bo2b4o29b2o2b2o375bobo8bobo$41bo36b2o374bo14bo217bob3ob 3obo$38bo6bo32bo375b2ob2o6b2ob2o215b2o2b3ob3o2b2o$38b3obo2bo192b2o5b2o 35bo36b3ob3o131b2o6b2o218b2o2bo5bo2b2o247bo5bo$40b2o3bo193bo5bo35bobo 34bo2bobo2bo129b2ob6ob2o218b2o9b2o247b3o3b3o$41b3obo191bobo5bobo32bo3b o32bo3bobo3bo126b2obo8bob2o216b3o7b3o246bo2bo3bo2bo$40bo4b2o190bo9bo 33b3o33bo9bo130bo6bo219bob2ob2ob2ob2obo244b3o7b3o$39b2o2b3o189b2o3bo3b o3b2o69bo5bo359b3o2b2ob2o2b3o245bobo5bobo$39b2o2bo192b2o2b2ob2o2b2o30b 2o3b2o30bobo7bobo356bobo3bobo3bobo247b2o3b2o$39bo2bo194bo3bobo3bo28b2o 3bobo3b2o26b2obob2ob2obob2o128b8o222b3o3b3o246bo4bo3bo4bo$40bo199b2ob 2o31b2o3bobo3b2o25bobobo2bobo2bobobo127b2o4b2o221bob2o3b2obo250bo3bo$ 42bo198bobo30b2o5bobo5b2o22b2obo4bobo4bob2o356b2o5b2o246b2o3bo3bo3b2o$ 42bobo192bob3ob3obo30b2obobob2o25bo3bob2obobob2obo3bo353b3o7b3o246bo2b o3bo2bo$42b3o189b2ob2o7b2ob2o23bo6bobo6bo25bob3o3b3obo357b2o9b2o248bo 5bo$40bobo192b4o2bobo2b4o27b2o2bobo2b2o24b2o3bo2b2ob2o2bo3b2o$40b3obo 194bobobobo29bo2bobo3bobo2bo26b2o9b2o361b2ob2o254b3o$37b2o2b2obo230b2o 11b2o26bo11bo359bobo3bobo250b2o3b2o$37b2ob2o196bo2b3o2bo28b2o11b2o25bo bo9bobo356b4o5b4o251bo3bo$278bo7bo27bo15bo354bo3b2o3b2o3bo245bo2b2o$ 40bobo193b4obobob4o29b3o3b3o29bo11bo356bo3b2o3b2o3bo248bo3bo$39bob2o 193b6ob6o31bo3bo28b2obo11bob2o612bo3bo3b2o$38b3o197b2o5b2o30b2obo3bob 2o24bo3b2o9b2o3bo353bo2bo5bo2bo254bo$40bo195bo2bo5bo2bo30b2o3b2o27bo2b o11bo2bo357bo5bo249b2o5bo$38b2o2b2o235bobobobo32b2o5b2o361b2o5b2o$42b 2o192b3o7b3o66b2ob2o5b2ob2o357b2o7b2o$42b2o235bo2bo2bo29b4o7b4o356b2ob 2o3b2ob2o$234bo15bo29b2ob2o29b2o4b2ob2o4b2o358bobobobo$234b2o13b2o28b 2o3b2o32bob2ob2obo357b2obo3bobo3bob2o$40b3o191b2o13b2o25b2obo5bob2o28b 5ob5o358b2obobobobob2o$40b3o192b4o7b4o26b2o3b3o3b2o28b2o7b2o361bo5bo$ 40b2o197bo5bo30bob9obo395bo2bo9bo2bo$40b2o196bo7bo33b2ob2o35b2ob2o358b ob4ob2ob2ob4obo$40b3o237bo3bo35bo3bo359b3o11b3o$36b2obo3b2o190b3o9b3o 28bo2bobo2bo32bo5bo132bo6bo35b2o37b3o2b4o2b3o133bo9bo$36b2obo3b2o234bo bobobo34bo3bo132bobo4bobo30b2obo2bob2o32bo3bob4obo3bo$39bo241bobo173bo bo4bobo30b2o6b2o31bo6bo2bo6bo129b2o11b2o$39bo2bo192b3o9b3o31bobo174bo 6bo31bobo4bobo31bo3b2o6b2o3bo128bo15bo$39bo2bo195b2o5b2o33b2ob2o214b2o 2b2o35bo12bo131bo2bo7bo2bo$39bob2o194b2o2b3o2b2o209b3o4b3o31b2ob2ob2o 31bobo14bobo132bo5bo$39b2o193b3o2b2obob2o2b3o206b4o2b4o33bo2bo32b2obob 2o8b2obob2o128bobo7bobo$242bo217bo2bo34bo6bo29bobobobo10bobobobo$241bo bo213b3ob2ob3o31bo6bo28b2o3bobob2o4b2obobo3b2o127bo9bo$44bo196bobo213b 2o6b2o66bo3bobobob2o4b2obobobo3bo124bo2bo7bo2bo$40bobo413b2o8b2o30b8o 30bo4bobobo2bobobo4bo127bo2bo7bo2bo$38b2obobob2o450b2o6b2o26b2o6bo2bo 4bo2bo6b2o126bo9bo$39bobobobo409bo12bo73b3o4b3o$40b2ob2o408bo2bo10bo2b o30b2o182b2o11b2o$39bo5bo407bo2bo10bo2bo29bo2bo41b4o137bo11bo$38bobo3b obo499b2o137bobo9bobo$42bo413b3o6b3o32bo2bo180bobo11bobo$42bo413bo10bo 28b3ob4ob3o176b4o9b4o$39b2o3bo413bo6bo29bo12bo174b2ob3o7b3ob2o$39b2o 415b3o6b3o28bob2o4b2obo178bo2bo5bo2bo$38b3o2b2o455b4o183b2o7b2o$37b2ob 2o417bob2obo32bo2b4o2bo180b3o5b3o$37bo5bo416bo2bo34b2ob2ob2o182bobo3bo bo$456bob2ob2ob2obo29bob6obo180b2ob2ob2ob2o$37bo7b2o409b3o6b3o29bo8bo 181bobo3bobo$37b2ob4obo$39bob4o411bobo6bobo27bo5b2o5bo175b2o13b2o$43bo bo410bobo6bobo26b2o3b2o2b2o3b2o174b3o11b3o$44bo409b3ob3o2b3ob3o23bo2b 4o4b4o2bo173bo2b2o7b2o2bo$497bobo4bobo179bo3bo3bo3bo$239b2o3b2o36bo34b 3o5b3o168b3o6b3o181b3ob3o$237b2o2bobo2b2o33b3o33bobo5bobo168bo10bo176b o2bobobobobobo2bo$281b3o33bobo5bobo356b3o11b3o$241bobo71bob2o3bo3b2obo 