Return to Dean Hickerson's Life page
In February 2007, Eric Angelini suggested looking at patterns formed
from the digits of a number, using the font below:

    ooo.o.ooo.ooo.o.o.ooo.ooo.ooo.ooo.ooo
    o.o.o...o...o.o.o.o...o.....o.o.o.o.o
    o.o.o.ooo.ooo.ooo.ooo.ooo...o.ooo.ooo
    o.o.o.o.....o...o...o.o.o...o.o.o...o
    ooo.o.ooo.ooo...o.ooo.ooo...o.ooo.ooo

I've had some fun playing around with such patterns.  Some of our discussion
is on his website: Une suite pour la Vie

Contents:

Patterns which die
Still-lifes, oscillators, and spaceships
Pseudo still-lifes and oscillators
Infinite growth
Repeated strings of digits
Creating spaceships and gliders
Synthesis of glider gun


Patterns which die
------------------

Eric first asked if infinitely many such patterns die.  It's easy to see
that the answer is "yes"; e.g. numbers of the form 1444...444 all die in
9 gens.  Arbitrarily slow death is also possible; e.g. numbers of the form
1125344743766111...111947742, with an odd number of 1's, die by crashing
spaceships:

#C 1125344743766111111111947742 dies by crashing a MWSS and a LWSS.
x = 89, y = 5, rule = B3/S23
obob3ob3ob3obobobobob3obobob3ob3ob3ob3obobobobobobobobobob3obobob3ob3o
bobob3o$obo3bobo5bobobobobo3bobobo3bo3bobo3bo3bobobobobobobobobobobobo
bo3bo3bobobo3bo$obob3ob3ob3ob3ob3o3bob3ob3o3bob3ob3obobobobobobobobobo
b3ob3o3bo3bob3ob3o$obobo5bo3bo3bo3bo3bo3bo3bo3bobobobobobobobobobobobo
bobo3bo3bo3bo3bo3bobo$obob3ob3ob3o3bo3bo3bo3bob3o3bob3ob3obobobobobobo
bobobob3o3bo3bo3bo3bob3o!

Numbers of the form 1125344743766189077900222...2220066748424 are even
more amusing; here the number of 2's in the middle must be divisible
by 3 and >= 9:

#C 11253447437661890779002222222222222222222222220066748424
#C The 2's in the middle form two lines of blinkers, which decay from
#C opposite ends.
#C Dean Hickerson, dean.hickerson@yahoo.com (2/18/2007)
x = 217, y = 5, rule = B3/S23
obob3ob3ob3obobobobob3obobob3ob3ob3ob3obob3ob3ob3ob3ob3ob3ob3ob3ob3ob
3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob
3ob3ob3ob3ob3obobob3obobob3obobo$obo3bobo5bobobobobo3bobobo3bo3bobo3bo
3bobobobobobobo3bo3bobobobobobobo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo
3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bobobobobobo3bo5bobobobobobobo3bobob
o$obob3ob3ob3ob3ob3o3bob3ob3o3bob3ob3obob3ob3obobo3bo3bob3obobobobob3o
b3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob
obobobob3ob3o3bob3ob3ob3ob3ob3o$obobo5bo3bo3bo3bo3bo3bo3bo3bobobobobob
obobo3bobobo3bo3bo3bobobobobobo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo
3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bobobobobobobobo3bo3bobobo3bobo5bo$obob
3ob3ob3o3bo3bo3bo3bob3o3bob3ob3obob3ob3ob3o3bo3bob3ob3ob3ob3ob3ob3ob3o
b3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob
3o3bo3bob3o3bob3o3bo!

The sequence of numbers which die has been added to the On-Line
Encyclopedia of Integer Sequences: Integers which die in Life


Still-lifes, oscillators, and spaceships
----------------------------------------

Of course, death isn't the most interesting thing that can happen to
a Life pattern.  Here's a collection of numbers which produce small
still-lifes, oscillators, and spaceships.  In each of these, the named
object is produced by itself.  Most of these were found by observing
that some number produced an uncommon still-life, and then modifying
the initial and final digits to get rid of the debris.