354bo15bo$236bo4bobo4bo28b3o5b3o27b2o4bobo4b2o355b3o9b3o$236bo3bo3bo3b o70b2obob2o359b3o9b3o$236bo2bo5bo2bo28bobo5bobo30bo7bo359b3o7b3o$277bo bo5bobo30bobo3bobo362b2o3b2o$236bo11bo29bo7bo27b5o7b5o354b2o11b2o$236b o2b2o3b2o2bo28bo2bo3bo2bo25bo2bo11bo2bo353bo3bobobobo3bo$235bo3b2o3b2o 3bo28bob2ob2obo27bob3o7b3obo353bo2b2o7b2o2bo$236bo2bobobobo2bo26bo4bo 3bo4bo26bob2o5b2obo358b2o2bobo2b2o$236b2o3bobo3b2o26b6o3b6o25b2obobo3b obob2o358bob2ob2obo$239bobobobo29bo4bo3bo4bo25b3obo5bob3o$239bobobobo 30b2obo5bob2o400b2o3b2o$238b2obobob2o33bo3bo34b2o3b2o362bo2bobo2bo$ 241bobo32bo11bo32bobo363bobobobobobo$240b2ob2o31bo3bo3bo3bo29bo7bo357b 4obobobobob4o$277bo2bo3bo2bo30b2o5b2o356bo4bo2bobo2bo4bo$277bo2bo3bo2b o27b2o11b2o354bobo4bobo4bobo$41b2o35b2o27bo134bo29b3o3bobo3bobo3b3o20b ob2o11b2obo126bo6bo29bo12bo177b3o7b3o$43bobo29b2ob2o26b3o129bob2ob2obo 24bo2bo3b9o3bo2bo19b2o2b2o7b2o2b2o125bobo4bobo28bo12bo179bob2ob2obo$ 40bo3bob2o24b4o2bobo23b2ob3o2b3o123b2obobob2o24bo2bo2b2ob5ob2o2bo2bo 19bo2bo2bo5bo2bo2bo124bo2bo4bo2bo26bobo10bobo174bo4b2o3b2o4bo$41b5o25b o4bo4bo23bo2bob3o2bo121bob2obob2obo30b2o2bo2b2o27bo4bo5bo4bo126b2o6b2o 28bo12bo174b2o4bo5bo4b2o$72b2o7bo20b2obo4bobo3bo121bo7bo30b2o3bo3b2o 26bo2bo2bo3bo2bo2bo164bo12bo174b2o15b2o$81bo20b2obobo2bo5bo121bo7bo30b 2o7b2o23bo5bo9bo5bo119bo5bo4bo5bo25bo3b4o3bo176bo2b2o2bobo2b2o2bo$43bo 33b3o22bo8bo2bo121b2o3b3o3b2o31b2ob2o27bobo15bobo119bobo3bo6bo3bobo28b 4o183b4o3b4o$42bobo31bo24b2o12bobo118bo11bo28bo3bobo3bo28bo11bo122bo2b o3b2o4b2o3bo2bo23b4o4b4o180b2o5b2o$38bo2bo34bobo33b2obob2o116b2o11b2o 27bo3bobo3bo24bo3bobo7bobo3bo118bo2b2o3bo4bo3b2o2bo217bo3bo$37b2o2bo 33b2o32b5obobobo122bo34b2o2bobo2b2o24bo2bo3bo5bo3bo2bo165bo6bo180b2obo 5bob2o$37bo3bo32b3o31bo2bo2bo2bob2o113bo2b3o5b3o2bo28b3ob3o27b2o2b2o7b 2o2b2o167b2o2b2o180bobo2bo3bo2bobo$41bo3bo30bobo28bo6b2obo3bo113bo13bo 25b2ob2o5b2ob2o27bo9bo358b2ob2o3b2ob2o$42bobo33b2o26bo2bo7bo156bo2b2o 7b2o2bo$44bo31bo3bo25bo5b3obo3b2o117bo5bo27bo17bo25b5ob5o358bob3o3b3ob o$40bob2o32bo31bo2b2o126b2obob2o28bob3o7b3obo19bo6b2ob2ob2ob2o6bo351b 2o9b2o$39bo4bo29b3o28bobo2b3o122b4o7b4o27bo2bo3bo2bo21b3o7bo5bo7b3o 350bo11bo$39bo3bo29bo2bo27b2obobobo123b3o2b5o2b3o28b3o3b3o22bo2b2o5bo 5bo5b2o2bo$38bo33bo30bobo3bo129bo5bo29b2o4bobo4b2o21bo3b5o5b5o3bo350b 3o11b3o$38b2o62b2obo3bo125b2ob3obob3ob2o30bo3bo31bob2o5b2obo$38b2o2b2o 28bob2obo23bo4bobo127bo2bo5bo2bo27bo4bobo4bo21bo3bo15bo3bo350b6o3b6o$ 42b2o28bo3b3o25bobobob3o123bo11bo24bo6b2ob2o6bo18bob2o2bo11bo2b2obo 350b2obo2bobo2bob2o$41bo2bo30bo3bo21b2o3bobo3bo159b2o2b3obo3bob3o2b2o 17bob4o13b4obo351bobo2bobo2bobo$42b2o29bo32bo130bo4bo4bo23bo5b4o3b4o5b o19bo17bo354bobobo3bobobo$45bo28bobo28bobo4b2o124b2o5b2o25bo3b2o2bo3bo 2b2o3bo393bo2bo5bo2bo$42bobo28b2ob3o26bobo130b2o5b2o26b3o2bobo3bobo2b 3o19bo21bo352bo2b2o3b2o2bo$42bo3b2o24bobobob2o27bo202bobo19bobo355bo3b o$43b4o24b2obobo3bo25bo129bo3bo3bo3bo29b3o3b3o22bo25bo349bo5bobo5bo$ 74bo32b2o126bo4bo3bo4bo27b2o7b2o21bo3bo17bo3bo349b2o2bobobobo2b2o$71b 2obobo158b3obo5bob3o26b2o9b2o25bo15bo357b2obobob2o$40b4obo30bo199bobo 7bobo20b2o23b2o353bobobobo$40bo5bo25bo4bo199bo9bo23bo3bo2bo7bo2bo3bo 164bo6bo78b3o10b3o90bo3bo$46bo25bo2bo2b2o158bo7bo31bobo3bobo24bo3bobob o5bobobo3bo164bo6bo78bo2bo8bo2bo90b2ob2o$40bo4bo30b3o158b2o7b2o30bobo 3bobo24bo5bob2o3b2obo5bo163bobo4bobo77bo14bo88bobo3bobo$40b6o192bo7bo 30bo9bo23bo3b2obo7bob2o3bo250bo3bo6bo3bo89bo5bo$40bo2b2o191b3o7b3o28bo 9bo27b2o11b2o254bo3bo6bo3bo90bo3bo$40bo32b2o160bobo9bobo27bo3bobo3bo 25bo17bo166bo6bo79bo3bo4bo3bo90b3ob3o$40bo31bo2b2o201bo2bobo2bo25bo19b o164b3ob2ob3o83bo2bo93b3obobob3o$75b2o158b3o9b3o28bo2bobo2bo25bo4bo9bo 4bo164b3ob2ob3o84b2o94bobobobobobo$40bo35bo159bo11bo62b2o3b2o9b2o3b2o 163bobo4bobo81bobo2bobo92bo2bobo2bo$39bobo194b3o7b3o30b3ob3o25b2o3bobo 7bobo3b2o165bo4bo83bo6bo92bo2bobo2bo$39bo2b4o26b2o2bo202bobobobo25b2o 3b2o3b3o3b2o3b2o164b2o4b2o83b2o2b2o92b3obobob3o$39bob3o29b3o204b5o26b 3o2b3obo3bob3o2b3o159b3o3bo4bo3b3o76bo8bo89bo4bobo4bo$46bo27bo162bo9bo 26b3o11b3o24bob2obo3bob2obo164bo3bo6bo3bo77b10o90bo3bobo3bo$41b2o3bo 27bobo158b2obo7bob2o24b3o11b3o20b2o3b2obo5bob2o3b2o165b2o2b2o81bo3bo2b o3bo90bo7bo$46bo27bobo158bo3bo5bo3bo22bo3bo11bo3bo19bob2o3bobobobo3b2o bo161bobo10bobo76bobobo2bobobo87bobo9bobo$37b2obo33bo159b3obo7bob3o25b o11bo31bobobo169bobo10bobo75b2obo2b2o2bob2o87b2o9b2o$37b2o2bo33bo161b 2o7b2o29bo9bo29bo9bo167bo12bo79b8o88bo15bo$38bobobo192bob2o7b2obo22bo 3bo3bobobo3bo3bo24b3o5b3o257bobo8bobo86bo2bo7bo2bo$41b3o192b3o7b3o24b 2o4bo5bo4b2o27b2obob2o167b2ob2o8b2ob2o74bobo8bobo88bobo5bobo$40b3o195b o7bo27bo15bo28b7o167b2ob2o8b2ob2o79bo2bo94bo7bo$41bo2bo191bobo7bobo26b 3o9b3o27b3o5b3o166b3o10b3o80b4o$41b2o2bo193b2o3b2o30bo5bo5bo27b2obobob obob2o355b3o11b3o$45bo192b4ob4o34b3o31bo3bo5bo3bo164b3o2bo4bo2b3o81b2o 93b3o7b3o$42bobobo189bo2bobobobo2bo31b2ob2o35b2ob2o174bo4bo84b2o2b2o 91bo2bo5bo2bo$240bo3bo35b5o29bo2bobobobobobo2bo167bobo2bobo82bo6bo$42b 2o195b2o3b2o31b3o2bo2b3o27b4o7b4o166bo10bo80bo6bo90bo11bo$42b2o195b2o 3b2o29bo13bo28bo7bo167b2obo8bob2o77bo8bo89bobo7bobo$41bob2o230bobo9bob o28bo7bo261bo6bo91b3o5b3o$42b3o195bo3bo32bo9bo27b2obo2bobo2bob2o163bo 4bo6bo4bo78b6o93b2o5b2o$44bo194bobobobo28bobo11bobo202bob3o3b2o3b3obo 177bobo3bobo$44bobo191bo7bo26bo2bo11bo2bo26b2o5b2o168b2o3bo2bo3b2o180b o5bo$41b3o194bo7bo27b2o13b2o209bo2bo$42b2ob2o192bo5bo254b4o$45bo272bo 7bo$43b2o195b2ob2o73b3o3b3o171b3o2b3o$44bo195bo3bo72bo2bo3bo2bo$41b3o 196bo3bo73bo7bo173bo2bo$41bo3bo195b3o73bo2bo3bo2bo172b4o$41b2o197bo3bo 75b2ob2o174bo4bo$239b2o3b2o75bobo176b4o$42bo276bobobobo$42bobo273bo3bo 3bo$38b3o2b3o272bo7bo173b4o$37bo3b2ob2o189b2o3bo3bo3b2o71bobo177b2o$ 41b5o190b4o5b4o67b2obo5bob2o171bo2bo$38bo198b2o7b2o68b2o2bo3bo2b2o170b 2o2b2o$40bobo273bo11bo170b2o2b2o$42b2o273bo9bo169bo8bo$40b3o272bobo9bo bo167bo3b2o3bo$39bob2o271b4o9b4o168bo4bo$38b2obob2o269b2obobo5bobob2o 169bo2bo180b2o13b2o25bob3o3b3obo30b3ob3o$38bo4b3o267bo2bo11bo2bo161b3o 3bo4bo3b3o175bobo7bobo26b2ob2obobob2ob2o28bo2bobo2bo$37b3o6bo271bobo3b obo172bo4bo178bo3bob2o3b2obo3bo22bo2b2o2bobo2b2o2bo26bo3bobo3bo$36bo8b o271b2obo3bob2o165bo2bo10bo2bo173b5o7b5o27bo2bobo2bo30bo9bo$37bobo3bo 269bo2bo3b2ob2o3bo2bo165bob6obo217bo4bobobobo4bo28bo5bo$39bob2o275bo2b obo2bo167bo2bobo4bobo2bo213b2o2bobobobobobo2b2o24bobo7bobo$315bo2bob2o b2obo2bo167bob2o2b2obo177bobo11bobo22b2o6bobo6b2o23b2obob2ob2obob2o$ 43b4o269bobobobobobobo168bo2b4o2bo177bo3bobo3bobo3bo23bobo3b2ob2o3bobo 23bobobo2bobo2bobobo$42b2o2bo270b2o2bobo2b2o165bo3bo3b2o3bo3bo173bo3b 3o3b3o3bo24b2o2bobobobo2b2o23b2obo4bobo4bob2o$41bobobo272bobo3bobo166b o2bo10bo2bo179bo3bo29b2o2b2obobob2o2b2o21bo3bob2obobob2obo3bo$40b2obob 2o272b2o3b2o170bo10bo179bobo5bobo33bobo32bob3o3b3obo$38b2ob2o2b2o269b 2o9b2o164b2o14b2o178bo5bo29bo5bobo5bo22b2o3bo2b2ob2o2bo3b2o$43bobo270b 3o7b3o361b2ob2o29bobo3b2ob2o3bobo25b2o9b2o$37bo2bo4bo270bobo7bobo164b 2o14b2o180bobo35bobobobo30bo11bo$43bo270b2o2bo7bo2b2o163bo14bo178b2obo bob2o27bo3b2obobob2o3bo24bobo9bobo$38b2o2b2o270b2o13b2o356bo3bobo3bo 26bobo4bobo4bobo23bo15bo$38b3obo277bo3bo169b2o12b2o174b2o5bobo5b2o25bo 