#C Small pattern collection
#C This contains numeric predecessors of various still-lifes,
#C oscillators, the "familiar fours" (and some less familiar ones), and
#C the 4 common spaceships.  The numbers with at most 6 digits are probably
#C minimal; the larger ones probably aren't.
#C
#C Names of the less common objects are taken from Andrzej Okrasinski's
#C Game of Life Statistics ( http://www.geocities.com/conwaylife/lf020n.pdf ).
#C
#C blinker (p2)               29
#C block                      70
#C tub                        3906
#C boat                       24
#C beehive                    163
#C ship                       516
#C barge                      243
#C toad (p2)                  8696
#C beacon (p2)                3671
#C aircraft carrier           186176
#C snake                      341957652114
#C loaf                       60
#C long boat                  587
#C eater                      1084557
#C long snake                 6065270247413614
#C
#C pond                       36
#C mango                      857
#C long barge                 127515
#C long ship                  154235114
#C tub with tail              2557376
#C canoe                      52104106503114
#C shillelagh                 157796
#C hook with tail             112108350204
#C bipole (p2)                7020200455
#C long shillelagh            8330423935
#C very long boat             4476
#C hat                        249681
#C up boat with tail          18019138
#C down boat with tail        19333076503
#C tub with long tail         1599435990114
#C
#C integral sign              1135274716
#C tub with nine              187597582
#C very long ship             31808650070114
#C boat tie                   7200647110228
#C block and table            41275676414
#C beehive with tail          10846421
#C up barge with tail         55540559353
#C down barge with tail       1552921912246414
#C claw with tail             91254643267
#C cis shillelagh             111410294065111068
#C loop                       3317286570681
#C unnamed 11-bit still-life  761314714
#C elevener                   1858705011164
#C unnamed 11-bit still-life  21590971031
#C eater siamese snake        147432532023
#C
#C trans loaf with tail       149059473114
#C trans long boat with tail  6733116821185776
#C ship boat tie              1125100561957
#C cis boat and table         18710583610
#C pair of tables             33108318
#C ship tie                   141225452
#C trans legs and block       11317113569
#C eater siamese eater        410754245114
#C cis block and long hook    1006382171456
#C unnamed 12-bit still-life  127745053
#C beehive with bend tail     7961412233308125408
#C cis snorkel loop           16635966646711066148
#C unnamed 13-bit still-life  38923541681
#C beehive at loaf            277305174681
#C half bakery                76109
#C
#C cis loaf at loaf           189422808541
#C paper clip                 324637
#C big S                      14172002
#C hat siamese hat            1130132
#C racetrack II siamese hat   22798258254132
#C fourteener                 23144355435681
#C cis mirrored R-bee         380718
#C trans rotated R-bee        4104645072
#C cis rotated R-bee          7621392111674
#C bookends                   18030383
#C cis hook and R-bee         113021797020694
#C pond and table             604123154231147
#C block and dock             141247457341871
#C beehive and cap            410173645421961
#C dock siamese carrier       14644309288681
#C
#C unnamed 14-bit still-life  13673415404000183
#C cis boat and dock          6581004399314
#C bi-pond                    141207310
#C moose antlers              7686328
#C cis mirrored long hook     113183
#C beehive and dock           340412204591456712
#C cis mirrored R-loaf        410813883110
#C scorpion                   1803712066986301
#C twin peaks                 66695034197110359
#C unnamed 18-bit still-life  1893303515
#C cis mirrored R-mango       4110080033111
#C cis rotated R-mango        669019610699
#C dead spark coil            4108303132
#C trans rotated C            6587961971
#C unnamed 18-bit still-life  13554271714
#C
#C pond and dock              182530867166
#C cis long hook and dock     122915233114
#C unnamed 19-bit still-life  7161006176
#C cis mirrored dock          25410808131018
#C unnamed 21-bit still-life  46725681
#C long worm and blocks       13801006728751
#C cis mirrored worm          6308383830114
#C cis mirrored long dock     630800000080010 ( found by Nicolay Beluchenko )
#C unnamed 26-bit still-life  180303033818720
#C unnamed 28-bit still-life  180010010081
#C unnamed 38-bit still-life  70310003114
#C
#C traffic light              1
#C blockade                   67
#C honey farm                 78
#C fleet                      7108
#C bakery                     1672
#C land of lakes              1635661
#C 4 eaters                   11300
#C
#C pulsar (p3)                0
#C pentadecathlon (p15)       1445481003304129144171771
#C queen bee shuttle (p30)    1983263225470666662666647618  ( found jointly )
#C twin bees shuttle (p46)    397301133310                  ( with Nicolay  )
#C twin bees shuttle (p46)    331101301133310               ( Beluchenko    )
#C
#C glider                     90
#C LWSS                       3207
#C MWSS                       94174
#C HWSS                       185598100297311043114
#C Dean Hickerson, dean.hickerson@yahoo.com (3/26/2007)
x = 736, y = 428, rule = B3/S23
b3o12b3ob3o60b2o13b3ob3o46b2o15bobob3ob3ob3ob3obobob3obob3o33b2o13bobo
bob3ob3ob3ob3obobob3ob3obobobobo37bo16bob3ob3obobob3ob3ob3ob3ob3ob3obo
bobo25bo16bob3ob3ob3ob3obobobob3obobob3obobob3ob3ob3obob3ob3o15b2o13bo
b3ob3ob3ob3ob3ob3ob3ob3obob3ob3o43b3o14bo$18bobobo59bo2bo14bobo48bo16b
obo3bobo5bo3bobobo3bobobo34bo2bo12bobobobobobobobo3bobobobo3bo3bobobob
obo36bobo15bobobobobobobo3bo3bobobobobobobobo3bobobo24bobo15bo3bobo5bo
3bobobobobo3bobobobobobobobobobobobobobobo3bo14bo2bo12bobobo3bobo5bobo
bobobobo5bobobo3bo62bo$16b3ob3o59bo2bo12b3ob3o47b3o13bobob3ob3ob3o3bob
3o3bobob3o32bobo13bob3ob3obobob3ob3ob3o3bob3obobob3o35bo2bo15bob3ob3ob
3ob3ob3ob3obobob3ob3ob3obo24bobo15bob3ob3o3bob3ob3obob3ob3obobob3obobo
bobobobobob3ob3o14bo2bo12bob3ob3ob3ob3obobob3ob3o3bobob3ob3o41bo5bo12b
o$16bo5bo60b2o15bobobo50bo12bobo3bo3bobo5bo3bo3bobobobo33bo14bo3bo3bob
obo3bo3bo3bo3bo3bobobo3bo36b2ob2o13bobobo3bo3bobo3bo3bobobobobobo3bo3b
obo25bob2o13bo3bobobo3bo3bo3bobo3bo3bobobo3bobobobobobobobobobo3bo15b
2o13bobobobo5bo3bobobobobobobo3bobobobobobo41bo5bo12bo$16b3ob3o75b3ob
3o49b2o12bobob3ob3ob3o3bo3bo3bobob3o30b3o15bo3bob3ob3ob3ob3o3bo3bob3ob
obo3bo38bo2bo12bob3ob3o3bob3ob3ob3ob3ob3ob3o3bobo27bobo12bob3ob3o3bob
3o3bobob3o3bob3o3bob3ob3ob3obob3ob3o30bob3ob3ob3ob3ob3ob3ob3o3bobob3ob
3o41bo5bo12bo$231bo96bobo82bo2bo86b4o$329bo84b2o86bo4bo98b3o$502b2o2b
2o8$665b3ob3o$665bobobobo$665b3obobo$667bobobo$665b3ob3o2$601b2o$601b
2o2b2o$605b2o7$2b2o12b3ob3o59b2o14b3ob3ob3o42bo16bob3ob3ob3ob3ob3ob3ob
3ob3o34b2o12b3ob3ob3ob3obobob3ob3ob3obobob3ob3ob3ob3ob3o24b2o14b3ob3ob
obob3ob3ob3o47bo14b3ob3ob3obob3ob3obobob3ob3ob3ob3obobobo26b2o2b2o12bo
b3ob3ob3obob3ob3ob3ob3obobobobo64b3ob3o$2b2o14bobobo58bo2bo13bobobo5bo
41bobo15bobobo3bobo3bobo3bobo3bobo3bo33bobo12bo5bo3bo3bobobobo3bobo3bo
bobobobobo5bo3bobo25bo2bo15bo3bobobobo5bo3bo46bobo13bo3bo3bobobobobobo
bobobo3bobobobobo3bobobobo26bo4bo12bo3bo3bobobobobo5bo3bo3bobobobobo
64bo5bo$18bobobo59bo2bo12b3ob3o3bo42bobo14bob3o3bob3ob3o3bob3ob3ob3o
32bobo13b3o3bob3ob3obobob3ob3ob3obobob3ob3o3bo3bob3o23b2obo13b3ob3ob3o
b3ob3o3bo47b2o13b3ob3ob3obobobobobob3ob3ob3ob3ob3obob3o27b4o13bob3ob3o
b3obob3ob3ob3ob3obobob3o64b3o3bo$18bobobo60b2o13bobo3bo3bo44bo14bobobo
3bo3bo3bo3bo3bobobobo33bobo14bobo3bo3bo3bobobobobobobobo3bobobobo3bo3b
o3bobobo24bob2o14bobo5bobobo3bo3bo62bobo3bobobobobobobobo3bo3bo3bo3bo
3bobo3bo44bobo3bo5bobo3bobo5bo3bobobo3bo64bobo3bo$18bob3o75b3ob3o3bo
44bobo12bob3o3bob3ob3o3bob3ob3ob3o31bo16b3o3bob3ob3obobob3ob3ob3obobob
3ob3o3bo3bob3o24bo2bo12b3ob3o3bob3ob3o3bo45b4o13b3ob3ob3obob3ob3o3bob
3ob3ob3ob3obo3bo27b4o13bob3ob3ob3obob3ob3ob3ob3obobo3bo64b3o3bo$154b2o
75b2o96b2o80bo4bo85bo3bo$411b2o2b2o85b2o5$605b2o$605b2o2b2o$609b2o2$
665b3ob3ob3ob3o$667bo3bobobo3bo$665b3ob3obobo3bo$667bobo3bobo3bo$665b
3ob3ob3o3bo7$604bo$603bobo$603bobo$604bo$2bo13b3ob3ob3ob3o53bo13bob3ob
3ob3obob3o34b2o15b3obob3ob3ob3ob3ob3ob3ob3ob3ob3obobobobo14b2o16bobob
3ob3obob3ob3ob3ob3obob3ob3ob3o37b2o13bobobobob3ob3ob3ob3ob3o37b2o5b2o
12b3ob3ob3ob3ob3ob3ob3o47b2o15b3obob3obob3ob3ob3obob3ob3o70b3ob3o$bobo
14bobobobobobo54bobo12bo3bo3bobo3bobo36bobo16bobobobobobobobobo3bo3bob
obobo3bobobobobobobo14bobo15bobo3bobo3bobobobobobo3bo3bobobobo5bo36bo
2bo12bobobobo3bo3bobobobobo3bo37bo7bo14bobo3bobobo5bo3bobobo47b2o17bob
obo3bobobobobobo3bo3bobo48b2o7b2o15bobobo$2bo13b3ob3obobob3o51bobo13bo
b3o3bob3obob3o35bobo13b3obob3obobob3ob3ob3obobobobo3bobobobobob3o15b2o
15bobob3ob3obobobobobob3ob3obob3ob3o3bo36bob2o12bob3obo3bob3obobobobob
3o38b3ob3o15bob3ob3ob3ob3ob3ob3o51bo14bobob3obobobobobob3obo3bob3o45bo
2bo5bo2bo14bob3o$18bo3bobobobobo50bobo14bobo5bo3bobo3bo36bobo14bobobob