4bobo4bo27bo11bo$38bo2b2ob2o269bo4bo3bo4bo353bobo5bobo5bobo21b2o6bobo 6b2o21b2obo11bob2o$40bo4bo269b2o3bo3bo3b2o354b2o2b2obobob2o2b2o26b3obo bob3o24bo3b2o9b2o3bo$37b2o2b2obo271bo2bo5bo2bo355bo3b2obobob2o3bo24bo 4b2ob2o4bo23bo2bo11bo2bo$316b3o7b3o355b2o5bobo5b2o22b2o6bobo6b2o26b2o 5b2o$43bo271bobo9bobo354bo15bo22bobo2b2obobob2o2bobo23b2ob2o5b2ob2o$ 43bo2bo268b2o11b2o355bo4bo3bo4bo31bobo31b4o7b4o$43bo2bo268bobo4bo4bobo 360bo3bo32b2o2bobo2b2o26b2o4b2ob2o4b2o$44bobo268b2o4b3o4b2o360b2ob2o 31b2o2bo3bo2b2o29bob2ob2obo$44bo270b2o3bo3bo3b2o400b2ob2o32b5ob5o$42b 2o270b3o4b3o4b3o357b2o5b2o29b2o9b2o28b2o7b2o$42b2o2bo265b2o17b2o355b2o 5b2o29b2o9b2o$42b2obo265bo5b2o2bobo2b2o5bo352bo11bo26bobo9bobo30b2ob2o $42bo643bobo7bobo25bo15bo29bo3bo$40b4o267bo2bob3ob2ob2ob3obo2bo352bobo 7bobo25bo15bo28bo5bo$45bo271b3o5b3o396bo15bo29bo3bo$40b2o277b3ob3o359b obob2o3b2obobo26b3o7b3o$43bobo268bo4b2obob2o4bo355b3ob2ob2ob3o30bo5bo$ 43bobo274bo3bo362bob3ob3obo29bobo5bobo$42bob2o640b2o9b2o30b2o3b2o$42bo 277b2ob2o362b5ob5o30bob2ob2obo$42bo641bob3o2bobo2b3obo26bo3bobo3bo$ 684b3o3b2ob2o3b3o26bo2bo3bo2bo$43bobo640bo2b2o3b2o2bo$38b2o2b3o642b2o 7b2o31b2o3b2o$39bob2o685bo2bobo2bo$39b2obo645b2obobob2o34bobo$40b2o 645bo3bobo3bo30b2obobob2o$39bo648b2obobob2o31b2obobob2o$39bobo644bobob 2ob2obobo28b2o2bobo2b2o$38bo3bo642bo3bo5bo3bo29bo5bo$37bo2b3o643b2o9b 2o$37bo650bo7bo$686bo11bo$41bob2o235bo3bo74bo5bo318b2o13b2o$39b2o2b3o 232b9o71b3o3b3o317bo2bo9bo2bo$41b3o2bo310b2o2bobo2b2o315bo17bo$41bo5bo 233b3o73b2o2bobo2b2o316bo4b2o3b2o4bo$40b2o3b2o233b5o73bo2bobo2bo319b2o b2o3b2ob2o$41b2o234b2o7b2o69bo3bobo3bo322b2ob2o$39bo3bo232b3o7b3o68bo 4bo4bo$39bo4bo230bo13bo67bo9bo321b3ob3o$40bo3bo312bo9bo$40bo2bo234b3o 3b3o70bo9bo$275b2o11b2o67bo3b3o3bo$39b2o2b2o230b2o4bobo4b2o69bo2bo2bo$ 39b2o2b2o233bobo3bobo72bobobobo$37b2o6b2o230b2o7b2o71bo5bo$36bob2o4b2o bo230bobo3bobo69bo2bo5bo2bo$36bo10bo229bo2bo3bo2bo67b2o11b2o$37bo8bo 230bobobobobobo70b2o5b2o$36b2o2b4o2b2o228b3o7b3o65bob2ob2o3b2ob2obo$ 37bobo4bobo229b3o7b3o65bo5b2ob2o5bo$38b2o4b2o230b3o7b3o70bo5bo$37bo3b 2o3bo230b2o7b2o70bo2bobo2bo94b2o121bo14bo$37bo8bo230b2o7b2o71bobobobo 94bo2bo119bobo12bobo$36bo10bo230b3o3b3o73bo3bo95bo2bo118b2ob2o10b2ob2o $37bo8bo231b3obob3o172bo4bo117b2o2bo10bo2b2o$281bobo175bo4bo120bobo8bo bo$40b2o2bo234bob3obo174b4o121bobo8bobo$40bo3b2o233bo5bo173b2o2b2o117b 2obob2o6b2obob2o$38bo3b2o235bo5bo173bo4bo118bobo12bobo$38bo3b2o232b3ob o3bob3o170bo4bo119b2ob2o6b2ob2o$37bo6b2o230bo2bob3obo2bo296bob2obo2bob 2obo$36bo2bo2b4o230bob2o5b2obo299bobo2bobo93bo5bo69b3o9b3o$37b2o2bo3bo 414b4o121b2obobo2bobob2o89bobo3bobo68bo2bo7bo2bo$42bo418b2o122b2o3b4o 3b2o88bo2bo3bo2bo66b2o13b2o$586bo3bo2bo3bo90b2o5b2o65b2obo3bo5bo3bob2o $587bo2bo2bo2bo168b3ob2o3b2ob3o$585b4o6b4o85bo5bo3bo5bo60bo21bo$583b2o 2bo8bo2b2o82bobo3bo5bo3bobo60bobob5o3b5obobo$582bo3bo10bo3bo80bo2bo3b 2o3b2o3bo2bo59bo3bo2b2o3b2o2bo3bo$582bo4bo8bo4bo80bo2b2o3bo3bo3b2o2bo 59bo3b3o7b3o3bo$582bo4b2o6b2o4bo160bo4bo9bo4bo$583b2o2bo8bo2b2o165b3o 7b3o$583b2obo10bob2o164bo2b2o5b2o2bo$768b2o5b2o$764b2o4bo3bo4b2o$583b 2o14b2o162bo3bo3bobo3bo3bo$582bo2bo12bo2bo158b2ob3obobobobobobob3ob2o$ 582bo2bo12bo2bo157bo5b2o4bobo4b2o5bo$583b2o14b2o157bo4b2o15b2o4bo$758b 3o8bo5bo8b3o$767b2o7b2o$322bo445bo2bobo2bo$321bobo436bo8b2o3b2o8bo$ 320bo3bo437bo6bo5bo6bo$321b3o434bo3b2o17b2o3bo$759bo25bo$319b2o3b2o 434b2o2bo15bo2b2o$316b2o3bobo3b2o430bo3bo17bo3bo$316b2o3bobo3b2o432b2o bo15bob2o$314b2o5bobo5b2o427bo2bo2b2o13b2o2bo2bo$318b2obobob2o432b2obo 3b2o9b2o3bob2o$44bo269bo6bobo6bo428b2o2b2ob2o9b2ob2o2b2o$43bobo271b2o 2bobo2b2o437b3o9b3o$42bo2bo269bo2bobo3bobo2bo435bo13bo$43b2o270b2o11b 2o434bob2o9b2obo$315b2o11b2o436bo11bo$39bo5bo272bo7bo440bo9bo$38bobo3b o273b3o3b3o439bo11bo$37bo2bo3b2o274bo3bo440b2ob2o5b2ob2o$37bo2b2o3bo 271b2obo3bob2o440b2o5b2o$319b2o3b2o440bo2bo5bo2bo$319bobobobo438bo15bo $768b2o5b2o$319bo2bo2bo438bob2o9b2obo$320b2ob2o$319b2o3b2o440b3o7b3o$ 765b3o9b3o$318bo2b3o2bo437bo3b4ob4o3bo$317b11o438b4obobob4o$317b2obo3b ob2o437b2obo2bobo2bob2o$765b2obo2bobo2bob2o$768bob2ob2obo$770bo3bo$ 769bo5bo2$764b3o11b3o$765bo13bo$765bo13bo$763bobo13bobo$764bo15bo11$ 143bo5bo$142b3o3b3o208bo5bo$141b2obo2b2obo207b3o3b3o$141b3o3b3o207bo2b o3bo2bo$142b2o4b2o206b3o7b3o$147bo209bobo5bobo$143bobob2obo208b2o3b2o$ 143bo2bobo206bo4bo3bo4bo$147bo212bo3bo$146b2o207b2o3bo3bo3b2o$144bo2bo 209bo2bo3bo2bo$144bo214bo5bo364bo3bo73b3o3b3o$144bo3bo581bo3bo73bo2bob o2bo$143b5obo212bo366bobobobo71bo3bobo3bo$143bob2o2b2o209b2ob2o444bobo bobo$142bo5b3o577bo7bo72bo5bo$146bo213b2ob2o360bob2o2bobo2b2obo69b2o3b 2o$143bo3bo211bo2bo2bo359bobo2b2ob2o2bobo70b2ob2o$142bo3bo212bobobobo 358bob2obobobobob2obo69b2ob2o$142bo2b2o210b2o3bo3b2o441bo5bo$141bo215b 2ob5ob2o362bo3bo70b3o9b3o$142bo2bo214b2ob2o439bo2b2o7b2o2bo$143bobo 211bobo5bobo358b2ob2o3b2ob2o65bo15bo$358bobo3bobo359b2o9b2o69bo7bo$ 143bo4b3o209b2ob2o364b2o3b2o69bo2bo7bo2bo$145bo2bo2bo208b2ob2o365bo3bo 70bobo9bobo$142b2o4bo580bo5bo69b2o11b2o$141bo3bo2bo213bo365bobo3bobo 66bo3b3o5b3o3bo$146bobo213bo364b4o3b4o65bo5bo5bo5bo$141b2o2bo214bobobo 361bo2bo5bo2bo69b2o5b2o$143b2o3b3o208b2o3b2o360bob2o5b2obo66bo5bobo5bo $147b3o578bo7bo71bob2ob2obo$146b2o209bo9bo360b2o5b2o70bo3bobo3bo$144bo 5b2o205bo9bo441b2o3b2o$144bobo3b2o206bo7bo363bo3bo73b3o3b3o$145bobo 212bo3bo364bo5bo72bobo3bobo$729bo5bo71bo9bo$808bobo3bobo$143b3o583b2o 3b2o73bo5bo$729bobobobo74bo3bo$730b2ob2o73b4ob4o$731bobo74bo7bo$731bob o75bo5bo$728b2obobob2o72bo5bo$728b2obobob2o$727bo3bobo3bo68b3ob2ob2ob 3o$726b3ob2ob2ob3o66bo3b2o3b2o3bo$726b2o9b2o65bo2bo2bo3bo2bo2bo$726b3o 7b3o65b2o3b2o3b2o3b2o$726bo2bo5bo2bo65bob5o3b5obo$724b2o3b2o3b2o3b2o 69b2ob2o$725b2ob3o3b3ob2o64b5o7b5o$726bo2bo5bo2bo64b4ob2o5b2ob4o$727bo 2bo3bo2bo65b3o3b2o3b2o3b3o$727b2ob2ob2ob2o70bob2ob2obo$729bobobobo74b 2ob2o$725bobo2bo3bo2bobo67bobo5bobo$725bo2bo7bo2bo66bob2o5b2obo$729bo 5bo69b2o2bo5bo2b2o$804b2o13b2o$728bobo3bobo70bo2b2ob2o2bo$730bo3bo69b 2o4b2ob2o4b2o$728bobo3bobo73bo3bo$727bo2bo3bo2bo69b4o3b4o$728bo7bo69bo 4bobo4bo$729bo5bo70bob2obobob2obo$805b2ob2obobob2ob2o$724b2o2b2o5b2o2b 2o63b3o11b3o$724b3o3bo3bo3b3o65bo11bo$727b4o3b4o68bo11bo$726bo4bobo4bo 65b3o11b3o$727bo2bo3bo2bo69b3o5b3o$727bo9bo70b2o5b2o2$807b3o5b3o$807b 2o7b2o$809bo5bo$808b2obobob2o$807bo9bo$807bo3bobo3bo2$807b3o5b3o$806bo 11bo$807bobo5bobo$805bo2bobo3bobo2bo$805b4obo3bob4o$804bo3bob2ob2obo3b o$804bo2b2o7b2o2bo$803b2obo3b2ob2o3bob2o$806bob2obobob2obo$803b5obo5bo b5o$803bo6bo3bo6bo$808bo7bo$807bo2bo3bo2bo$811bobo$811bobo$808b2obobob 2o$808bo2bobo2bo$808bo2bobo2bo2$807b2o7b2o$807b2o7b2o$807b2o7b2o3$806b o2bo5bo2bo46$808bo7bo$807b3o5b3o$807bo2bo3bo2bo$808b2obobob2o$804bo3b 2obobob2o3bo$803bobo5bobo5bobo$802b2ob2o3b2ob2o3b2ob2o$803bo7bobo7bo$ 803bo7bobo7bo$803bo2bo3b2ob2o3bo2bo$804bo15bo$808b3o3b3o$806b2obo5bob 2o$809bo5bo$809b2o3b2o$810b2ob2o2$807bo3bobo3bo2$809bobobobo$809bobobo bo$810b2ob2o$810bo3bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 800 HEIGHT 600 ]]
Spaceships by width
(click above to open LifeViewer)
RLE: here Plaintext: here