obobobobobobo3bobobobobo3bobobobobo3bo17b2o13bobobo5bobobobobobo3bobob
obo3bo3bo3bo33b2obo15bo3bobo3bobo3bobobobobo42bobo17bobobobobobobo3bob
o3bobo47b5o14bobobobobobobobobobobobo3bobobo46b2o7b2o15bobobo$16b3ob3o
b3ob3o51bo15bob3o3bob3obob3o37b2o12b3obob3ob3ob3ob3ob3ob3ob3o3bob3obob
o3bo17bobo12bobob3ob3obob3ob3ob3ob3obob3ob3o3bo33bo2bo15bo3bobo3bob3ob
3ob3ob3o41bo18bob3ob3ob3ob3ob3ob3o46bo19bobob3obob3ob3ob3obo3bob3o72bo
b3o$235bo90b2o174bobob2o96bo$503b2ob2o95bobo$603bobo$604bo7$665b3obobo
bob3obobo$665bobobobobo3bobobo$665b3ob3obo3bob3o$667bo3bobo3bo3bo$665b
3o3bobo3bo3bo11$2bo13b3obobo59b2o14bob3obobob3ob3ob3obobobobo24bo16b3o
b3ob3ob3ob3obobob3obobob3ob3ob3ob3o20b2o12bob3ob3obob3ob3ob3ob3ob3obob
3o42bo15bobob3ob3obob3ob3o46b2o16bobobobob3ob3ob3ob3obob3o44b2o2b2o12b
3ob3obobobob3ob3ob3ob3obob3obob3obob3o38b2o16b3obob3ob3o$bobo14bobobo
59bobo13bobo3bobo3bo3bobo3bobobobo23bobo17bo3bobobobobobo3bobo3bobobob
obo3bo3bobobo17bo2bo13bobobo3bobobobobo3bobo3bobo3bobobo40b5o13bobo3bo
bobobo3bo3bo45bo2bo15bobobobo3bobobo3bo3bobobobo44bo4bo14bobo3bobobobo
bobobobobobobobo3bobobobobobobo38bobo17bobobobobobo$b2o13b3ob3o60bobo
12bob3ob3ob3ob3ob3obobob3o24b2o17bob3obobobobob3ob3o3bobobobobob3ob3ob
3o16bobobo13bob3o3bobobobob3ob3ob3ob3obobobo39bo5bo12bobob3obobobob3ob
3o45bo2bo15bob3obob3obobo3bob3obobobo45b4o13b3ob3ob3obobobob3obobob3ob
ob3obobobobob3o39b2o17bobobobob3o$16bo5bo61b2o12bo3bo3bobo5bo3bobobo3b
o26b2o15bobo3bobobobobobo3bo3bobobobobobo3bo3bobo17b2ob2o12bobobo3bobo
bobo3bobobo3bobobobobobo40b5o13bobo3bobobobo3bobo48b2ob2o13bo3bobobo3b
obo3bo3bobobobo62bo5bo3bobobobobobobobobobobo3bobobobobobobo41b2o15bob
obobobobo$16b3o3bo75bob3o3bob3ob3ob3obobo3bo26bobo14bob3ob3ob3ob3o3bo
3bobobob3ob3ob3ob3o34bob3o3bobob3ob3ob3ob3ob3obob3o42bo15bobob3ob3obob
3ob3o48bo2bo12bo3bobob3ob3o3bob3obob3o45b4o13b3ob3o3bobob3ob3ob3ob3obo
b3obob3obob3o34b2o5bobo14bobob3ob3o$154bo258bo2bo85bo4bo93bobo5b2o$
414b2o86b2o2b2o94b2o$604b2o$604bobo$605b2o6$665bob3ob3ob3ob3ob3obob3ob
3ob3ob3ob3ob3obobob3obobob3obobobobo$665bobobobo3bo3bobobobobobobobobo
3bobobo3bo3bobobobobobobo3bobobobobo$665bob3ob3ob3ob3ob3obobobobobob3o
b3o3bob3obobobobob3ob3obobob3o$665bobobo3bo3bo3bobobobobobobobobo5bo3b
o3bobobobobo3bo3bobobo3bo$665bob3ob3ob3ob3ob3obob3ob3ob3ob3o3bob3obobo
b3o3bob3obobo3bo11$b2o13bob3ob3o57bo15b3ob3ob3ob3ob3ob3ob3o27bo2bo12bo
bobob3ob3ob3ob3ob3ob3obobobobobo26bo2bo12b3ob3obob3ob3ob3obob3o52bo15b
3ob3ob3ob3ob3ob3ob3ob3ob3ob3obobobob3ob3o15b2o15bobob3obob3ob3o59b2o
13bobob3ob3ob3ob3ob3ob3obo56b2o16bob3ob3ob3o$o2bo12bobo5bo56bobo16bobo
3bo5bo3bo3bobo29b4o12bobobo3bo3bobo3bo5bobo3bobobobobo26b4o14bo3bobobo
bobobo3bobobobo50b5o15bo3bo3bobobobobo3bobo3bobo3bobo3bobobo3bo3bo15bo
3bo12bobo3bobobobo3bo59bobo12bobobo5bo3bobo3bo3bobobo55bo2bo15bobo5bo
3bo$b2o13bob3ob3o57bobo13b3ob3ob3o3bob3o3bob3o43b3obob3o3bob3ob3o3bob
3ob3obob3o42b3ob3obobobob3ob3obob3o49bo5bo12b3ob3o3bob3ob3ob3ob3ob3ob
3ob3ob3obob3ob3o16b4o12bobob3obob3ob3o61bo12b3ob3o3bob3ob3ob3ob3obo55b
obo16bob3o3bob3o$16bobobo3bo59bo13bo5bo3bo3bo3bo3bobobo29b2o14bobobo5b
o3bobobo3bobobo3bobo3bo26b4o14bo3bobobobobobo3bobobobo50bob3o13bo3bo5b
o3bobobobo5bobobobo5bo3bobo3bobo34bobo3bobobobo3bo57b4o15bobobo3bobo5b
obobobobobo53b2obo3bo13bobobo3bobo$16bob3ob3o59b2o12b3ob3ob3o3bob3o3bo
b3o29b2o14bobob3o3bob3ob3o3bob3o3bobo3bo26bo2bo12b3ob3obob3ob3ob3obob
3o51b2o15b3ob3o3bob3ob3ob3ob3ob3ob3ob3o3bobob3ob3o16b4o12bobob3obob3ob
3o57bo18bob3o3bob3ob3ob3ob3obo52bo2bo3bobo12bob3o3bob3o$412bo3bo83b2ob
ob2o94bobo3bo2bo$412b2o86bo2bob2o95bo3bob2o$501b2o102bobo$604bo2bo$
605b2o21$2b2o12b3obob3o59b2o12b3ob3obob3obobobob3ob3ob3ob3ob3obobobobo
9b2o12bob3ob3obobob3obobob3obo40b2o12bobobobob3ob3ob3obobob3ob3o48b2o
14b3ob3obobobobobob3ob3ob3obobob3ob3ob3ob3obo16b2o2b2o12b3obobob3obobo
bob3ob3ob3obobob3ob3obobobob3ob3ob3obob3o8b2ob2o13bob3ob3ob3obob3ob3ob
3ob3ob3ob3ob3ob3obo36b2o16bob3ob3ob3ob3ob3obo$bobo12bo3bobo62bo12bo5bo
bobobobobobobobobo3bo3bobo3bobobobobo9bo13bobobobobobobobo3bobo3bobo
39bobo12bobobobo3bo3bobo3bobobo5bo48bobo15bo3bobobobobobo3bobo3bo3bobo
3bobo3bo3bobobo16bo4bo14bobobobobobobobo3bo3bobobobobobo3bobobobobobo
3bo5bobo3bo8b2ob2o13bo3bobobobobobobobobobobo5bo3bobobo3bobo3bo35bo2bo
15bobo5bobo3bo3bo3bo$b2o13b3obob3o59bo13b3ob3obobobob3obobobob3ob3obob
ob3obobob3o6b2obo13bobobob3ob3ob3ob3ob3obo39b2o13bob3obob3ob3ob3ob3ob
3ob3o50bo13b3ob3obob3ob3ob3ob3ob3ob3ob3ob3ob3ob3obo17b4o13b3ob3obobob
3obob3ob3obobob3ob3ob3obob3ob3ob3o3bobob3o26bob3ob3obobobobobobobob3o
3bob3ob3o3bob3obo35bo2bo15bob3ob3ob3ob3ob3obo$18bobobobo56bobo16bobo3b
obobo3bobobobobobo3bobobo3bobobo3bo5bo2bo14bobobobobo3bobobo3bobo3bo
37b2o15bo3bobobo3bo5bo3bo3bobo52b2o12bo5bobo3bo3bo3bo3bo3bo3bo3bo3bobo
bobobobo36bo3bobobo3bobobo3bo3bobo3bo3bo3bobo3bo3bobobo3bobobo10b5o13b
o3bobobobobobobobobobobobo3bobo3bobo3bo3bobo36b2ob2o13bobobo3bo3bobobo
bobobo$16b3obob3o56b2o15b3ob3obob3o3bobob3ob3ob3ob3ob3obobo3bo6b2o15bo
b3ob3o3bob3o3bob3obo36bobo15bo3bobob3ob3ob3o3bob3ob3o47b2obo13b3ob3obo
3bo3bob3ob3ob3o3bob3ob3ob3ob3obo19b2o13b3o3bob3o3bobob3ob3ob3o3bob3ob
3obo3bob3ob3o3bobob3o7bo5bo12bob3ob3ob3obob3ob3ob3o3bob3ob3o3bob3obo
38bo2bo12bob3ob3ob3ob3ob3obo$231b2o94bo2bo82bo2bo84bobo2b2o99bo2bo$
328b2o84b2o86b2o104b2o$598b2o$597bo2bo$597bo2bo$598b2ob2o$600bo2bo$
600bo2bo$601b2o17$2bo13b3obobob3o56b2o13bob3ob3ob3ob3ob3o31b2o16b3ob3o
b3obobob3ob3ob3ob3ob3ob3ob3o21b2ob2o12bobob3obob3obobob3ob3ob3ob3o47b
2o13b3ob3ob3ob3obob3o49bo14bobobob3ob3obob3ob3ob3ob3obobob3o35b2o15b3o
b3ob3ob3ob3ob3ob3ob3ob3ob3obobobobo32bo7bo15bobob3ob3ob3o$bobo14bobobo
3bo57bo13bobo5bo3bobobobo34bo16bo3bo3bo3bobobobobo3bo3bobo3bobo5bo22bo
b2o12bobo3bobo3bobobo3bobo3bo3bobo46bo2bo14bobobobobo3bobobobo48bobo
13bobobobobobobobo3bobobobobo3bobobobobo34bobo15bo5bobobobobo3bobobo3b
obobo3bobobobobobobo30b3o7b3o13bobo3bobobobobo$obo13b3ob3ob3o56bo14bob
3o3bo3bob3ob3o32bobo14b3ob3ob3ob3obobob3ob3ob3ob3ob3ob3o22bo15bobob3ob
o3bobobob3ob3ob3ob3o47b3o12b3ob3obobo3bobob3o48bo2bo12b3obobobob3obob
3ob3ob3ob3obobobobo34bo4bo12b3ob3obobob3ob3ob3ob3ob3ob3obobobobob3o29b
o13bo12bobob3obobobobo$bo14bo5bo3bo56bobo12bo3bo3bo3bo3bobobo33bobo15b
o3bo3bo3bobobo3bo3bo3bo3bo3bo3bo23b3o12bobo3bobo3bobobo3bo3bobobo3bo
64bobobobobo3bobobobo49b3o14bobobobobobobo3bobobobobo3bobobobobo35b5o
12bobo3bobobobobo3bobobo3bobobo3bobobobobo3bo29b2o11b2o12bobo3bobobobo
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b3ob3ob3o25bo12bobob3obo3bobobob3ob3ob3ob3o47b3o12b3ob3ob3o3bobob3o66b
obob3ob3obob3ob3ob3ob3obobob3o52b3ob3ob3ob3ob3ob3ob3ob3ob3ob3obobo3bo
56bobob3ob3ob3o$154bo173bo2bo82b3o86b5o$329b2o82bo2bo85bo4bo$413bobo
86bobo$414bo88b2o3$596b2o11b2o$596bo13bo$597b3o7b3o$599bo7bo16$2bo13b
3ob3ob3ob3o53b2o12bobob3obob3ob3ob3ob3ob3ob3ob3obobo13bo15bob3ob3ob3ob
3ob3obob3obob3ob3obobob3obobobobobo13bo12bobobob3ob3ob3obobob3obobob3o
bobobobo36bo17bobobob3obobob3obobob3ob3ob3ob3o33b2o13bob3ob3ob3ob3obob
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3ob3ob3obob3o$o2bo12bobobo3bobobo55bo13bobo3bobobobobobo3bobo3bobo3bob
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12bobobobobo3bobo3bobo3bobobobo3bobobobo35bobo16bobobobobobobobo3bobob
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2bo12b3ob3ob3ob3o50b2obo13bobob3obobobob3ob3ob3obobob3obobob3o11bobobo
13bob3ob3ob3ob3ob3obob3obob3ob3ob3ob3ob3obob3o10bo15b3obobobo3bob3ob3o
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obobobobobobobob3obobobobobobobo$bo14bobobobo3bobobo50bobo14bobobo3bob
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o3bobo3bo10b2o16bobobobo3bo3bo3bobo5bo3bobobo3bo36b2ob2o15bobobobo3bob
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3bobobobo16b2ob2o13bobo3bobobobobobobobobobobobobobobobobobobobobobobo
bobobo$16b3ob3ob3ob3o67bobob3obob3ob3ob3ob3ob3ob3ob3o3bo15b2o12bob3ob
3ob3ob3ob3obob3obob3ob3o3bob3o3bobo3bo11bo16bobob3o3bob3o3bob3o3bob3ob
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b3ob3ob3ob3ob3ob3ob3ob3obo17bobo14b3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3o
b3obob3o$234bobo92bobo80bo2bo85bobobobo$235b2o93bo82b2o86b2o3b2o19$
600bo5bo$600bo5bo$600b2o3b2o2$596b3o2b2ob2o2b3o$2o14b3ob3ob3obo52b2o
15b3ob3ob3ob3ob3ob3ob3obobob3ob3o17b2o12b3obob3ob3obobob3obobob3ob3ob
3ob3o23b2o15bob3ob3ob3ob3ob3ob3obob3obobobob3ob3o35b2o13b3ob3ob3obob3o
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bobobo14b3o$o17bobo5bobo52bo18bobobo3bobobo3bobobobobobobobo3bo18bobo
12bobobo3bobo3bobobo3bobo3bo3bobo5bo23bo3bo12bobobobobobo5bobobo3bobo
3bobobobobo3bo36bo2bo14bobo5bobo3bobobo3bobobobobo5bobobo26b3o13bo3bo
3bo3bobobo3bobo3bobobobobobo3bobobobobo3bobo3bobo10bo3bo2bo12bobobobob
o3bobobo3bobobo3bo3bobobobobobo3bo3bobobo25b2o3b2o16bobo$3bo12b3ob3o3b
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b3ob3ob3o3bo24b4o12bobobobobob3ob3ob3ob3obo3bobob3ob3ob3o34b3o15bob3ob
3obob3ob3ob3obobobob3o3bob3o29bo12b3ob3ob3ob3ob3obobob3ob3obob3o3bobob
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48bobo$2b2o14bobobo3bobo56bo14bobobobo3bobobo3bobobobo3bo3bo3bo17bo15b
obobo5bo3bobobo3bo3bobo3bobo3bo40bobobobobobobo3bobobobo3bo3bobo3bo3bo
bobo52bobobobo3bo3bo3bobo3bobobobobo3bo3bo26b3o13bobobobobobo3bo3bobob
o3bo3bobo3bo3bobobobobo3bo3bo3bo30bobobobobo3bobobo3bobobo3bo3bobobobo