Known spaceships by height

Velocity Asymmetric Odd-symmetric (strict) Even-symmetric (strict) Gutter (strict) Odd glide-symmetric (strict) Even glide-symmetric (strict)
(1,0)c/2 8[38][39] 8 8 8 - -
(1,0)c/3 5[38][39] 6[40] 7[40] 6[40] - -
(1,0)c/4 8[38][39][40] 9[40] 10[41] 9[40] - -
(2,0)c/4 6[38][39] 7[40] 8[40] 7[40] 6 7[40]
(1,0)c/5 8[38][42] 8 8 8 - -
(2,0)c/5 11[43] 11 10 11 - -
(1,0)c/6 9[43] < h ≤ 12 9 9 9 - -
(2,0)c/6 7[44] < h ≤ 9 7 7 7 7 7
(3,0)c/6 9[38] < h ≤ 13 9 9 9 - -
(1,0)c/7 8[43] < h ≤ 10 8 8 8 - -
(2,0)c/7 8[38] < h ≤ 12 8 8 8 - -
(3,0)c/7 7[38] < h ≤ 42 7 7 7 - -
x = 65, y = 70, rule = B3/S23 6bo17bo$5b3o15b3o$3b2ob3o13b3ob2o$4bo2bob2o4bo4b2obo2bo$b2obo4bobob2ob 2obobo4bob2o$b2obobo2bobo7bobo2bobob2o$bo8b3obobob3o8bo$2o7b2o9b2o7b2o 13$15bo$8b2ob3ob3o$8b2o4bo2b2ob2o$7bo2bob2o3bo2b2o$19bo2bo16$3bo53bo$ 3bo7b3o11b3o28b3o$2bobo4b2o5b3o36b2obo$9b5ob5o4bo2bo27b3o$7bobo2bo2bo 3bo5bo30b2o$3b6o3bo2b2o4b6o$4b2o6bobo2b2o3bo$14bo6bo13$11bo7bo33bo$5b 2obobob2o3b2obobob2o26b3o$2b3obob3o9b3obob3o22bo3bo$2bo3bobo5bobo5bobo 3bo22b2ob2o5bo$6b2o6bobo6b2o36b2o$3b2o9bobo9b2o22b4obo5bob2o$3b2ob2o 15b2ob2o23bo2bo2b3o2bo$7bo15bo33b3o$61bo$61bob2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 800 HEIGHT 600 ]]
Spaceships by height
(click above to open LifeViewer)
RLE: here Plaintext: here

Known diagonal spaceships by diagonal width and height

These are measured in half-diagonals, as the width of the intersection of a 1-cell-wide orthogonal ray with the cells that turn on during the spaceship's motion.

Minimum width
Velocity Asymmetric Symmetric Gutter Glide-symmetric
(1,1)c/4 4 11 11 4
strict 15[45] 15[45]
(1,1)c/5 15 27 27 -
(1,1)c/6 w ≤ 26 w ≤ 33 w ≤ 55 26[45]
(1,1)c/7 w ≤ 31 w ≤ 31 w ≤ 65 -
(1,1)c/8 w ≤ 24 w ≤ 51 w ≤ 51 w ≤ 24
(2,2)c/8 w ≤ 24 w ≤ 51 w ≤ 51 w ≤ 35
Minimum height
Velocity Asymmetric Symmetric (strict) Gutter (strict) Glide-symmetric (strict)
(1,1)c/4 5[41] 13[41] 14[41] 5[41]
(1,1)c/5 12[1] 12[1] 12[1] -
(1,1)c/6 12[46] 12[46] 11[46] 11[46]

Known spaceships by population

Herein, "strict" is used to refer to spaceships that cannot be decomposed into multiple smaller spaceships which still behave equivalently. (For instance, MWSS on MWSS 1's MWSSs would emit their side sparks in both phases if separated, so it is strict, where a LWSS pair is not.)

The evolution sequences of all patterns with up to 8 cells have been classified, so all stable objects of ≤ 8 cells (or with predecessors thereof) are known. As such, all negative results here have 8 as an additional lower bound.[47]

Velocity Asymmetric Odd-symmetric Even-symmetric Gutter Odd glide-symmetric Even glide-symmetric
(1,0)c/2 64[48] 64[48] 66[48] 70[48] - -
(1,0)c/3 25[49] 34[49] 44[49] 50[49] - -
strict 52[50]
(1,0)c/4 37[51] 46[52] 58[53] 46[52] - -
(1,1)c/4 5 10[54] - 10[54] - 5
strict 9[54] < p ≤ 37 9[54] < p ≤ 50
(2,0)c/4 9 18 18 18 9 18
strict 20[50][55] 34[56] < p ≤ 48 20[50][55] p ≤ 32
(1,0)c/5 p ≤ 58 p ≤ 58 p ≤ 116 p ≤ 58 - -
(1,1)c/5 p ≤ 58 p ≤ 58 - p ≤ 58 - -
(2,0)c/5 30[57] 44[58] 31[57] < p ≤ 60 44[58] - -
strict 31[57] < p ≤ 70
(1,0)c/6 p ≤ 56 p ≤ 112 p ≤ 56 p ≤ 112 - -
(1,1)c/6 p ≤ 77 p ≤ 77 - p ≤ 154 - p ≤ 170
(2,0)c/6 p ≤ 72 p ≤ 72 p ≤ 128 p ≤ 72 p ≤ 110 p ≤ 129
(2,1)c/6 p ≤ 282 - - - - -
(3,0)c/6 p ≤ 86 p ≤ 86 p ≤ 104 p ≤ 108 - -
(1,0)c/7 p ≤ 20 p ≤ 40 p ≤ 40 p ≤ 40 - -
strict p ≤ 90 p ≤ 684 p ≤ 90
(1,1)c/7 p ≤ 83 p ≤ 83 - p ≤ 166 - -
(2,0)c/7 p ≤ 36 p ≤ 72 p ≤ 36 p ≤ 72 - -
(3,0)c/7 p ≤ 232 p ≤ 232 ? p ≤ 232 - -
(1,1)c/8 p ≤ 68 ? - ? - p ≤ 68
(2,0)c/8 p ≤ 74 p ≤ 121 p ≤ 148 p ≤ 148 p ≤ 74 p ≤ 148
(2,2)c/8 p ≤ 89 ? - ? ? -
(4,0)c/8 p ≤ 31 p ≤ 58 p ≤ 62 p ≤ 58 p ≤ 62 p ≤ 62

Full Censuses

This section contains details on searches that completely cover all ships in a particular search space. For example, all c/4 orthogonal ships of width 10. There are infinitely many such ships, but a finite collection can be made that includes all possible rows present in a width-10 c/4 orthogonal ship. This section only includes census containing at least one ship.

c/2 orthogonal

c/3 orthogonal

  • All (1,0)c/3 ships up to a population of 49 cells[49]
  • All (1,0)c/3 odd-symmetric ships up to a population of 67 cells (26 strict ships)[63]
  • All (1,0)c/3 even-symmetric ships up to a population of 86 cells (29 strict ships)[64]
  • All (1,0)c/3 ships up to width 13[65]
  • All (1,0)c/3 ships up to height 6 (5 ships)[40]
  • All (1,0)c/3 odd-symmetric ships up to width 19 (1 width-15 ship; infinitely many width-17+ ships)[65]
  • All (1,0)c/3 even-symmetric ships up to width 20 (1 width-12 ship; infinitely many width-14+ ships)[65]
  • All (1,0)c/3 gutter-symmetric ships up to width 21 (1 width-17 ship; infinitely many width-19+ ships)[65]
  • All (2,0)c/6 even-symmetric ships up to width 18[6]
  • All (2,0)c/6 even-glide-symmetric ships up to width 18[6]

c/4 orthogonal

c/4 diagonal

  • All (1,1)c/4 ships up to a population of 9 cells (1 ship)[67]
  • All (1,1)c/4 symmetric ships in an 18 × 18 bounding box (1 strict ship)[1]
  • All (1,1)c/4 gutter-symmetric ships in a 19 × 19 bounding box (1 strict ship)[1]
  • All (1,1)c/4 ships up to diagonal height 12 (1 ship)[41]
  • All (1,1)c/4 ships up to diagonal width 13 (4 ships)[45]
  • All (1,1)c/4 ships up to orthogonal width 10 (5 ships)[45]
  • All (1,1)c/4 ships up to single-phase orthogonal width 9 (15 ships)[45]

c/5 orthogonal

  • All (1,0)c/5 ships up to height 8[68]
  • All (1,0)c/5 even-symmetric ships up to width 18[65]
  • All (1,0)c/5 gutter-symmetric ships up to width 19[65]

c/5 diagonal

  • All (1,1)c/5 ships up to diagonal height 12 (1 ship)[1]
  • All (1,1)c/5 ships up to diagonal width 16 (1 ship)[40]
  • All (1,1)c/5 symmetric ships up to diagonal width 27 (2 ships: 86P5H1V1 and this ship)[69]
  • All (1,1)c/5 gutter-symmetric ships up to diagonal width 29 (1 ship)[40]

2c/5 orthogonal

  • All (2,0)c/5 ships up to a population of 31 cells (1 ship)[57]
  • All (2,0)c/5 odd-symmetric ships up to a population of 44 cells (1 ship)[58]
  • All (2,0)c/5 ships up to width 12 (1 width-10 ship; infinitely many width-11 ships; infinitely many width-12 ships)[65]
  • All (2,0)c/5 odd-symmetric ships up to width 17 (1 width-15 ship; infinitely many width-17 ships)[65]
  • All (2,0)c/5 even-symmetric ships up to width 20 (1 ship)[65]
  • All (2,0)c/5 gutter-symmetric ships up to width 21 (1 width-15 ship; 1 width-19 ship; infinitely many width-21 ships)[65]
  • All (4,0)c/10 odd-symmetric ships up to width 15 (3 period-10 ships)[2]

c/6 orthogonal

  • All (1,0)c/6 even-symmetric ships up to width 18 (1 ship)[65]

2c/7 orthogonal

c/10 orthogonal

  • All (1,0)c/10 even-symmetric ships up to width 12 (1 width-10 ship; infinitely many width-12 ships)[2]

See also

Notes

  1. 1.0 1.1 1.2 1.3 1.4 1.5 Note that this is not recognised as a single contiguous spaceship by apgsearch's object separation.