bobo3bobo3bobo25b2o3b2o16bobo$16b3ob3o3bobo55b2o14bob3ob3ob3ob3ob3ob3o
3bob3ob3o14b3o14b3obob3ob3o3bob3o3bob3ob3ob3o3bo24b2o14bob3ob3ob3ob3ob
3ob3obo3bobo3bob3ob3o34b3o15bob3ob3obob3ob3ob3obobobob3o3bo3bo25bo16b
3ob3ob3ob3ob3ob3ob3o3bobob3o3bobobob3ob3ob3ob3o11b6o13bob3ob3ob3ob3ob
3ob3ob3ob3ob3obob3o3bob3ob3o23bobobobobobo14b3o$151bo81b2o92bo2bo82b3o
84bo3bo2bo88b3o2b2ob2o2b3o$328b2o86bo83b2o4b2o$413b3o184b2o3b2o$413bo
186bo5bo$600bo5bo16$609bo$608bobo3$608b3o$2b2o12bob3ob3obob3ob3o49b2o
12b3ob3ob3ob3obobob3ob3ob3ob3ob3o16b2o13bobobobobobob3ob3ob3obobob3ob
3ob3obobobob3ob3ob3o5b2o17bob3ob3ob3obobob3ob3ob3ob3o46b2o14bob3ob3ob
3ob3ob3ob3ob3o37bo18bob3ob3ob3ob3ob3ob3ob3obob3o37b2o3b2o12bob3ob3ob3o
bob3ob3obob3ob3ob3obo49b3o12bobobobobob3obobob3obob3ob3ob3ob3ob3obobob
ob3ob3obobobobobobob3obob3ob3obo$o2bo12bobobobo3bo3bobo50bobo12bobo3bo
3bobobobobo3bo3bobobo3bobo18bobo12bobobobobobobobo3bobobobobobobobo3bo
3bobobobobobo3bobo5bobo16bo3bo3bo3bobobobo3bobobo5bo46bo2bo12bobobobob
o3bobobo3bobobo3bo36bobo17bobobobobo3bo3bobobo3bobo3bobo39bobobobo12bo
bobobobobobobobobobobobobobobobobobobo50bo13bobobobobobo3bobobobobobob
obobo3bo3bobobobobobo3bobobobobobobobobo3bobo3bo3bobo$2o14bob3ob3obo3b
ob3o48bo14b3ob3ob3obobob3ob3ob3ob3ob3ob3o18bo12bobobob3obobobob3ob3ob
3obobob3ob3obobobobobob3ob3o7bo16bob3o3bo3bob3ob3obobob3ob3o47b3o12bob
3obobob3obobob3ob3ob3o36bo2bob2o13bob3ob3ob3ob3obobob3ob3obob3o39bobo
14bob3obobobobobobobobobobobobobobob3obo64bob3ob3ob3ob3ob3obobobobobob
3ob3obobob3obob3ob3obob3ob3obo3bobo3bo3bobo$16bobobobobobo3bobobo49bo
13bobo3bo3bobobo3bobo5bo3bo3bo3bo17bo13bobobo3bobobobobo5bo3bobobobobo
3bobobobobobobobobobo7b3o14bobo5bo3bo3bo3bobobo3bo3bo62bobobobobo3bobo
bo3bobobo3bo37bobobobo12bobobo3bo3bo3bobobo3bo3bobo3bo39bobo14bobobobo
bobobobobobobobobobobobobobobobo64bo3bo3bo3bo3bobobobobobobobo3bo3bobo
bo3bobobo5bobo3bo3bobo3bobo3bo3bobo$16bob3ob3obo3bob3o50bo12b3ob3ob3ob
3o3bob3ob3ob3ob3ob3o14bobo14bobobo3bobob3ob3ob3o3bob3ob3ob3obobobob3ob
3ob3o10bo13bob3o3bo3bo3bob3ob3ob3ob3o47b3o12bob3ob3ob3ob3ob3ob3ob3o38b
2o3bo12bob3ob3ob3ob3ob3ob3ob3obob3o38b2ob2o13bob3ob3ob3obob3ob3obob3ob
3ob3obo50bo13bo3bo3bob3o3bob3obob3ob3ob3ob3ob3o3bobob3ob3obo3bo3bobo3b
obo3bo3bobo$84b2o65b2o81bobo91bo2bo81b3o87bobo102b3o$235bo92b2o83bo89b
obo102b3o$501bobobobo$501b2o3b2o$608bobo$609bo20$2b2o12b3obobobob3ob3o
b3ob3ob3ob3obobobobo27bo13bobobobob3ob3o38b2ob2o12b3ob3obob3ob3ob3ob3o
b3ob3ob3ob3ob3obo18b2o14b3ob3ob3obobobobob3ob3ob3ob3ob3ob3ob3obob3ob3o
bobob3ob3o8bo3b2o12bobob3ob3ob3obob3ob3ob3ob3ob3ob3ob3ob3obobo17b2o13b
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3ob3ob3ob3ob3obobob3ob3obob3o$2bo15bobobobobobobo5bobo3bo5bobobobobo
26bobo12bobobobo3bobo41bobo15bo3bobo3bo3bobobobo3bo5bobobobo3bobobo17b
o2bo15bobobobo3bobobobo3bo3bo3bo3bo3bobobobobobo3bobo3bobobobobobo7bob
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o3bobobobobo39bo3bo22bobobobobo3bo3bobo5bo3bo3bobo3bobo3bobobobo3bo3bo
3bo3bo5bobo3bo3bo3bo3bobo3bobo3bobobo$3bo12b3ob3obob3ob3o3bob3ob3ob3ob
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obobo14bobob3obobob3obo3bob3o3bobobob3obobob3ob3ob3o15bo2bo13b3obobobo
bobobob3obobobobob3ob3obobobo29bo7bo14bobobob3obobobobobobobob3obobob
3o32b2o5bo26bob3ob3ob3ob3ob3ob3ob3ob3ob3ob3o3bobobob3ob3ob3ob3ob3ob3ob
3ob3ob3ob3ob3o3bob3obob3o$2b2o14bo3bobo3bo3bo3bobobo3bobo3bobo3bo24bob
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12bo3bobobo3bobo3bobo3bobo3bo5bo3bo3bobobobobobobobobobobobobobo3bobob
obobobobobo3bo3bobobobobobo$16b3o3bobob3ob3o3bob3ob3ob3obobo3bo24b2o
17bo3bo3bob3o55b3ob3obo3bob3ob3ob3ob3o3bob3ob3ob3obo18b3o15bob3ob3obo
3bobob3ob3ob3ob3ob3ob3ob3obob3ob3o3bob3ob3o26bobob3ob3ob3obo3bob3o3bob
3ob3ob3ob3ob3o3bo34bobobob3ob3ob3ob3ob3ob3ob3obobobo52bob3ob3obob3ob3o
b3ob3obobo3bo39bo12b2o12bob3ob3ob3ob3ob3ob3ob3ob3ob3o3bo3bob3ob3ob3ob
3ob3ob3ob3ob3ob3ob3ob3o3bo3bob3obob3o$233bo178b3o85b7o89bo3bo$412bo2bo
83bo7bo90bobo$413bo2bo82bob2ob2obo$414b2o84bobobobo20$582b2o2b2o4bo2b
2o12b2o$582b2ob2o6b2obo12b2o$2bo13b3ob3o59bo15b3obobob3ob3ob3obo35bo
13b3ob3obob3obobobob3obobobo38b2o12bob3ob3ob3ob3ob3ob3ob3ob3obobob3ob
3obobob3ob3ob3obobobob3o9b2o13b3ob3obobobob3ob3obob3obobob3ob3obobobob
ob3o14bo19b3ob3ob3ob3obob3ob3obob3ob3ob3ob3o114bobo6bo27b3ob3ob3ob3ob
3obobob3ob3ob3obob3o$bobo12bo3bobo59b3o15bobobobobobo3bobobo34bobo14bo
bo3bo3bobobobo3bobobobo36bo2bo12bobo3bo5bobo3bobobo3bo3bo3bobobo5bobob
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bobo3bo13bobo18bo3bo3bobobobobobobobo3bobobobo3bobobobo115b2o4b3o29bob
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33bo2bo14bob3obob3obob3o3bobob3o35bob2o13bob3ob3ob3ob3ob3ob3ob3ob3ob3o
b3o3bobobobobob3ob3obob3ob3o6bobo2bo12b3obobob3obob3ob3obob3ob3ob3ob3o
bobob3o3bo13bo2bob2o14b3ob3ob3obobobob3ob3obobobob3ob3ob3o151b3ob3o3bo
b3obobobobob3ob3ob3obobobo$b2o13bobobobo59b3o13bo5bo3bobobobobobo33bob
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o3bobobobobobobobobobo3bobobo6bo2b2o13bobobobo3bobobo5bobo3bo3bobo5bob
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3o29bo3bo3bo3bobobobobo3bo3bo3bobobobo$16b3ob3o59bo15b3o3bob3ob3ob3obo
32b2ob2o14bob3obob3obo3bo3bobo3bo36b3o13bob3ob3ob3ob3ob3ob3ob3ob3o3bob
3o3bobobob3ob3ob3obo3bob3o5b2o17b3ob3o3bobob3ob3obob3o3bob3ob3obobo3bo
3bo15b2obo2bo12b3ob3ob3ob3obob3ob3obob3ob3ob3ob3o114bobo6bo27b3ob3o3bo
b3ob3obobob3ob3ob3obob3o$235bo178bobo168b2o6b2obo12b2o$415bo170b2o4bo
2b2o12b2o22$582b2o2b2o4bo2b2o12b2o$582b2ob2o6b2obo12b2o$2b2o12b3ob3ob
3o54b2o15bob3ob3obob3obob3ob3o31b2o12bob3ob3ob3ob3ob3ob3ob3obobobob3ob
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6bo27b3ob3obobob3obob3ob3obobob3ob3ob3obob3o$bobo12bo3bobo3bo55bo15bob
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23bobo14bobobobobo3bo3bobo3bobobobo3bobobo38b2obobo12bobobobo3bobobo3b
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123b2o4b3o29bo3bobobobobobo3bobobobobo3bo3bo3bobobobo$obo13b3ob3o3bo
55bobo13bob3obobobob3obob3ob3o29b3o13bob3ob3ob3o3bobobob3obobobobobob
3ob3o25bo12b3ob3ob3ob3ob3ob3ob3obob3ob3obo38b2obo14bob3obob3ob3o3bob3o
b3o3bob3ob3obob3o3bobo18b3o13b3obobobob3ob3obobob3obob3ob3o159b3ob3obo
bobobobob3obobobobob3ob3ob3obobobo$bo16bobobo3bo56bobo12bobobobobobo3b
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3bobo5bo3bo3bobobobobobobo41bo14bo3bobobo5bo3bo3bo3bo3bo3bo3bobobobo3b
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bo3bo3bo3bobobobo$16b3ob3o3bo57b2o12bob3ob3obob3obob3ob3o27bobo15bob3o
b3ob3o3bob3ob3ob3obobobob3o3bo21bo16b3ob3ob3ob3ob3ob3o3bobob3ob3obo41b
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3obob3ob3o122bobo6bo27b3ob3obobob3obob3ob3obobob3ob3ob3obob3o$150b2o
81bo96b2o80bo3bo165b2ob2o6b2obo12b2o$232b2o178b2ob2o165b2o2b2o4bo2b2o
12b2o24$o15bob3ob3obobob3ob3ob3o44bo12bob3ob3ob3ob3ob3ob3ob3ob3ob3ob3o
11b2o2b2o12b3obob3ob3ob3ob3ob3obob3ob3obo30bo13b3ob3ob3ob3ob3ob3obob3o
bobob3ob3obo37b2o13bobobob3obob3ob3ob3obobob3obobob3obob3ob3obo15b2o
17b3ob3ob3ob3ob3ob3obob3ob3obo$3o13bobobobobobobobo3bo5bo42b3o12bobobo
3bo3bo3bobobo3bobo3bo3bobo3bo11bobo2bo14bobobo3bobobobobobo3bobobobo3b
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13bobo13b3obob3ob3obobob3o3bobobobob3obo28bo2bo12b3o3bo3bob3obobob3obo
3bob3ob3ob3obo36b4o12b3obobobobo3bob3ob3ob3ob3ob3ob3obob3ob3obo17bo2b
2o12b3ob3ob3o3bob3ob3obob3o3bobo$2b2o12bobobobobo3bo3bo3bo3bo40bobo14b
o3bo3bo3bo3bobobo3bobobo3bobobo3bo13b2o14bo3bo3bo3bobobo3bo3bobobobo3b
obo27bob2o13bo5bo3bo3bobobo3bobo3bo3bobobobobobo54bobobobobo3bo3bobobo
3bo3bo3bobo3bo3bobobobo15bobobobo12bobo3bobobo3bo3bobobobo3bo3bobo$16b
ob3ob3o3bob3ob3o3bo41b2o14bob3ob3ob3ob3ob3o3bob3ob3ob3ob3o29b3obob3ob
3ob3ob3o3bobob3ob3obo26bobo15b3o3bo3bob3ob3ob3obo3bo3bob3ob3obo36b2o
16bobob3obo3bob3ob3o3bob3o3bob3obob3ob3obo15b2o2bo14b3ob3ob3o3bob3ob3o
bob3o3bobo$231bobo93bo2bo83bobo$232bo95b2o85b2o24$b2o13b3ob3ob3ob3ob3o
b3ob3ob3obobob3obobobob3ob3obobobo6bo16bob3ob3ob3obobob3ob3ob3ob3ob3ob
obobobo11b2o12bobobob3obobob3ob3ob3ob3ob3ob3ob3ob3o22bo13b3ob3obob3ob
3o60b2o2b2o12bobobob3obobobobob3ob3ob3ob3ob3ob3ob3ob3obo20bo13bob3ob3o
b3obobob3ob3obob3obobobo$bo14bo3bobobo3bo5bo3bobobo3bobobo3bobobobo3bo
bo3bobobo5bobo15bobo3bobobobobobo3bobo3bobobobobobobobobobo10bobo12bob
obo3bobobo3bo3bobo5bo3bobobo3bo3bo21bobo14bobo3bobobobobo60bobo2bo12bo
bobobo3bobobobo3bobobobobo3bobobobobobo3bobobo19bobo12bo3bobo3bo3bobo
3bo3bobo3bobobobo$2bo13b3obobob3ob3ob3o3bobobob3ob3o3bob3obob3ob3obob
3o6bo2b2o12bob3ob3ob3ob3ob3ob3ob3ob3obobobobob3o10bo14bob3o3bob3ob3ob
3ob3ob3ob3obobob3ob3o20bo2bo14bob3obobobob3o62b2o14bob3ob3ob3ob3ob3obo
bob3ob3ob3ob3ob3ob3obo18bo2bo12bob3ob3ob3ob3ob3o3bobo3bobob3o$3bo12bob
obobobobo3bobo5bobobobo5bo3bo3bobo3bobobobo3bo7b2obo12bo3bo3bo3bo3bo3b
o3bo3bo3bobobobobo3bo9b2o14bo3bo3bo3bo3bobo5bo3bobo3bobobo5bo19bob2o
15bobobobobobo3bo62bo15bo3bobobo3bo3bo3bobobo3bobo3bobobobobobobobobo
14b2o2bobo13bo3bo3bo3bo3bobo5bobo3bobo3bo$2b2o12b3ob3ob3ob3ob3o3bob3ob
3o3bo3bo3bobob3ob3obo3bo23bob3ob3ob3o3bob3ob3ob3ob3ob3obobo3bo9bo15bo
3bo3bo3bob3ob3ob3ob3ob3ob3ob3ob3o18bobo17bob3obob3ob3o60bobo15bo3bob3o
3bo3bob3ob3ob3ob3ob3ob3ob3ob3obo14bobob2o14bob3ob3ob3o3bob3o3bobo3bobo
3bo$153bo76bo2bo92b2o83bo$152b2o77b2o176bobo$409b2o!


Pseudo still-lifes and oscillators
----------------------------------

Here are some numbers which produce close combinations of still-lifes:

#C Numeric predecessors of pseudo still-lifes (and oscillators).
#C (These are made up of 2 or more components which don't touch but which
#C are close enough to each other so that some dead cell has more than 3
#C live neighbors, but fewer than 3 in any component.)
#C
#C 2 blocks                   80
#C 2 loaves                   883
#C 2 loaves                   275663827376
#C 2 beehives                 381
#C 2 boats                    6644
#C 2 boats                    257737559
#C 2 ships                    30031
#C 2 ponds                    1138776244
#C 2 integral signs           80103310388
#C
#C block + beehive            73502
#C block + loaf               1422748
#C block + boat               7948
#C block + ship               7275956915
#C block + pond               14451055111
#C block + beacon             5297
#C block + eater              2545096704
#C block + eater              1135175288242
#C block + eater              2028108936114
#C block + long boat          18910901366304
#C
#C beehive + loaf             16131
#C beehive + boat             113765110794
#C beehive + ship             46613734575114
#C beehive + pond             11360422608
#C beehive + long boat        11357520813221914
#C beehive + eater            1602019736801
#C
#C loaf + boat                41847380114
#C loaf + boat                4123729009911
#C loaf + ship                76834931422
#C loaf + long boat           4108798044
#C loaf + beacon              1602821988
#C loaf + pond                160929718134670
#C
#C pond + boat                5513614
#C pond + beacon              57693896365995215
#C boat + eater               149945894301
#C
#C 4 blocks (2x2)             31100381
#C 4 blocks (1x4)             1131013
#C pond + 2 blocks            60787781
#C loaf + block + beehive     18910428084
#C block + pond + beehive     1447774240
#C 2 blocks + 2 beehives      4108108104
#C Dean Hickerson, dean.hickerson@yahoo.com (3/20/2007)
x = 508, y = 277, rule = B3/S23
5b2o12b3ob3o59bo13b3ob3ob3ob3ob3o46b2o13bob3obob3obo73bo13bobobob3obob
ob3ob3ob3ob3obobobobo38bo14b3ob3obob3ob3obobobo60b2ob2o12b3obobob3ob3o
b3ob3obo$5b2o12bobobobo55b2obobo14bo3bobo3bobo3bo45bo2bo12bobo3bo3bobo
72bobo12bobobobobobobo3bo3bobobobobobobobobo37bobo13bo3bo3bo3bobo3bobo
bo60b2ob2o14bobobobobobobo3bobobobo$19b3obobo55b2obobo14bob3ob3obobob
3o46b2o13bob3obob3obo71bo2bo12b3obob3ob3o3bob3ob3obobobobob3o38b2o13b
3ob3obob3ob3obob3o77b3obobobobobobob3ob3obo$5b2o12bobobobo59bo15bo3bo
3bobobobo63bobobobo3bobo72b2o15bobobobo3bo3bo3bobobobobobobo3bo55bo3bo
bo3bobobobo3bo60b2ob2o14bobobobobobobo3bobobobo$5b2o12b3ob3o75bob3ob3o
b3ob3o46b2o13bob3obob3obo89bobob3o3bo3bob3ob3ob3obobo3bo38b2o13b3ob3ob
ob3ob3obo3bo60b2ob2o12b3obobob3ob3ob3ob3obo$163bo2bo97b2o87bo2bo$163bo
bo97bobo87bo2bo$164bo99bo89b2o20$455b2o$455b2o2$5bo13b3ob3ob3o54bo14bo
bobob3ob3ob3obobob3o41bo13bobob3ob3ob3ob3obobob3ob3ob3obobo42b2o3bo13b
obobob3ob3ob3ob3ob3ob3ob3ob3ob3obobo24b2o19b3ob3ob3ob3ob3ob3ob3ob3ob3o
b3ob3ob3ob3ob3ob3obob3o21b2o12bobob3obob3obob3o$4bobo12bobobobo3bo50b
2obobo13bobobo3bo3bo3bobobobobo40bobo12bobo3bo3bobo3bo3bobobobo3bobobo
bobo41bo2bobobo12bobobo3bo3bo3bo3bobobobobobobobobobobobobo24b2o4b2o
13bo5bobo3bobo3bobobobobobo5bobo3bo3bobobobobo5bobobo23b2o12bobo3bobob
obobo3bo$3bo2bo12b3ob3ob3o50b2obo2bo12bob3ob3ob3o3bob3ob3o40b2o13bobob
3o3bob3ob3obobobobo3bob3ob3o42bobob2o13b3obob3ob3o3bob3ob3obobobobob3o
b3obobo26b2obo2bo12b3o3bob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3obob3o
35bobob3obobobobob3o$4b2o13bobobobo3bo54b2o13bo3bobo3bo5bo3bobobo55bob
o3bo3bobobo3bobobobobo3bo3bo3bo43bo19bobobo5bo3bobo5bobobobobo3bo3bobo
bo26b2obo2bo14bo3bobobo3bo3bobobo3bobobo3bobobo3bo3bo3bo3bobo3bo3bo21b
2o12bobo3bobobobobo3bo$19b3ob3ob3o69bo3bob3ob3o3bo3bob3o40b2o13bobob3o
3bob3ob3obobob3o3bob3o3bo63bobob3ob3o3bob3ob3ob3ob3ob3ob3obobo30b2o13b
3o3bob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3obob3o21b2o12bobob3obob3obo
b3o$4b2o157bo2bo$3bo2bo157b2o289b2o$4bobo448b2o$5bo22$4bo14b3ob3ob3ob
3ob3ob3ob3ob3ob3ob3ob3ob3o19bo13b3ob3obobob3o51b2o12bobob3ob3obob3ob3o
b3obobob3ob3ob3obobobobo32b2o3b2o12b3ob3ob3ob3obobob3ob3obobobob3ob3o
29b2o18bobobob3ob3obobob3ob3ob3obobob3ob3obo39b2o16b3ob3ob3ob3ob3ob3ob
3obo$3bobo15bo3bobo3bo3bo5bobobo3bo3bo3bo3bobo20bobo14bobobobobobobo
50bobo12bobobo3bo3bo3bo3bo3bobobobo5bobo3bobobobo31bo2bobobo14bobo3bob
o3bobobobobo3bobobobo3bo3bo29bo5bo13bobobobobobobobobobo3bobobobobobo
3bobobobo39b2o16bo3bobo3bobobo3bo3bobobobo$3bo2bo12b3o3bob3ob3ob3ob3ob
3ob3o3bob3o3bob3o19b2o14bob3ob3ob3o50b2o13b3ob3ob3obob3o3bob3ob3ob3o3b
ob3obobob3o32bobob2o15bob3ob3ob3ob3ob3ob3obob3ob3ob3o30b3obobo12bob3ob
3ob3ob3ob3ob3ob3ob3ob3obobobo57b3obobo3bob3o3bo3bob3obo$4b2o13bo5bo3bo
bobobobo3bobobobo5bo3bo3bobobo35bo3bo3bobobo67bobobobobobo3bo3bo3bo3bo
3bo3bo3bobobo3bo33bo19bobobobobo3bo3bo3bo3bobo3bobo3bo34bob2o13bo3bo3b
o3bo3bo3bobobo3bo3bo3bobobobo39b2o16bobobobo3bobobo3bo3bobobobo$19b3o
3bob3ob3ob3ob3ob3ob3o3bob3o3bob3o19b2o14bob3o3bob3o50b2o15bob3ob3obob
3o3bob3o3bob3o3bob3obobo3bo53bob3ob3ob3o3bob3ob3obo3bob3ob3o49bo3bob3o
b3o3bob3ob3ob3o3bob3ob3obo38bo2bob2o12b3ob3o3bob3o3bo3bob3obo$4b2o79b
2o76bo2bo283bo2bob2o$3bo2bo157b2o285b2o$4bobo$5bo22$4b2o13b3ob3obo57b
2o12b3ob3ob3ob3ob3ob3ob3ob3obob3o24b2o3bo13bobob3ob3ob3obobob3ob3ob3ob
3ob3o46bo14bobobob3ob3ob3ob3ob3ob3obobobobo131b2o6bo13bob3ob3obob3obob
ob3ob3ob3ob3obobo$3bo2bo14bobobobo56bobo14bo3bo3bobo3bobobo3bo3bobobob
o25bo2bobobo12bobo3bobo3bobobobo3bo3bobo3bobobobo42b2obobo13bobobobobo
bobo3bobobobobobobobobobobo130bo2bob2obobo12bobobobobobobobobobo3bobob
obobobobobobo$4b2o13b3ob3obo56b2o15bob3o3bob3ob3ob3ob3ob3obob3o23bo2bo
bobo12bobob3ob3obobob3ob3ob3ob3obobob3o41bobobo2bo12b3obobobob3o3bob3o
b3obobob3ob3o131bobob2obobo12bob3ob3obobobob3ob3ob3obobob3ob3o$21bobob
obo73bobo5bo3bo3bo3bobobo3bobo3bo24b2o3bo13bobo3bobobobobo3bobo3bo3bob
obobobobo40bobo3b2o15bobobobobobo3bo3bobobobobo3bo3bo132bo6bo13bobobo
3bobobobo3bobo3bobobobobobo3bo$4b2o13b3ob3obo56b2o15bob3o3bob3ob3ob3ob
3ob3obob3o43bobob3ob3ob3o3bob3ob3ob3ob3ob3o41bo21bobob3ob3o3bob3ob3ob
3o3bo3bo153bob3ob3obob3o3bob3ob3ob3ob3o3bo$3bo2bo77b2o$4b2o24$5bo13b3o
b3obobobobo47b2o16bobobobobob3obob3ob3ob3obobobo31b2o14bobob3ob3ob3ob
3ob3ob3ob3obob3ob3ob3obob3obobobo23b2o18bob3ob3ob3ob3ob3obob3ob3ob3o
136b2o3bo13bobobobobob3ob3ob3obobob3obobob3o$4bobo12bo3bo3bobobobo46bo
2bob2o12bobobobobobo3bobobobo3bo3bobobo30bo2bo13bobo3bobo5bobo5bobobob
obobo3bo3bo3bobobobobobobo22bo2bob2o14bobo3bobo3bobobo3bobobobobobobob
o135bo2bobobo12bobobobobo3bo3bo3bobobo3bobobobobo$5b2o12b3ob3ob3ob3o
46bo2bob2o12bob3ob3ob3obobobob3ob3obobobo31b2o14bobob3ob3o3bob3ob3obob
ob3obob3ob3ob3obob3obob3o23bobobo15bob3obobob3ob3ob3obob3ob3ob3o135bo
2bobobo12bob3ob3o3bo3bo3bob3ob3ob3obobo$19bobobobo3bo3bo47b2o16bo3bo3b
o3bobobobo3bo3bobobobo47bobo3bo3bo3bo3bobo3bobobobobo3bobo3bo3bo3bobo
3bo24bo5bo12bobobobobobo3bobobo3bo3bobobobobo136b2o3bo13bo3bo3bo3bo3bo
3bo3bobo5bobobo$5b2o12b3ob3o3bo3bo65bo3bo3bob3obob3ob3ob3obobobo31b2o
14bobob3ob3o3bob3ob3ob3ob3obob3ob3ob3obob3obo3bo29b2o12bob3ob3ob3ob3ob
3obob3ob3ob3o155bo3bo3bo3bo3bo3bo3bob3o3bob3o$4bobo156bobo284b2o$5bo
158bobo283b2o$165bo19$454b2o$453bo2bo$454b2o2$5bo13b3ob3ob3ob3ob3ob3ob
3ob3ob3o28b2ob2o12b3ob3ob3ob3o51bo13bob3ob3ob3ob3obob3ob3ob3ob3ob3ob3o
bo35b2o3bo14bob3ob3ob3ob3ob3ob3obob3obob3obobob3ob3ob3o122b2o13bobobob
3ob3obob3ob3obob3obobo$b2obobo14bobo5bo3bo3bo3bobo3bo3bobo28b2ob2o12bo
5bobobo3bo47b2obobo12bobo3bobo3bobobobobobo3bo3bobo3bobobobobo34bo2bob
obo13bobo3bobobobo3bobobo3bobobobobo3bobobobo5bobobo122b2o13bobobobobo
bobobobobobobobobobobobo$obob2o13b3ob3o3bo3bob3o3bob3ob3ob3o26b2o17b3o
b3ob3o3bo46bobobobo12bob3obobob3obobobob3o3bob3ob3ob3obobobo34bo2bobo
2bo12bob3obobob3ob3ob3o3bobob3obob3ob3ob3o3bobobo137b3obobobob3obobobo
b3obobobob3o$bo17bo5bo3bo3bo3bo3bo3bo3bo3bo26b2o19bobo5bo3bo46bo4bo13b
obobobobobo3bobobo3bo3bo3bobobobobobobobo35b2o3b2o13bobobobobo3bobo5bo
3bobobobobo3bo3bobobo3bobobo122b2o15bobobobobobobobobobobobobobo3bo$
19b3ob3o3bo3bob3o3bob3ob3ob3o45b3ob3ob3o3bo45b2o18bob3ob3ob3ob3obob3o
3bob3ob3ob3ob3obo55bob3ob3ob3ob3ob3o3bobob3obob3o3bob3o3bob3o122b2o15b
obob3ob3obob3ob3obob3o3bo2$454b2o$453bo2bo$454b2o22$5b2o12b3ob3ob3ob3o
bo49b2o12b3ob3obobob3ob3ob3ob3ob3ob3obobo$4bobo14bobobobobo3bobo49b2o
14bobo3bobobo3bobobobobo5bobobobobo$4b2o13b3obobobobob3obo63b3ob3ob3ob
3obobob3ob3o3bobobob3o$21bobobobobo3bobo49b2o12bo5bo3bo3bobobo3bobobo
3bobobo3bo$4b2o13b3ob3ob3ob3obo50bo12b3ob3o3bob3ob3ob3ob3o3bob3o3bo$4b
obo76b3o$5b2o76bo24$4b2o13bobob3ob3ob3ob3ob3ob3obobobobo31b2o12bobob3o
b3obob3ob3ob3ob3ob3ob3obobob3o$3bo2bo12bobo3bobobo3bo3bobo5bobobobobo
31b2o12bobo3bobo3bo3bobo5bobobobobo3bobobo3bo$3bo2bo12bobob3ob3o3bo3bo
b3ob3ob3ob3o45bobob3ob3obo3bob3ob3ob3ob3ob3ob3ob3o$4b2o13bobo3bobobo3b
o3bobobobo5bo3bo31b2o12bobo3bo3bobo3bo3bobo3bobobobobo5bobo$19bobob3ob
3o3bo3bob3ob3o3bo3bo31bo13bobob3ob3obo3bob3ob3ob3ob3ob3o3bob3o$4b2o77b
obo$3bo2bo76b2o$3bo2bo$4b2o22$2b2o15b3ob3obob3ob3ob3obob3ob3ob3ob3o22b
2ob2o14b3ob3ob3ob3obob3ob3ob3ob3ob3obobobobo$2bo16bobobobobobobo3bo3bo
bobobo3bobobobobo22b2obo17bobobo3bobobobobobobobobobo3bobo3bobobobo$3b
3o13b3obobobobobob3ob3obobobob3ob3ob3o26b3o12b3obobob3ob3obobobob3ob3o
b3ob3obobob3o$6bo12bobobobobobobo3bo3bobobobo3bobobobobo28bo12bo3bobob
o3bobobobobobobo3bo3bobobobobo3bo$5b2o12b3ob3obob3ob3ob3obob3ob3ob3ob
3o41b3ob3ob3ob3obob3ob3ob3ob3ob3obobo3bo2$5b2o$6bo$3b3o$2bo$2b2o20$83b
2o14bob3ob3obob3ob3ob3obob3ob3ob3ob3ob3obobo$83b2o14bobobobobobobobobo
bobobobo3bobo3bo5bobobobobo$99bob3ob3obobobob3obobobob3ob3ob3ob3obobob
3o$83b2o14bobobo3bobobobo3bobobobo3bobobobobo3bobobo3bo$83bobo13bob3ob
3obob3ob3ob3obob3ob3ob3ob3ob3o3bo$84bobo$85bo!


Infinite growth
---------------

I think the smallest number that produces infinite population growth is
154299.  It produces a block-laying Corderman switch engine along with
some other junk.  And 41140732 makes the other known type of switch
engine; it's probably not the minimal example:

#C Two examples of infinite growth
#C 154299 creates a stabilized Corderman switch engine heading southeast
#C in gen 539; the engine produces 8 blocks every 96 gens.
#C 41140732 creates an engine heading northwest in gen 148; after a while
#C it produces 3 blocks, 4 blinkers, 2 beehives, a boat, a loaf, a ship,
#C and a glider (also headed northwest) every 384 gens.
x = 35, y = 155, rule = B3/S23
ob3obobob3ob3ob3o$obo3bobo3bobobobobo$ob3ob3ob3ob3ob3o$o3bo3bobo5bo3bo
$ob3o3bob3ob3ob3o146$obobobobobob3ob3ob3ob3ob3ob3o$obobobobobobobo3bo
3bo3bo3bobo$3obobob3obobo3bob3ob3ob3ob3o$2bobobo3bobobo3bo3bobo5bobobo
$2bobobo3bob3o3bob3ob3ob3ob3o!


Repeated strings of digits
--------------------------

Long strings of a single digit produce 4 different results:

A string of 1's, 3's, 4's, 6's, 8's, or 9's dies quickly, except at the
ends.  These are useful for large constructions, since they allow us to
connect various components, as long as the components can be embedded
between two strings of dying digits.  For example, the bi-ship
predecessor given earlier is made from an embeddable digit string which
produces a fleet (...11150038111...) and one which produces a LWSS
(...11131041653546111...).  Most of my experiments have been with such
embeddable digit strings.

As noted earlier, a long string of 2's produces two lines of blinkers; so
does a string of 5's.

A string of 0's produces a wick which is stable in the middle but decays
from the ends at 4c/5, leaving behind a lot of debris.  There are at least
5 different fuses of this type, formed, for example, by the numbers
1000..., 2000..., 6000..., 7000..., and 8000... .  (To see these in action
requires too many 0's to include the patterns here.)  Here's a short string
of 0's, stabilized with tubs at the ends; I don't know if there are strings
of digits that can be put at the ends to stabilize the wick:

#C 00000000 with tubs at the ends
x = 39, y = 5, rule = B3/S23
4b3ob3ob3ob3ob3ob3ob3ob3o$bo2bobobobobobobobobobobobobobobobo2bo$obobo
bobobobobobobobobobobobobobobobobo$bo2bobobobobobobobobobobobobobobobo
2bo$4b3ob3ob3ob3ob3ob3ob3ob3o!

A string of 7's becomes, in 6 gens, a long line with some dying debris
in the middle, plus some junk at the ends.  If we put 61 at the left end
and 22 at the right end, then the junk dies out without affecting the
line.  This line then expands north and south while shrinking from east
and west, leaving behind a large quantity of debris.

#C 61777...77722 (with 60 7's) creates a line of length 235.  This
#C finishes in gen 6642 with a population of 4240.
x = 253, y = 5, rule = B3/S23
3obob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3o
b3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob
3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3o$o3bo3bo3bo3bo3bo3bo
3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo
3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo
3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo$3obo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3b
o3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo
3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo
3bo3bo3bob3ob3o$obobo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo
3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo
3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bobo3bo$
3obo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo
3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo
3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bob3ob3o!

Longer lines produce patterns with a fractal structure resembling a
Sierpinski gasket:

#C This is gen 7 of 61777...77722, with 2048 7's.  It creates a line of
#C length 8187.  This finishes in gen 15210 with a population of 461428
#C in even gens, 461564 in odd gens.
x = 8209, y = 9, rule = B3/S23
8200b3o4b2o$8201b2o4b2o$8201bo5bo$obo9b8185o8bo$b3o8b8185o6b2obo$2bobo
7b8185o7bo2bo$8203bo3bo$8203bo2bo$8203bobo!


Some repeated strings of more than one digit are also interesting.  Of
the 45 distinct patterns formed by repeating a pair of digits, 21 die
(except perhaps at the ends) and 22 end up with a line of still-lifes
and blinkers.  Of the remaining two, ...39393939... produces a line of
blinkers and a line of gliders, and ...171717... expands at 7c/40 north
and south, while decaying from both ends.  The interior is complicated;
I don't know exactly what it does.  (This is a relative of a "titanic
toroidal traveler", a pattern that lives on a cylinder of width 6,
discovered by Robert Wainwright in 1971.)  Here's a small piece of the
...171717... pattern; to see the traveler in action you'll need to use
a bigger piece, or use a Life program that can handle a cylindrical
universe.

#C 1717...1717 (with 64 17's)
x = 383, y = 5, rule = B3/S23
ob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3ob
ob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3ob
ob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3ob
ob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3obob3ob
ob3obob3obob3obob3obob3obob3obob3obob3o$o3bobo3bobo3bobo3bobo3bobo3bob
o3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bob
o3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bob
o3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bob
o3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bob
o3bobo3bo$o3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bob
o3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bob
o3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bob
o3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bob
o3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bo$o3bobo3bobo3bobo3bob
o3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bob
o3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bob
o3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bob
o3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bob
o3bobo3bobo3bobo3bo$o3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bob
o3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bob
o3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bob
o3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bob
o3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bo!


Several repeated strings of 3 digits also produce relatives of the same
titanic toroidal traveler: 025, 052, 088, 258, and 285.  And 569 produces
a different one (found by Bill Gosper in 1971):  Starting in gen 187 it
grows north and south at c/2; the top and bottom move with period 10,
but the interior is complicated.

#C 569569...569569 (with 25 569's)
x = 299, y = 5, rule = B3/S23
3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob
3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob
3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob
3ob3ob3ob3ob3ob3o$o3bo3bobobo3bo3bobobo3bo3bobobo3bo3bobobo3bo3bobobo
3bo3bobobo3bo3bobobo3bo3bobobo3bo3bobobo3bo3bobobo3bo3bobobo3bo3bobobo
3bo3bobobo3bo3bobobo3bo3bobobo3bo3bobobo3bo3bobobo3bo3bobobo3bo3bobobo
3bo3bobobo3bo3bobobo3bo3bobobo3bo3bobobo3bo3bobobo3bo3bobo$3ob3ob3ob3o
b3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob
3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob
3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob
3ob3o$2bobobo3bo3bobobo3bo3bobobo3bo3bobobo3bo3bobobo3bo3bobobo3bo3bob
obo3bo3bobobo3bo3bobobo3bo3bobobo3bo3bobobo3bo3bobobo3bo3bobobo3bo3bob
obo3bo3bobobo3bo3bobobo3bo3bobobo3bo3bobobo3bo3bobobo3bo3bobobo3bo3bob
obo3bo3bobobo3bo3bobobo3bo3bobobo3bo3bobobo3bo$3ob3ob3ob3ob3ob3ob3ob3o
b3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob
3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob
3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3o!

Repeated strings of 013 and 001 produce rows of rare still-lifes
(hat siamese hat and cis mirrored long dock); short versions of these
were shown in the small pattern collection.


Creating spaceships and gliders
-------------------------------

The small pattern collection shown earlier was the result of running lots
of numeric patterns and seeing what they produce.  In some cases, the
still-life or oscillator was produced along with some other stuff, and
the ends of the numbers had to be modified to eliminate the debris.  No
doubt a few other things could be produced in this way.  But it's also
possible to build things that don't occur naturally.

First, there are many embeddable digit strings that produce gliders.
These gliders can crash to form a few things.  For example, here's
another way to create an eater:

#C 1415073111111103975114 makes 2 gliders, which crash to form an eater.
x = 65, y = 5, rule = B3/S23
obobobob3ob3ob3ob3obobobobobobobob3ob3ob3ob3ob3obobobobo$obobobobo3bob
o3bo3bobobobobobobobobobo3bobobo3bobo3bobobobo$ob3obob3obobo3bob3obobo
bobobobobobobob3ob3o3bob3obobob3o$o3bobo3bobobo3bo3bobobobobobobobobob
o3bo3bo3bo3bobobo3bo$o3bobob3ob3o3bob3obobobobobobobob3ob3ob3o3bob3obo
bo3bo!

But most patterns can't be built with just 2 gliders, so we need a way
to send more than one glider along close parallel paths.  Fortunately
there are also some embeddable digit strings that produce spaceships
moving either east or west, and there are combinations of these in which
the spaceships crash to form gliders.  Here are the pure spaceship
producers that I've found:

#C ...1119477425111... and ...111424746405017111... produces westward LWSSs.
#C ...11194711556134111..., ...11131041653546111..., and
#C ...111553318811576425111... produce eastward LWSSs.
#C ...11147297575111... and ...111253447437666... produce eastward MWSSs.
x = 73, y = 245, rule = B3/S23
obobobobob3obobob3ob3obobob3ob3obobobobobo$obobobobobobobobo3bo3bobobo
3bobo3bobobobobo$3obobobob3ob3o3bo3bob3ob3ob3obobobob3o$2bobobobo3bo3b
o3bo3bo3bobo5bobobobo3bo$2bobobobob3o3bo3bo3bo3bob3ob3obobobo3bo36$obo
bobobobobob3obobob3obobob3obobob3ob3ob3obob3obobobobobo$obobobobobobo
3bobobo3bobobobo3bobobobobo3bobobo3bobobobobobo$3obobobob3ob3ob3o3bob
3ob3ob3obobob3obobobo3bobobobob3o$2bobobobo3bobo5bo3bo3bobobo3bobobo3b
obobobo3bobobobo3bo$2bobobobo3bob3o3bo3bo3bob3o3bob3ob3ob3obo3bobobobo
3bo36$obobobobob3obobob3obobob3ob3ob3obob3obobobobobobobo$obobobobobob
obobo3bobobobo3bo3bo3bo3bobobobobobobobo$3obobobob3ob3o3bobobob3ob3ob
3obob3ob3obobobob3o$2bobobobo3bo3bo3bobobo3bo3bobobobo3bo3bobobobo3bo$
2bobobobob3o3bo3bobobob3ob3ob3obob3o3bobobobo3bo36$obobobobob3obob3obo
bobob3ob3ob3ob3obobob3obobobobobo$obobobobo3bobobobobobobobo3bo5bobo3b
obobo3bobobobobo$3obobobob3obobobob3obob3ob3ob3ob3ob3ob3obobobob3o$2bo
bobobo3bobobobo3bobobobo3bo3bo3bo3bobobobobobo3bo$2bobobobob3obob3o3bo
bob3ob3ob3ob3o3bob3obobobo3bo36$obobobobob3ob3ob3ob3obob3ob3obobob3ob
3ob3obobob3ob3obobobobobo$obobobobobo3bo5bo3bobobobobobobobobo5bobo3bo
bo3bobo3bobobobobo$3obobobob3ob3ob3ob3obob3ob3obobob3o3bob3ob3ob3ob3ob
obobob3o$2bobobobo3bo3bo3bo3bobobobobobobobo3bo3bobobo3bobo5bobobobo3b
o$2bobobobob3ob3ob3ob3obob3ob3obobob3o3bob3o3bob3ob3obobobo3bo36$obobo
bobobobob3ob3ob3ob3ob3ob3ob3obobobobobo$obobobobobobo3bo3bobobo3bobo5b
obo3bobobobobo$3obobobob3o3bob3ob3o3bob3o3bob3obobobob3o$2bobobobo3bo
3bobo5bo3bo3bo3bo3bobobobo3bo$2bobobobo3bo3bob3ob3o3bob3o3bob3obobobo
3bo36$obobobobob3ob3ob3obobobobob3obobob3ob3ob3ob3ob3obo$obobobobo3bob
o5bobobobobo3bobobo3bo3bobo3bo3bo3bo$3obobobob3ob3ob3ob3ob3o3bob3ob3o
3bob3ob3ob3obo$2bobobobobo5bo3bo3bo3bo3bo3bo3bo3bobobobobobobobo$2bobo
bobob3ob3ob3o3bo3bo3bo3bob3o3bob3ob3ob3obo!

Here are the combinations of these that I've found which produce
gliders.  No doubt there are many more, which can produce gliders on
any desired path with any desired phase.

#C 5 collisions between spaceships produce gliders.
#C There are 2 NEward gliders, 2 NWward gliders, and 1 SWward glider.
x = 395, y = 205, rule = B3/S23
78bobobobobob3obob3obobobob3ob3ob3ob3obobob3obobob3obob3obobobob3ob3ob
3ob3obobob3obobobobobobobobobobobobobobobobobobob3obobob3obobob3obobob
3ob3ob3obob3obobobobobobobobobobobob3obobob3obobob3obobob3ob3ob3obob3o
bobobobobo$78bobobobobo3bobobobobobobobo3bo5bobo3bobobo3bobo3bobobobob
obobobo3bo5bobo3bobobo3bobobobobobobobobobobobobobobobobobo3bobobo3bob
obobo3bobobobobo3bobobo3bobobobobobobobobobobobo3bobobo3bobobobo3bobob
obobo3bobobo3bobobobobobo$78b3obobobob3obobobob3obob3ob3ob3ob3ob3ob3ob
obob3obobobob3obob3ob3ob3ob3ob3ob3obobobobobobobobobobobobobobobobob3o
b3ob3o3bob3ob3ob3obobob3obobobo3bobobobobobobobobobob3ob3ob3o3bob3ob3o
b3obobob3obobobo3bobobobob3o$80bobobobo3bobobobo3bobobobo3bo3bo3bo3bob
obobobo3bobobobo3bobobobo3bo3bo3bo3bobobobobobobobobobobobobobobobobob
obo3bobo5bo3bo3bobobo3bobobo3bobobobo3bobobobobobobobobobo3bobo5bo3bo
3bobobo3bobobo3bobobobo3bobobobo3bo$80bobobobob3obob3o3bobob3ob3ob3ob
3o3bob3obobob3obob3o3bobob3ob3ob3ob3o3bob3obobobobobobobobobobobobobob
obobo3bob3o3bo3bo3bob3o3bob3ob3ob3obo3bobobobobobobobobobo3bob3o3bo3bo
3bob3o3bob3ob3ob3obo3bobobobo3bo46$70bobobobobobobob3ob3ob3ob3ob3ob3ob
3obobobobobobobobobobob3obob3obobobob3ob3ob3ob3obobob3obobobobobobobob
obobobobobobobobobobob3obobob3obobob3obobob3ob3ob3obob3obobobobobobobo
bobobobobobobobobobobobobobobob3obobob3ob3obobob3ob3obobobobobo$70bobo
bobobobobo3bo3bobobo3bobo5bobo3bobobobobobobobobobo3bobobobobobobobo3b
o5bobo3bobobo3bobobobobobobobobobobobobobobobobobo3bobobo3bobobobo3bob
obobobo3bobobo3bobobobobobobobobobobobobobobobobobobobobobobobobobobo
3bo3bobobo3bobo3bobobobobo$70b3obobobob3o3bob3ob3o3bob3o3bob3obobobobo
bobobobobobob3obobobob3obob3ob3ob3ob3ob3ob3obobobobobobobobobobobobobo
bobobob3ob3ob3o3bob3ob3ob3obobob3obobobo3bobobobobobobobobobobobobobob
obobobobobobobobob3ob3o3bo3bob3ob3ob3obobobob3o$72bobobobo3bo3bobo5bo
3bo3bo3bo3bobobobobobobobobobobo3bobobobo3bobobobo3bo3bo3bo3bobobobobo
bobobobobobobobobobobobobobo3bobo5bo3bo3bobobo3bobobo3bobobobo3bobobob
obobobobobobobobobobobobobobobobobobobo3bo3bo3bo3bo3bobo5bobobobo3bo$
72bobobobo3bo3bob3ob3o3bob3o3bob3obobobobobobobobobobob3obob3o3bobob3o
b3ob3ob3o3bob3obobobobobobobobobobobobobobobobo3bob3o3bo3bo3bob3o3bob
3ob3ob3obo3bobobobobobobobobobobobobobobobobobobobobobobob3o3bo3bo3bo
3bob3ob3obobobo3bo46$obobobobob3ob3ob3obobobobob3obobob3ob3ob3obob3obo
bob3obobob3ob3ob3obob3obobobobobobobobobobobobobobobobobobobobobobobob
3obob3obobobob3ob3ob3ob3obobob3obobobobobobobobobobobobobobobobobobob
3obobob3obobob3obobob3ob3ob3ob3ob3obob3obobob3ob3obobob3obobobobobob3o
bobob3obobob3obobob3ob3ob3obob3obobobobobo$obobobobo3bobo5bobobobobo3b
obobo3bo3bobo3bobobobobo3bobobobo3bo3bo3bo3bobobobobobobobobobobobobob
obobobobobobobobobobo3bobobobobobobobo3bo5bobo3bobobo3bobobobobobobobo
bobobobobobobobobobo3bobobo3bobobobo3bobobobobo3bobobobobo3bobobobobo
3bo3bobobo3bobobobobobo3bobobo3bobobobo3bobobobobo3bobobo3bobobobobobo
$3obobobob3ob3ob3ob3ob3o3bob3ob3o3bob3obob3ob3o3bobobob3ob3ob3obob3ob
3obobobobobobobobobobobobobobobobobobobobobob3obobobob3obob3ob3ob3ob3o
b3ob3obobobobobobobobobobobobobobobobob3ob3ob3o3bob3ob3ob3obobob3obobo
b3ob3obob3ob3o3bo3bob3ob3ob3obob3ob3ob3o3bob3ob3ob3obobob3obobobo3bobo
bobob3o$2bobobobobo5bo3bo3bo3bo3bo3bo3bo3bobobobo3bo3bo3bobobo3bo3bobo
bobo3bo3bobobobobobobobobobobobobobobobobobobobobobo3bobobobo3bobobobo
3bo3bo3bo3bobobobobobobobobobobobobobobobobobobo3bobo5bo3bo3bobobo3bob
obo3bobobobobo3bobo3bo3bo3bo3bo3bobo5bobo3bobo5bo3bo3bobobo3bobobo3bob
obobo3bobobobo3bo$2bobobobob3ob3ob3o3bo3bo3bo3bob3o3bob3obob3o3bo3bobo
bob3ob3ob3obob3o3bobobobobobobobobobobobobobobobobobobobobobob3obob3o
3bobob3ob3ob3ob3o3bob3obobobobobobobobobobobobobobobobo3bob3o3bo3bo3bo
b3o3bob3ob3ob3ob3ob3obob3o3bo3bo3bo3bob3o3bobo3bob3o3bo3bo3bob3o3bob3o
b3ob3obo3bobobobo3bo46$2bobobobobobobob3ob3ob3ob3ob3ob3ob3obobobobob3o
bobob3obobob3ob3ob3obob3obobobobobobobobobobobobobobobobobobobobobobob
ob3obob3obobobob3ob3ob3ob3obobob3obobobobobobobobobobobobobobobobobobo
b3obobob3obobob3obobob3ob3ob3obobob3obob3obobob3ob3obobob3ob3obobobobo
bobobobobobobobobobobobobobobobob3obobob3ob3obobob3ob3obobobobobo$2bob
obobobobobo3bo3bobobo3bobo5bobo3bobobobobobobobo3bobobobo3bo3bo3bo3bob
obobobobobobobobobobobobobobobobobobobobobobo3bobobobobobobobo3bo5bobo
3bobobo3bobobobobobobobobobobobobobobobobobo3bobobo3bobobobo3bobobobob
o3bobobobobo3bobobobobo3bo3bobobo3bobo3bobobobobobobobobobobobobobobob
obobobobobobobobo3bo3bobobo3bobo3bobobobobo$2b3obobobob3o3bob3ob3o3bob
3o3bob3obobobobob3ob3o3bobobob3ob3ob3obob3ob3obobobobobobobobobobobobo
bobobobobobobobobob3obobobob3obob3ob3ob3ob3ob3ob3obobobobobobobobobobo
bobobobobobob3ob3ob3o3bob3ob3ob3obobob3obobobobob3obob3ob3o3bo3bob3ob
3ob3obobobobobobobobobobobobobobobobobobobobob3ob3o3bo3bob3ob3ob3obobo
bob3o$4bobobobo3bo3bobo5bo3bo3bo3bo3bobobobobo3bo3bo3bobobo3bo3bobobob
o3bo3bobobobobobobobobobobobobobobobobobobobobobo3bobobobo3bobobobo3bo
3bo3bo3bobobobobobobobobobobobobobobobobobobo3bobo5bo3bo3bobobo3bobobo
3bobobobobo3bobo3bo3bo3bo3bo3bobo5bobobobobobobobobobobobobobobobobobo
bobobo3bo3bo3bo3bo3bobo5bobobobo3bo$4bobobobo3bo3bob3ob3o3bob3o3bob3ob
obobobob3o3bo3bobobob3ob3ob3obob3o3bobobobobobobobobobobobobobobobobob
obobobobob3obob3o3bobob3ob3ob3ob3o3bob3obobobobobobobobobobobobobobobo
bo3bob3o3bo3bo3bob3o3bob3ob3ob3obobob3obob3o3bo3bo3bo3bob3ob3obobobobo
bobobobobobobobobobobobobobobobob3o3bo3bo3bo3bob3ob3obobobo3bo46$obobo
bobob3obob3obobobob3ob3ob3ob3obobob3obob3obobob3obobob3ob3ob3obob3obob
obobobobobobobobobobobobobobobobobobobobobob3obob3obobobob3ob3ob3ob3ob
obob3obobobobobobobobobobobobobobobobobobob3obobob3obobob3obobob3ob3ob
3obobob3obob3obobob3ob3obobob3ob3obobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobob3obobob3ob3obobob3ob3obobobob
obo$obobobobo3bobobobobobobobo3bo5bobo3bobobo3bobobobobo3bobobobo3bo3b
o3bo3bobobobobobobobobobobobobobobobobobobobobobobobo3bobobobobobobobo
3bo5bobo3bobobo3bobobobobobobobobobobobobobobobobobo3bobobo3bobobobo3b
obobobobo3bobobobobo3bobobobobo3bo3bobobo3bobo3bobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo3bo3bobob
o3bobo3bobobobobo$3obobobob3obobobob3obob3ob3ob3ob3ob3ob3obob3ob3o3bob
obob3ob3ob3obob3ob3obobobobobobobobobobobobobobobobobobobobobob3obobob
ob3obob3ob3ob3ob3ob3ob3obobobobobobobobobobobobobobobobob3ob3ob3o3bob
3ob3ob3obobob3obobobobob3obob3ob3o3bo3bob3ob3ob3obobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobob3ob3o3bo3bob3o
b3ob3obobobob3o$2bobobobo3bobobobo3bobobobo3bo3bo3bo3bobobobo3bo3bo3bo
bobo3bo3bobobobo3bo3bobobobobobobobobobobobobobobobobobobobobobo3bobob
obo3bobobobo3bo3bo3bo3bobobobobobobobobobobobobobobobobobobo3bobo5bo3b
o3bobobo3bobobo3bobobobobo3bobo3bo3bo3bo3bo3bobo5bobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobo3bo3bo3bo3bo
3bobo5bobobobo3bo$2bobobobob3obob3o3bobob3ob3ob3ob3o3bob3obob3o3bo3bob
obob3ob3ob3obob3o3bobobobobobobobobobobobobobobobobobobobobobob3obob3o
3bobob3ob3ob3ob3o3bob3obobobobobobobobobobobobobobobobo3bob3o3bo3bo3bo
b3o3bob3ob3ob3obobob3obob3o3bo3bo3bo3bob3ob3obobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobob3o3bo3bo3bo3bob3ob
3obobobo3bo!


Synthesis of glider gun
-----------------------

As an example of what can be done with reactions like these, here's a
number which produces a glider gun:

#C Numeric predecessor of period 30 glider gun
#C This quickly becomes 4 gliders and 40 spaceships headed east and
#C west.  The spaceships crash to form more gliders, for a total of
#C 6 headed NE and 6 headed NW.  The first 4 collide in pairs to form
#C 2 blocks.  The next 4 form 2 ponds, which the next 2 turn into
#C ships.  The last 2 turn the ships into queen bee shuttles,
#C forming a gun aimed SW in generation 4140.
#C The number, which has 740 digits, is shown here, with spaces
#C separating its components:
#C 411 31041653546 11 31041653546 1144444444444444444444444444444
#C 31041653546 11 31041653546 11444444444444444 31041653546 11
#C 31041653546 11444444444444444444 31041653546 11 31041653546
#C 111444444444444 15073 114444 5473 11444444444 2474640508 444444
#C 2474640508 444444444444444444444 2474640508 444444 2474640508 4444
#C 2474640508 444444 2474640508 4444444444444444444444 2474640508
#C 444444 2474640508 414 7297575 114 9471155613 414444444444
#C 31041653546 11 2534474376 1 9471155613 414444444444 31041653546 114
#C 7297575 114 9471155613 414444444444 31041653546 114 7297575 118
#C 9471155613 414444444444 31041653546 18 6703 1444 107579 1114444
#C 2474640508 51 947742 414444444441 947742 414444444444 2474640508
#C 51 947742 414444444441 947742 41444 2474640508 51 947742 414
#C 2474640508 414444444444444 2474640508 51 947742 414444444441
#C 947742 414
#C Dean Hickerson, dean.hickerson@yahoo.com (3/5/2007)
x = 2761, y = 5, rule = B3/S23
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3obobobob3obob3ob3ob3ob3ob3ob3obob3ob3o3bobobob3obob3ob3ob3obobobo3bob
3o3bob3obobobob3ob3ob3ob3ob3ob3o3bob3ob3ob3obobob3obobob3ob3obob3ob3o
3bo3bob3ob3ob3obob3ob3ob3ob3ob3ob3ob3ob3ob3obob3ob3o3bo3bob3ob3ob3obob
3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3o3bob3ob3ob3obobob3obobob3ob3obob3ob
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obobobo3bo3bobo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bobobobo3bobobobo3bo3bo
3bo3bobobobobo3bo3bobo5bo3bo3bo3bo3bobobo3bo3bo3bo3bobobo3bo3bobobobo
3bo3bobo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bobobobo3bobobobo3bo3bo3bo3bobo
bobobo3bo3bobo5bo3bo3bo3bo3bobobobobo3bo3bo3bobobo3bo3bobobobo3bo3bobo
3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bobobobo3bobobobo3bo3bo3bo3bobobobobobo
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3bobobo3bobobo3bobobobobo3bobo3bo3bo3bo3bo3bobo5bobo3bo3bo3bo3bo3bo3bo
3bo3bo3bobo3bo3bo3bo3bo3bobo5bobo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bobo5bo3b
o3bobobo3bobobo3bobobobobo3bobo3bo3bo3bo3bo3bobo5bobo3bo3bo3bo3bo3bo3b
o3bo3bo3bobo3bo3bo3bo3bo3bobo5bobo3bo3bo3bobo5bo3bo3bobobo3bobobo3bobo
bobobo3bobo3bo3bo3bo3bo3bobo5bobo3bobo5bo3bo3bobobo3bobobo3bobobobobo
3bobo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bobo5bo3bo3bobobo3bobobo3bob
obobobo3bobo3bo3bo3bo3bo3bobo5bobo3bo3bo3bo3bo3bo3bo3bo3bo3bobo3bo3bo
3bo3bo3bobo5bobo3bo$2bobobob3obob3o3bobob3ob3ob3ob3o3bob3obobob3obob3o
3bobob3ob3ob3ob3o3bob3obobo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo
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3o3bo3bo3bob3o3bob3ob3ob3ob3o3bo3bo3bo3bo3bo3bob3o3bo3bo3bob3o3bob3ob
3ob3ob3o3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3b
o3bob3o3bo3bo3bob3o3bob3ob3ob3ob3o3bo3bo3bo3bo3bo3bob3o3bo3bo3bob3o3bo
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bob3o3bobo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bob3obob3o3bobob3ob3ob3ob3o3bob
3obobob3ob3ob3o3bo3bo3bo3bob3o3bob3obob3o3bo3bobobob3ob3ob3obob3o3bobo
3bo3bo3bo3bo3bo3bo3bo3bo3bo3bob3obob3o3bobob3ob3ob3ob3o3bob3obobo3bo3b
ob3ob3o3bob3o3bob3obobo3bob3o3bo3bobobob3ob3ob3obob3o3bobo3bo3bo3bo3bo
3bo3bo3bo3bo3bo3bob3obob3o3bobob3ob3ob3ob3o3bob3obobo3bo3bob3ob3o3bob
3o3bob3obobob3ob3o3bo3bobobob3ob3ob3obob3o3bobo3bo3bo3bo3bo3bo3bo3bo3b
o3bo3bob3obob3o3bobob3ob3ob3ob3o3bob3obob3ob3o3bob3ob3obo3bo3bo3bobob
3o3bob3o3bob3obobobo3bo3bo3bo3bob3o3bo3bo3bob3o3bob3ob3ob3ob3ob3obob3o
3bo3bo3bo3bob3o3bobo3bo3bo3bo3bo3bo3bo3bo3bo3bobob3o3bo3bo3bo3bob3o3bo
bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bob3o3bo3bo3bob3o3bob3ob3ob3ob3ob3obob3o
3bo3bo3bo3bob3o3bobo3bo3bo3bo3bo3bo3bo3bo3bo3bobob3o3bo3bo3bo3bob3o3bo
bo3bo3bo3bob3o3bo3bo3bob3o3bob3ob3ob3ob3ob3obob3o3bo3bo3bo3bob3o3bobo
3bob3o3bo3bo3bob3o3bob3ob3ob3ob3o3bobo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3b
o3bo3bob3o3bo3bo3bob3o3bob3ob3ob3ob3ob3obob3o3bo3bo3bo3bob3o3bobo3bo3b
o3bo3bo3bo3bo3bo3bo3bobob3o3bo3bo3bo3bob3o3bobo3bo!

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