References

  1. 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Matthias Merzenich (December 6, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  2. 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20 2.21 2.22 2.23 Matthias Merzenich (March 17, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  3. 3.0 3.1 Tim Coe (December 18, 2015). Re: 3c/7 othogonal and 2c/9 diagonal spaceships (discussion thread) at the ConwayLife.com forums
  4. praosylen (May 13, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  5. 5.0 5.1 5.2 5.3 5.4 Matthias Merzenich (April 14, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  6. 6.0 6.1 6.2 6.3 Tim Coe (April 13, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  7. Keith Amling (January 18, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  8. 8.0 8.1 Tim Coe (June 11, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  9. 9.0 9.1 9.2 Matthias Merzenich (December 24, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  10. Matthias Merzenich (June 14, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  11. Tomas Rokicki (March 1, 2018). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  12. 12.0 12.1 Matthias Merzenich (April 26, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  13. 13.0 13.1 13.2 13.3 13.4 Checked with knight2.c
  14. 14.0 14.1 14.2 14.3 14.4 14.5 Tim Coe (April 17, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  15. Checked by Paul Tooke with gfind
  16. Dylan Chen (January 10, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  17. 17.0 17.1 Matthias Merzenich (November 29, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  18. Matthias Merzenich (February 25, 2020). Re: Help me finish this c/8 search (discussion thread) at the ConwayLife.com forums
  19. Matthias Merzenich (December 22, 2022). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  20. 20.0 20.1 20.2 Tim Coe (April 21, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  21. Tanner Jacobi (December 3, 2015). Re: 3c/7 othogonal and 2c/9 diagonal spaceships (discussion thread) at the ConwayLife.com forums
  22. 22.0 22.1 22.2 AforAmpere (November 5, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  23. 23.0 23.1 praosylen (December 27, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  24. 24.0 24.1 praosylen (December 28, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  25. praosylen (December 25, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  26. Matthias Merzenich (March 26, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  27. 27.0 27.1 27.2 Tim Coe (March 1, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  28. 28.0 28.1 28.2 28.3 28.4 28.5 28.6 praosylen (January 5, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  29. 29.0 29.1 AforAmpere (November 13, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  30. AforAmpere (December 10, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  31. AforAmpere (November 5, 2017). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  32. Matthias Merzenich (April 19, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  33. 33.0 33.1 Tim Coe (February 1, 2016). Re: 3c/7 othogonal and 2c/9 diagonal spaceships (discussion thread) at the ConwayLife.com forums
  34. 34.0 34.1 praosylen (December 25, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  35. 35.0 35.1 lordlouckster (July 13, 2022). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  36. 36.0 36.1 36.2 36.3 36.4 36.5 36.6 36.7 Matthias Merzenich (May 5, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  37. Ivan Fomichev using gfind under OS X 10.9.5
  38. 38.0 38.1 38.2 38.3 38.4 38.5 38.6 38.7 Checked by Matthias Merzenich using WLS.
  39. 39.0 39.1 39.2 39.3 Keith Amling (November 29, 2023). Re: LLSSS min height search results (discussion thread) at the ConwayLife.com forums
  40. 40.00 40.01 40.02 40.03 40.04 40.05 40.06 40.07 40.08 40.09 40.10 40.11 40.12 40.13 40.14 Matthias Merzenich (December 1, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  41. 41.0 41.1 41.2 41.3 41.4 41.5 Matthias Merzenich (February 19, 2024). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  42. Keith Amling (November 29, 2023). Re: LLSSS min height search results (discussion thread) at the ConwayLife.com forums
  43. 43.0 43.1 43.2 Matthias Merzenich (February 20, 2024). Re: LLSSS min height search results (discussion thread) at the ConwayLife.com forums
  44. Matthias Merzenich (February 22, 2024). Re: LLSSS min height search results (discussion thread) at the ConwayLife.com forums
  45. 45.0 45.1 45.2 45.3 45.4 45.5 Matthias Merzenich (November 27, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  46. 46.0 46.1 46.2 46.3 Matthias Merzenich (March 28, 2011). Re: New small c/6 diagonal ship. (discussion thread) at the ConwayLife.com forums
  47. Nick Gotts (November 28, 2018). Systematic survey of small patterns (discussion thread) at the ConwayLife.com forums
  48. 48.0 48.1 48.2 48.3 Keith Amling (November 14, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  49. 49.0 49.1 49.2 49.3 49.4 Keith Amling (November 12, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  50. 50.0 50.1 50.2 Keith Amling (December 1, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  51. 51.0 51.1 Keith Amling (November 22, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  52. 52.0 52.1 Keith Amling (November 29, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  53. 53.0 53.1 Keith Amling (November 30, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  54. 54.0 54.1 54.2 54.3 Keith Amling (November 13, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  55. 55.0 55.1 55.2 "Life Object Counts". Mark Niemiec. Retrieved on December 9, 2023.
  56. 56.0 56.1 Keith Amling (December 6, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  57. 57.0 57.1 57.2 57.3 Keith Amling (November 15, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  58. 58.0 58.1 58.2 Keith Amling (February 1, 2024). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  59. Keith Amling (January 15, 2024). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  60. Keith Amling (November 13, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  61. 61.0 61.1 Matthias Merzenich (March 22, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  62. Matthias Merzenich (May 7, 2018). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  63. Keith Amling (December 6, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  64. Keith Amling (December 6, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  65. 65.00 65.01 65.02 65.03 65.04 65.05 65.06 65.07 65.08 65.09 65.10 65.11 65.12 65.13 65.14 "knightt results". Matthias Merzenich. Retrieved on February 17, 2024.
  66. Keith Amling (March 2, 2024). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  67. Keith Amling (November 14, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  68. Matthias Merzenich (December 6, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  69. Matthias Merzenich (November 28, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
  70. Matthias Merzenich (March 21, 2021). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums