## Discussion thread for infinite growth patterns

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
M. I. Wright
Posts: 372
Joined: June 13th, 2015, 12:04 pm

### Re: Discussion thread for infinite growth patterns

...they mean the same thing.
gamer54657 wrote:God save us all.
God save humanity.

hgkhjfgh
nutshelltlifeDiscord 'Conwaylife Lounge'

Gamedziner
Posts: 795
Joined: May 30th, 2016, 8:47 pm
Location: Milky Way Galaxy: Planet Earth

### Re: Discussion thread for infinite growth patterns

M. I. Wright wrote:...they mean the same thing.
Oh.

Code: Select all

x = 81, y = 96, rule = LifeHistory
58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27. A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A$4.2A18$4.2A$4.2A2.2A$8.2A!  muzik Posts: 3925 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### Re: Discussion thread for infinite growth patterns A c/1084 extending glider arm thing: Code: Select all x = 263, y = 409, rule = B3/S23 5bo$4b2o$4bobo3$3o$2bo$bo23$35bo$34b2o$34bobo3$30b3o$32bo$31bo23$65bo$
64b2o$64bobo3$60b3o$62bo$61bo23$95bo$94b2o$94bobo3$90b3o$92bo$91bo23$125bo$124b2o$124bobo3$120b3o$122bo$121bo23$155bo$154b2o$154bobo3$150b
3o$152bo$151bo23$185bo$184b2o$184bobo3$180b3o$182bo$181bo23$215bo$214b
2o$214bobo3$210b3o$212bo$211bo6$243b2o$243b2o3$246b2o$246b2o2$243b2o$
243b2o9$245bo$244b2o$244bobo3$240b3o4b4o$242bo3b3o2bo$241bo4bo3bo3b2o
5b2o$247bo2bo3b2o6bo$247b3o11bo$251b2o8b2o$251b2o3$254b2o$254b2o18$2bo$b2o$bobo28$32bo$31b2o$31bobo28$62bo$61b2o$61bobo28$92bo$91b2o$91bobo
11$120b2o$120b2o3$123b2o$123b2o2$120b2o$120b2o9$122bo$121b2o$121bobo3$
124b4o$123b3o2bo$123bo3bo3b2o5b2o$124bo2bo3b2o6bo$124b3o11bo$128b2o8b 2o$128b2o3$131b2o$131b2o!

Should we come up with a name for this family/class of patterns? My suggestion is Extendo.

EDIT: or possibly windscreen wiper. Here's a c/5884:

Code: Select all

x = 1703, y = 2007, rule = B3/S23
447bo$446b2o$446bobo3$3o$2bo$bo23$477bo$476b2o$476bobo3$30b3o$32bo$31b o23$507bo$506b2o$506bobo3$60b3o$62bo$61bo23$537bo$536b2o$536bobo3$90b 3o$92bo$91bo23$567bo$566b2o$566bobo3$120b3o$122bo$121bo23$597bo$596b2o$596bobo3$150b3o$152bo$151bo23$627bo$626b2o$626bobo3$180b3o$182bo$181b o23$657bo$656b2o$656bobo3$210b3o$212bo$211bo23$687bo$686b2o$686bobo3$240b3o$242bo$241bo23$717bo$716b2o$716bobo3$270b3o$272bo$271bo23$747bo$746b2o$746bobo3$300b3o$302bo$301bo23$777bo$776b2o$776bobo3$330b3o$332b
o$331bo23$807bo$806b2o$806bobo3$360b3o$362bo$361bo23$837bo$836b2o$836b
obo3$390b3o$392bo$391bo23$867bo$866b2o$866bobo3$420b3o$422bo$421bo23$
897bo$896b2o$896bobo3$450b3o$452bo$451bo23$927bo$926b2o$926bobo3$480b 3o$482bo$481bo23$957bo$956b2o$956bobo3$510b3o$512bo$511bo23$987bo$986b 2o$986bobo3$540b3o$542bo$541bo23$1017bo$1016b2o$1016bobo3$570b3o$572bo
$571bo23$1047bo$1046b2o$1046bobo3$600b3o$602bo$601bo23$1077bo$1076b2o$
1076bobo3$630b3o$632bo$631bo23$1107bo$1106b2o$1106bobo3$660b3o$662bo$661bo23$1137bo$1136b2o$1136bobo3$690b3o$692bo$691bo23$1167bo$1166b2o$
1166bobo3$720b3o$722bo$721bo23$1197bo$1196b2o$1196bobo3$750b3o$752bo$751bo23$1227bo$1226b2o$1226bobo3$780b3o$782bo$781bo23$1257bo$1256b2o$
1256bobo3$810b3o$812bo$811bo23$1287bo$1286b2o$1286bobo3$840b3o$842bo$841bo23$1317bo$1316b2o$1316bobo3$870b3o$872bo$871bo23$1347bo$1346b2o$
1346bobo3$900b3o$902bo$901bo23$1377bo$1376b2o$1376bobo3$930b3o$932bo$931bo23$1407bo$1406b2o$1406bobo3$960b3o$962bo$961bo23$1437bo$1436b2o$
1436bobo3$990b3o$992bo$991bo23$1467bo$1466b2o$1466bobo3$1020b3o$1022bo
$1021bo23$1497bo$1496b2o$1496bobo3$1050b3o$1052bo$1051bo23$1527bo$1526b2o$1526bobo3$1080b3o$1082bo$1081bo23$1557bo$1556b2o$1556bobo3$1110b3o$1112bo$1111bo23$1587bo$1586b2o$1586bobo3$1140b3o$1142bo$1141bo 23$1617bo$1616b2o$1616bobo3$1170b3o$1172bo$1171bo23$1647bo$1646b2o$
1646bobo3$1200b3o$1202bo$1201bo14$1683b2o$1683b2o3$1686b2o$1686b2o2$
1683b2o$1683b2o$1677bo$1676b2o$1676bobo2$1693b3o$1230b3o459bo3bo$1232b o$1231bo459bo$1692b5o$1695bo2$1701bo$1700bobo$1701b2o2$1694b2o5b2o$1694b2o6bo$1701bo$1691b2o8b2o$1691b2o3$1694b2o$1694b2o12$1260b3o$1262b
o$1261bo28$1290b3o$1292bo$1291bo28$1320b3o$1322bo$1321bo28$1350b3o$1352bo$1351bo28$1380b3o$1382bo$1381bo28$1410b3o$1412bo$1411bo28$1440b 3o$1442bo$1441bo26$444bo$443b2o$443bobo28$474bo$473b2o$473bobo28$504bo
$503b2o$503bobo28$534bo$533b2o$533bobo28$564bo$563b2o$563bobo28$594bo$
593b2o$593bobo28$624bo$623b2o$623bobo28$654bo$653b2o$653bobo28$684bo$683b2o$683bobo28$714bo$713b2o$713bobo28$744bo$743b2o$743bobo28$774bo$
773b2o$773bobo28$804bo$803b2o$803bobo28$834bo$833b2o$833bobo28$864bo$863b2o$863bobo28$894bo$893b2o$893bobo28$924bo$923b2o$923bobo19$960b2o$
960b2o3$963b2o$963b2o2$960b2o$960b2o$954bo$953b2o$953bobo2$970b3o$969b o3bo2$968bo$969b5o$972bo2$978bo$977bobo$978b2o2$971b2o5b2o$971b2o6bo$
978bo$968b2o8b2o$968b2o3$971b2o$971b2o!

Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

muzik
Posts: 3925
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Discussion thread for infinite growth patterns

c/63484:

Code: Select all

x = 16744, y = 22976, rule = B3/S23
8812b2o$8812b2o3$8809b2o$8809b2o8b2o$8819bo$8812b2o6bo$8811bobo5b2o2$8812bo$8810bo2bo$8811b4o$8813b2o$8811bo$8810b2o$8810bo2bo$8811b3o$8812bo2$8795bobo$8795b2o$8796bo2$8801b2o$8801b2o2$8804b2o$8804b2o3$8801b2o$8801b2o18$8765bobo$8765b2o$8766bo28$8735bobo$8735b2o$8736bo28$8705bobo$8705b2o$8706bo28$8675bobo$8675b2o$8676bo28$8645bobo$8645b2o$8646bo28$8615bobo$8615b2o$8616bo28$8585bobo$8585b2o$8586bo28$8555bobo$8555b2o$8556bo28$8525bobo$8525b2o$8526bo28$8495bobo$8495b2o$8496bo28$8465bobo$8465b2o$8466bo28$8435bobo$8435b2o$8436bo28$8405bobo$8405b2o$8406bo28$8375bobo$8375b2o$8376bo28$8345bobo$8345b2o$8346bo28$8315bobo$8315b2o$8316bo28$8285bobo$8285b2o$8286bo28$8255bobo$8255b2o$8256bo28$8225bobo$8225b2o$8226bo28$8195bobo$8195b2o$8196bo28$8165bobo$8165b2o$8166bo28$8135bobo$8135b2o$8136bo28$8105bobo$8105b2o$8106bo28$8075bobo$8075b2o$8076bo28$8045bobo$8045b2o$8046bo28$8015bobo$8015b2o$8016bo28$7985bobo$7985b2o$7986bo28$7955bobo$7955b2o$7956bo28$7925bobo$7925b2o$7926bo28$7895bobo$7895b2o$7896bo28$7865bobo$7865b2o$7866bo28$7835bobo$7835b2o$7836bo28$7805bobo$7805b2o$7806bo28$7775bobo$7775b2o$7776bo28$7745bobo$7745b2o$7746bo28$7715bobo$7715b2o$7716bo28$7685bobo$7685b2o$7686bo28$7655bobo$7655b2o$7656bo28$7625bobo$7625b2o$7626bo28$7595bobo$7595b2o$7596bo28$7565bobo$7565b2o$7566bo28$7535bobo$7535b2o$7536bo28$7505bobo$7505b2o$7506bo28$7475bobo$7475b2o$7476bo28$7445bobo$7445b2o$7446bo28$7415bobo$7415b2o$7416bo28$7385bobo$7385b2o$7386bo28$7355bobo$7355b2o$7356bo28$7325bobo$7325b2o$7326bo28$7295bobo$7295b2o$7296bo28$7265bobo$7265b2o$7266bo28$7235bobo$7235b2o$7236bo28$7205bobo$7205b2o$7206bo28$7175bobo$7175b2o$7176bo28$7145bobo$7145b2o$7146bo28$7115bobo$7115b2o$7116bo28$7085bobo$7085b2o$7086bo28$7055bobo$7055b2o$7056bo28$7025bobo$7025b2o$7026bo28$6995bobo$6995b2o$6996bo28$6965bobo$6965b2o$6966bo28$6935bobo$6935b2o$6936bo28$6905bobo$6905b2o$6906bo28$6875bobo$6875b2o$6876bo28$6845bobo$6845b2o$6846bo28$6815bobo$6815b2o$6816bo28$6785bobo$6785b2o$6786bo28$6755bobo$6755b2o$6756bo28$6725bobo$6725b2o$6726bo28$6695bobo$6695b2o$6696bo28$6665bobo$6665b2o$6666bo28$6635bobo$6635b2o$6636bo28$6605bobo$6605b2o$6606bo28$6575bobo$6575b2o$6576bo28$6545bobo$6545b2o$6546bo28$6515bobo$6515b2o$6516bo28$6485bobo$6485b2o$6486bo28$6455bobo$6455b2o$6456bo28$6425bobo$6425b2o$6426bo28$6395bobo$6395b2o$6396bo28$6365bobo$6365b2o$6366bo28$6335bobo$6335b2o$6336bo28$6305bobo$6305b2o$6306bo28$6275bobo$6275b2o$6276bo28$6245bobo$6245b2o$6246bo28$6215bobo$6215b2o$6216bo28$6185bobo$6185b2o$6186bo28$6155bobo$6155b2o$6156bo28$6125bobo$6125b2o$6126bo28$6095bobo$6095b2o$6096bo28$6065bobo$6065b2o$6066bo28$6035bobo$6035b2o$6036bo28$6005bobo$6005b2o$6006bo28$5975bobo$5975b2o$5976bo28$5945bobo$5945b2o$5946bo28$5915bobo$5915b2o$5916bo28$5885bobo$5885b2o$5886bo28$5855bobo$5855b2o$5856bo28$5825bobo$5825b2o$5826bo28$5795bobo$5795b2o$5796bo28$5765bobo$5765b2o$5766bo28$5735bobo$5735b2o$5736bo28$5705bobo$5705b2o$5706bo28$5675bobo$5675b2o$5676bo28$5645bobo$5645b2o$5646bo28$5615bobo$5615b2o$5616bo28$5585bobo$5585b2o$5586bo28$5555bobo$5555b2o$5556bo28$5525bobo$5525b2o$5526bo28$5495bobo$5495b2o$5496bo28$5465bobo$5465b2o$5466bo28$5435bobo$5435b2o$5436bo28$5405bobo$5405b2o$5406bo28$5375bobo$5375b2o$5376bo28$5345bobo$5345b2o$5346bo28$5315bobo$5315b2o$5316bo28$5285bobo$5285b2o$5286bo28$5255bobo$5255b2o$5256bo28$5225bobo$5225b2o$5226bo28$5195bobo$5195b2o$5196bo28$5165bobo$5165b2o$5166bo28$5135bobo$5135b2o$5136bo28$5105bobo$5105b2o$5106bo28$5075bobo$5075b2o$5076bo28$5045bobo$5045b2o$5046bo28$5015bobo$5015b2o$5016bo28$4985bobo$4985b2o$4986bo28$4955bobo$4955b2o$4956bo28$4925bobo$4925b2o$4926bo28$4895bobo$4895b2o$4896bo28$4865bobo$4865b2o$4866bo28$4835bobo$4835b2o$4836bo28$4805bobo$4805b2o$4806bo28$4775bobo$4775b2o$4776bo28$4745bobo$4745b2o$4746bo28$4715bobo$4715b2o$4716bo28$4685bobo$4685b2o$4686bo28$4655bobo$4655b2o$4656bo28$4625bobo$4625b2o$4626bo28$4595bobo$4595b2o$4596bo28$4565bobo$4565b2o$4566bo28$4535bobo$4535b2o$4536bo28$4505bobo$4505b2o$4506bo28$4475bobo$4475b2o$4476bo28$4445bobo$4445b2o$4446bo28$4415bobo$4415b2o$4416bo28$4385bobo$4385b2o$4386bo28$4355bobo$4355b2o$4356bo28$4325bobo$4325b2o$4326bo28$4295bobo$4295b2o$4296bo28$4265bobo$4265b2o$4266bo28$4235bobo$4235b2o$4236bo28$4205bobo$4205b2o$4206bo28$4175bobo$4175b2o$4176bo28$4145bobo$4145b2o$4146bo28$4115bobo$4115b2o$4116bo28$4085bobo$4085b2o$4086bo28$4055bobo$4055b2o$4056bo28$4025bobo$4025b2o$4026bo28$3995bobo$3995b2o$3996bo28$3965bobo$3965b2o$3966bo28$3935bobo$3935b2o$3936bo28$3905bobo$3905b2o$3906bo28$3875bobo$3875b2o$3876bo28$3845bobo$3845b2o$3846bo28$3815bobo$3815b2o$3816bo28$3785bobo$3785b2o$3786bo28$3755bobo$3755b2o$3756bo28$3725bobo$3725b2o$3726bo28$3695bobo$3695b2o$3696bo28$3665bobo$3665b2o$3666bo28$3635bobo$3635b2o$3636bo28$3605bobo$3605b2o$3606bo28$3575bobo$3575b2o$3576bo28$3545bobo$3545b2o$3546bo28$3515bobo$3515b2o$3516bo28$3485bobo$3485b2o$3486bo28$3455bobo$3455b2o$3456bo28$3425bobo$3425b2o$3426bo28$3395bobo$3395b2o$3396bo28$3365bobo$3365b2o$3366bo28$3335bobo$3335b2o$3336bo28$3305bobo$3305b2o$3306bo28$3275bobo$3275b2o$3276bo28$3245bobo$3245b2o$3246bo28$3215bobo$3215b2o$3216bo28$3185bobo$3185b2o$3186bo28$3155bobo$3155b2o$3156bo28$3125bobo$3125b2o$3126bo28$3095bobo$3095b2o$3096bo28$3065bobo$3065b2o$3066bo28$3035bobo$3035b2o$3036bo28$3005bobo$3005b2o$3006bo28$2975bobo$2975b2o$2976bo28$2945bobo$2945b2o$2946bo28$2915bobo$2915b2o$2916bo28$2885bobo$2885b2o$2886bo28$2855bobo$2855b2o$2856bo28$2825bobo$2825b2o$2826bo28$2795bobo$2795b2o$2796bo28$2765bobo$2765b2o$2766bo28$2735bobo$2735b2o$2736bo28$2705bobo$2705b2o$2706bo28$2675bobo$2675b2o$2676bo28$2645bobo$2645b2o$2646bo28$2615bobo$2615b2o$2616bo28$2585bobo$2585b2o$2586bo28$2555bobo$2555b2o$2556bo28$2525bobo$2525b2o$2526bo28$2495bobo$2495b2o$2496bo28$2465bobo$2465b2o$2466bo28$2435bobo$2435b2o$2436bo28$2405bobo$2405b2o$2406bo28$2375bobo$2375b2o$2376bo28$2345bobo$2345b2o$2346bo28$2315bobo$2315b2o$2316bo28$2285bobo$2285b2o$2286bo28$2255bobo$2255b2o$2256bo28$2225bobo$2225b2o$2226bo28$2195bobo$2195b2o$2196bo28$2165bobo$2165b2o$2166bo28$2135bobo$2135b2o$2136bo28$2105bobo$2105b2o$2106bo28$2075bobo$2075b2o$2076bo28$2045bobo$2045b2o$2046bo28$2015bobo$2015b2o$2016bo28$1985bobo$1985b2o$1986bo28$1955bobo$1955b2o$1956bo28$1925bobo$1925b2o$1926bo28$1895bobo$1895b2o$1896bo28$1865bobo$1865b2o$1866bo28$1835bobo$1835b2o$1836bo28$1805bobo$1805b2o$1806bo28$1775bobo$1775b2o$1776bo28$1745bobo$1745b2o$1746bo28$1715bobo$1715b2o$1716bo26$15841bo$15842bo$15840b3o28$15811bo$15812bo$15810b3o28$15781bo$15782bo$15780b3o28$
15751bo$15752bo$15750b3o28$15721bo$15722bo$15720b3o28$15691bo$15692bo$
15690b3o28$15661bo$15662bo$15660b3o28$15631bo$15632bo$15630b3o28$15601bo$15602bo$15600b3o28$15571bo$15572bo$15570b3o28$15541bo$15542bo$15540b3o28$15511bo$15512bo$15510b3o28$15481bo$15482bo$15480b3o28$
15451bo$15452bo$15450b3o28$15421bo$15422bo$15420b3o28$15391bo$15392bo$
15390b3o28$15361bo$15362bo$15360b3o28$15331bo$15332bo$15330b3o28$15301bo$15302bo$15300b3o28$15271bo$15272bo$15270b3o28$15241bo$15242bo$15240b3o28$15211bo$15212bo$15210b3o28$15181bo$15182bo$15180b3o28$
15151bo$15152bo$15150b3o28$15121bo$15122bo$15120b3o28$15091bo$15092bo$
15090b3o28$15061bo$15062bo$15060b3o28$15031bo$15032bo$15030b3o13$16735b2o$16735b2o3$16732b2o$16732b2o8b2o$16742bo$16735b2o6bo$16734bobo 5b2o2$16735bo$16733bo2bo$16734b4o$16736b2o$16734bo$15001bo1731b2o$
15002bo1730bo2bo$15000b3o1731b3o$16735bo2$16718bobo$16718b2o$16719bo2$
16724b2o$16724b2o2$16727b2o$16727b2o3$16724b2o$16724b2o13$14971bo$14972bo$14970b3o3$16688bobo$16688b2o$16689bo23$14941bo$14942bo$14940b
3o3$16658bobo$16658b2o$16659bo23$14911bo$14912bo$14910b3o3$16628bobo$
16628b2o$16629bo23$14881bo$14882bo$14880b3o3$16598bobo$16598b2o$16599b o23$14851bo$14852bo$14850b3o3$16568bobo$16568b2o$16569bo23$14821bo$14822bo$14820b3o3$16538bobo$16538b2o$16539bo23$14791bo$14792bo$14790b
3o3$16508bobo$16508b2o$16509bo23$14761bo$14762bo$14760b3o3$16478bobo$
16478b2o$16479bo23$14731bo$14732bo$14730b3o3$16448bobo$16448b2o$16449b o23$14701bo$14702bo$14700b3o3$16418bobo$16418b2o$16419bo23$14671bo$14672bo$14670b3o3$16388bobo$16388b2o$16389bo23$14641bo$14642bo$14640b
3o3$16358bobo$16358b2o$16359bo23$14611bo$14612bo$14610b3o3$16328bobo$
16328b2o$16329bo23$14581bo$14582bo$14580b3o3$16298bobo$16298b2o$16299b o23$14551bo$14552bo$14550b3o3$16268bobo$16268b2o$16269bo23$14521bo$14522bo$14520b3o3$16238bobo$16238b2o$16239bo23$14491bo$14492bo$14490b
3o3$16208bobo$16208b2o$16209bo23$14461bo$14462bo$14460b3o3$16178bobo$
16178b2o$16179bo23$14431bo$14432bo$14430b3o3$16148bobo$16148b2o$16149b o23$14401bo$14402bo$14400b3o3$16118bobo$16118b2o$16119bo23$14371bo$14372bo$14370b3o3$16088bobo$16088b2o$16089bo23$14341bo$14342bo$14340b
3o3$16058bobo$16058b2o$16059bo23$14311bo$14312bo$14310b3o3$16028bobo$
16028b2o$16029bo23$14281bo$14282bo$14280b3o3$15998bobo$15998b2o$15999b o23$14251bo$14252bo$14250b3o3$15968bobo$15968b2o$15969bo23$14221bo$14222bo$14220b3o3$15938bobo$15938b2o$15939bo23$14191bo$14192bo$14190b
3o3$15908bobo$15908b2o$15909bo23$14161bo$14162bo$14160b3o3$15878bobo$
15878b2o$15879bo23$14131bo$14132bo$14130b3o3$15848bobo$15848b2o$15849b o23$14101bo$14102bo$14100b3o3$15818bobo$15818b2o$15819bo23$14071bo$14072bo$14070b3o3$15788bobo$15788b2o$15789bo23$14041bo$14042bo$14040b
3o3$15758bobo$15758b2o$15759bo23$14011bo$14012bo$14010b3o3$15728bobo$
15728b2o$15729bo23$13981bo$13982bo$13980b3o3$15698bobo$15698b2o$15699b o23$13951bo$13952bo$13950b3o3$15668bobo$15668b2o$15669bo23$13921bo$13922bo$13920b3o3$15638bobo$15638b2o$15639bo23$13891bo$13892bo$13890b
3o3$15608bobo$15608b2o$15609bo23$13861bo$13862bo$13860b3o3$15578bobo$
15578b2o$15579bo23$13831bo$13832bo$13830b3o3$15548bobo$15548b2o$15549b o23$13801bo$13802bo$13800b3o3$15518bobo$15518b2o$15519bo23$13771bo$13772bo$13770b3o3$15488bobo$15488b2o$15489bo23$13741bo$13742bo$13740b
3o3$15458bobo$15458b2o$15459bo23$13711bo$13712bo$13710b3o3$15428bobo$
15428b2o$15429bo23$13681bo$13682bo$13680b3o3$15398bobo$15398b2o$15399b o23$13651bo$13652bo$13650b3o3$15368bobo$15368b2o$15369bo23$13621bo$13622bo$13620b3o3$15338bobo$15338b2o$15339bo23$13591bo$13592bo$13590b
3o3$15308bobo$15308b2o$15309bo23$13561bo$13562bo$13560b3o3$15278bobo$
15278b2o$15279bo23$13531bo$13532bo$13530b3o3$15248bobo$15248b2o$15249b o23$13501bo$13502bo$13500b3o3$15218bobo$15218b2o$15219bo23$13471bo$13472bo$13470b3o3$15188bobo$15188b2o$15189bo23$13441bo$13442bo$13440b
3o3$15158bobo$15158b2o$15159bo23$13411bo$13412bo$13410b3o3$15128bobo$
15128b2o$15129bo23$13381bo$13382bo$13380b3o3$15098bobo$15098b2o$15099b o23$13351bo$13352bo$13350b3o3$15068bobo$15068b2o$15069bo23$13321bo$13322bo$13320b3o3$15038bobo$15038b2o$15039bo23$13291bo$13292bo$13290b
3o3$15008bobo$15008b2o$15009bo23$13261bo$13262bo$13260b3o3$14978bobo$
14978b2o$14979bo23$13231bo$13232bo$13230b3o3$14948bobo$14948b2o$14949b o23$13201bo$13202bo$13200b3o3$14918bobo$14918b2o$14919bo23$13171bo$13172bo$13170b3o3$14888bobo$14888b2o$14889bo23$13141bo$13142bo$13140b
3o3$14858bobo$14858b2o$14859bo23$13111bo$13112bo$13110b3o3$14828bobo$
14828b2o$14829bo23$13081bo$13082bo$13080b3o3$14798bobo$14798b2o$14799b o23$13051bo$13052bo$13050b3o3$14768bobo$14768b2o$14769bo23$13021bo$13022bo$13020b3o3$14738bobo$14738b2o$14739bo23$12991bo$12992bo$12990b
3o3$14708bobo$14708b2o$14709bo23$12961bo$12962bo$12960b3o3$14678bobo$
14678b2o$14679bo23$12931bo$12932bo$12930b3o3$14648bobo$14648b2o$14649b o23$12901bo$12902bo$12900b3o3$14618bobo$14618b2o$14619bo23$12871bo$12872bo$12870b3o3$14588bobo$14588b2o$14589bo23$12841bo$12842bo$12840b
3o3$14558bobo$14558b2o$14559bo23$12811bo$12812bo$12810b3o3$14528bobo$
14528b2o$14529bo23$12781bo$12782bo$12780b3o3$14498bobo$14498b2o$14499b o23$12751bo$12752bo$12750b3o3$14468bobo$14468b2o$14469bo23$12721bo$12722bo$12720b3o3$14438bobo$14438b2o$14439bo23$12691bo$12692bo$12690b
3o3$14408bobo$14408b2o$14409bo23$12661bo$12662bo$12660b3o3$14378bobo$
14378b2o$14379bo23$12631bo$12632bo$12630b3o3$14348bobo$14348b2o$14349b o23$12601bo$12602bo$12600b3o3$14318bobo$14318b2o$14319bo23$12571bo$12572bo$12570b3o3$14288bobo$14288b2o$14289bo23$12541bo$12542bo$12540b
3o3$14258bobo$14258b2o$14259bo23$12511bo$12512bo$12510b3o3$14228bobo$
14228b2o$14229bo23$12481bo$12482bo$12480b3o3$14198bobo$14198b2o$14199b o23$12451bo$12452bo$12450b3o3$14168bobo$14168b2o$14169bo23$12421bo$12422bo$12420b3o3$14138bobo$14138b2o$14139bo23$12391bo$12392bo$12390b
3o3$14108bobo$14108b2o$14109bo23$12361bo$12362bo$12360b3o3$14078bobo$
14078b2o$14079bo23$12331bo$12332bo$12330b3o3$14048bobo$14048b2o$14049b o23$12301bo$12302bo$12300b3o3$14018bobo$14018b2o$14019bo23$12271bo$12272bo$12270b3o3$13988bobo$13988b2o$13989bo23$12241bo$12242bo$12240b
3o3$13958bobo$13958b2o$13959bo23$12211bo$12212bo$12210b3o3$13928bobo$
13928b2o$13929bo23$12181bo$12182bo$12180b3o3$13898bobo$13898b2o$13899b o23$12151bo$12152bo$12150b3o3$13868bobo$13868b2o$13869bo23$12121bo$12122bo$12120b3o3$13838bobo$13838b2o$13839bo23$12091bo$12092bo$12090b
3o3$13808bobo$13808b2o$13809bo23$12061bo$12062bo$12060b3o3$13778bobo$
13778b2o$13779bo23$12031bo$12032bo$12030b3o3$13748bobo$13748b2o$13749b o23$12001bo$12002bo$12000b3o3$13718bobo$13718b2o$13719bo23$11971bo$11972bo$11970b3o3$13688bobo$13688b2o$13689bo23$11941bo$11942bo$11940b
3o3$13658bobo$13658b2o$13659bo23$11911bo$11912bo$11910b3o3$13628bobo$
13628b2o$13629bo23$11881bo$11882bo$11880b3o3$13598bobo$13598b2o$13599b o23$11851bo$11852bo$11850b3o3$13568bobo$13568b2o$13569bo23$11821bo$11822bo$11820b3o3$13538bobo$13538b2o$13539bo23$11791bo$11792bo$11790b
3o3$13508bobo$13508b2o$13509bo23$11761bo$11762bo$11760b3o3$13478bobo$
13478b2o$13479bo23$11731bo$11732bo$11730b3o3$13448bobo$13448b2o$13449b o23$11701bo$11702bo$11700b3o3$13418bobo$13418b2o$13419bo23$11671bo$11672bo$11670b3o3$13388bobo$13388b2o$13389bo23$11641bo$11642bo$11640b
3o3$13358bobo$13358b2o$13359bo23$11611bo$11612bo$11610b3o3$13328bobo$
13328b2o$13329bo23$11581bo$11582bo$11580b3o3$13298bobo$13298b2o$13299b o23$11551bo$11552bo$11550b3o3$13268bobo$13268b2o$13269bo23$11521bo$11522bo$11520b3o3$13238bobo$13238b2o$13239bo23$11491bo$11492bo$11490b
3o3$13208bobo$13208b2o$13209bo23$11461bo$11462bo$11460b3o3$13178bobo$
13178b2o$13179bo23$11431bo$11432bo$11430b3o3$13148bobo$13148b2o$13149b o23$11401bo$11402bo$11400b3o3$13118bobo$13118b2o$13119bo23$11371bo$11372bo$11370b3o3$13088bobo$13088b2o$13089bo23$11341bo$11342bo$11340b
3o3$13058bobo$13058b2o$13059bo23$11311bo$11312bo$11310b3o3$13028bobo$
13028b2o$13029bo23$11281bo$11282bo$11280b3o3$12998bobo$12998b2o$12999b o23$11251bo$11252bo$11250b3o3$12968bobo$12968b2o$12969bo23$11221bo$11222bo$11220b3o3$12938bobo$12938b2o$12939bo23$11191bo$11192bo$11190b
3o3$12908bobo$12908b2o$12909bo23$11161bo$11162bo$11160b3o3$12878bobo$
12878b2o$12879bo23$11131bo$11132bo$11130b3o3$12848bobo$12848b2o$12849b o23$11101bo$11102bo$11100b3o3$12818bobo$12818b2o$12819bo23$11071bo$11072bo$11070b3o3$12788bobo$12788b2o$12789bo23$11041bo$11042bo$11040b
3o3$12758bobo$12758b2o$12759bo23$11011bo$11012bo$11010b3o3$12728bobo$
12728b2o$12729bo23$10981bo$10982bo$10980b3o3$12698bobo$12698b2o$12699b o23$10951bo$10952bo$10950b3o3$12668bobo$12668b2o$12669bo23$10921bo$10922bo$10920b3o3$12638bobo$12638b2o$12639bo23$10891bo$10892bo$10890b
3o3$12608bobo$12608b2o$12609bo23$10861bo$10862bo$10860b3o3$12578bobo$
12578b2o$12579bo23$10831bo$10832bo$10830b3o3$12548bobo$12548b2o$12549b o23$10801bo$10802bo$10800b3o3$12518bobo$12518b2o$12519bo23$10771bo$10772bo$10770b3o3$12488bobo$12488b2o$12489bo23$10741bo$10742bo$10740b
3o3$12458bobo$12458b2o$12459bo23$10711bo$10712bo$10710b3o3$12428bobo$
12428b2o$12429bo23$10681bo$10682bo$10680b3o3$12398bobo$12398b2o$12399b o23$10651bo$10652bo$10650b3o3$12368bobo$12368b2o$12369bo23$10621bo$10622bo$10620b3o3$12338bobo$12338b2o$12339bo23$10591bo$10592bo$10590b
3o3$12308bobo$12308b2o$12309bo23$10561bo$10562bo$10560b3o3$12278bobo$
12278b2o$12279bo23$10531bo$10532bo$10530b3o3$12248bobo$12248b2o$12249b o23$10501bo$10502bo$10500b3o3$12218bobo$12218b2o$12219bo23$10471bo$10472bo$10470b3o3$12188bobo$12188b2o$12189bo23$10441bo$10442bo$10440b
3o3$12158bobo$12158b2o$12159bo23$10411bo$10412bo$10410b3o3$12128bobo$
12128b2o$12129bo23$10381bo$10382bo$10380b3o3$12098bobo$12098b2o$12099b o23$10351bo$10352bo$10350b3o3$12068bobo$12068b2o$12069bo23$10321bo$10322bo$10320b3o3$12038bobo$12038b2o$12039bo23$10291bo$10292bo$10290b
3o3$12008bobo$12008b2o$12009bo23$10261bo$10262bo$10260b3o3$11978bobo$
11978b2o$11979bo23$10231bo$10232bo$10230b3o3$11948bobo$11948b2o$11949b o23$10201bo$10202bo$10200b3o3$11918bobo$11918b2o$11919bo23$10171bo$10172bo$10170b3o3$11888bobo$11888b2o$11889bo23$10141bo$10142bo$10140b
3o3$11858bobo$11858b2o$11859bo23$10111bo$10112bo$10110b3o3$11828bobo$
11828b2o$11829bo23$10081bo$10082bo$10080b3o3$11798bobo$11798b2o$11799b o23$10051bo$10052bo$10050b3o3$11768bobo$11768b2o$11769bo23$10021bo$10022bo$10020b3o3$11738bobo$11738b2o$11739bo23$9991bo$9992bo$9990b3o3$11708bobo$11708b2o$11709bo23$9961bo$9962bo$9960b3o3$11678bobo$11678b2o
$11679bo23$9931bo$9932bo$9930b3o3$11648bobo$11648b2o$11649bo23$9901bo$9902bo$9900b3o3$11618bobo$11618b2o$11619bo23$9871bo$9872bo$9870b3o3$11588bobo$11588b2o$11589bo23$9841bo$9842bo$9840b3o3$11558bobo$11558b2o
$11559bo23$9811bo$9812bo$9810b3o3$11528bobo$11528b2o$11529bo23$9781bo$9782bo$9780b3o3$11498bobo$11498b2o$11499bo23$9751bo$9752bo$9750b3o3$11468bobo$11468b2o$11469bo23$9721bo$9722bo$9720b3o3$11438bobo$11438b2o
$11439bo23$9691bo$9692bo$9690b3o3$11408bobo$11408b2o$11409bo23$9661bo$9662bo$9660b3o3$11378bobo$11378b2o$11379bo23$9631bo$9632bo$9630b3o3$11348bobo$11348b2o$11349bo23$9601bo$9602bo$9600b3o3$11318bobo$11318b2o
$11319bo23$9571bo$9572bo$9570b3o3$11288bobo$11288b2o$11289bo23$9541bo$9542bo$9540b3o3$11258bobo$11258b2o$11259bo23$9511bo$9512bo$9510b3o3$11228bobo$11228b2o$11229bo23$9481bo$9482bo$9480b3o3$11198bobo$11198b2o
$11199bo23$9451bo$9452bo$9450b3o3$11168bobo$11168b2o$11169bo23$9421bo$9422bo$9420b3o3$11138bobo$11138b2o$11139bo23$9391bo$9392bo$9390b3o3$11108bobo$11108b2o$11109bo23$9361bo$9362bo$9360b3o3$11078bobo$11078b2o
$11079bo23$9331bo$9332bo$9330b3o3$11048bobo$11048b2o$11049bo23$9301bo$9302bo$9300b3o3$11018bobo$11018b2o$11019bo23$9271bo$9272bo$9270b3o3$10988bobo$10988b2o$10989bo23$9241bo$9242bo$9240b3o3$10958bobo$10958b2o
$10959bo23$9211bo$9212bo$9210b3o3$10928bobo$10928b2o$10929bo23$9181bo$9182bo$9180b3o3$10898bobo$10898b2o$10899bo23$9151bo$9152bo$9150b3o3$10868bobo$10868b2o$10869bo23$9121bo$9122bo$9120b3o3$10838bobo$10838b2o
$10839bo23$9091bo$9092bo$9090b3o3$10808bobo$10808b2o$10809bo23$9061bo$9062bo$9060b3o3$10778bobo$10778b2o$10779bo23$9031bo$9032bo$9030b3o3$10748bobo$10748b2o$10749bo23$9001bo$9002bo$9000b3o3$10718bobo$10718b2o
$10719bo23$8971bo$8972bo$8970b3o3$10688bobo$10688b2o$10689bo23$8941bo$8942bo$8940b3o3$10658bobo$10658b2o$10659bo23$8911bo$8912bo$8910b3o3$10628bobo$10628b2o$10629bo23$8881bo$8882bo$8880b3o3$10598bobo$10598b2o
$10599bo23$8851bo$8852bo$8850b3o3$10568bobo$10568b2o$10569bo23$8821bo$8822bo$8820b3o3$10538bobo$10538b2o$10539bo23$8791bo$8792bo$8790b3o3$10508bobo$10508b2o$10509bo23$8761bo$8762bo$8760b3o3$10478bobo$10478b2o
$10479bo23$8731bo$8732bo$8730b3o3$10448bobo$10448b2o$10449bo23$8701bo$8702bo$8700b3o3$10418bobo$10418b2o$10419bo23$8671bo$8672bo$8670b3o3$10388bobo$10388b2o$10389bo23$8641bo$8642bo$8640b3o3$10358bobo$10358b2o
$10359bo23$8611bo$8612bo$8610b3o3$10328bobo$10328b2o$10329bo23$8581bo$8582bo$8580b3o3$10298bobo$10298b2o$10299bo23$8551bo$8552bo$8550b3o3$10268bobo$10268b2o$10269bo23$8521bo$8522bo$8520b3o3$10238bobo$10238b2o
$10239bo23$8491bo$8492bo$8490b3o3$10208bobo$10208b2o$10209bo23$8461bo$8462bo$8460b3o3$10178bobo$10178b2o$10179bo23$8431bo$8432bo$8430b3o3$10148bobo$10148b2o$10149bo23$8401bo$8402bo$8400b3o3$10118bobo$10118b2o
$10119bo23$8371bo$8372bo$8370b3o3$10088bobo$10088b2o$10089bo23$8341bo$8342bo$8340b3o3$10058bobo$10058b2o$10059bo23$8311bo$8312bo$8310b3o3$10028bobo$10028b2o$10029bo23$8281bo$8282bo$8280b3o3$9998bobo$9998b2o$9999bo23$8251bo$8252bo$8250b3o3$9968bobo$9968b2o$9969bo23$8221bo$8222b o$8220b3o3$9938bobo$9938b2o$9939bo23$8191bo$8192bo$8190b3o3$9908bobo$
9908b2o$9909bo23$8161bo$8162bo$8160b3o3$9878bobo$9878b2o$9879bo23$
8131bo$8132bo$8130b3o3$9848bobo$9848b2o$9849bo23$8101bo$8102bo$8100b3o
3$9818bobo$9818b2o$9819bo23$8071bo$8072bo$8070b3o3$9788bobo$9788b2o$9789bo23$8041bo$8042bo$8040b3o3$9758bobo$9758b2o$9759bo23$8011bo$8012b o$8010b3o3$9728bobo$9728b2o$9729bo23$7981bo$7982bo$7980b3o3$9698bobo$
9698b2o$9699bo23$7951bo$7952bo$7950b3o3$9668bobo$9668b2o$9669bo23$
7921bo$7922bo$7920b3o3$9638bobo$9638b2o$9639bo23$7891bo$7892bo$7890b3o
3$9608bobo$9608b2o$9609bo23$7861bo$7862bo$7860b3o3$9578bobo$9578b2o$9579bo23$7831bo$7832bo$7830b3o3$9548bobo$9548b2o$9549bo23$7801bo$7802b o$7800b3o3$9518bobo$9518b2o$9519bo23$7771bo$7772bo$7770b3o3$9488bobo$
9488b2o$9489bo23$7741bo$7742bo$7740b3o3$9458bobo$9458b2o$9459bo23$
7711bo$7712bo$7710b3o3$9428bobo$9428b2o$9429bo23$7681bo$7682bo$7680b3o
3$9398bobo$9398b2o$9399bo23$7651bo$7652bo$7650b3o3$9368bobo$9368b2o$9369bo23$7621bo$7622bo$7620b3o3$9338bobo$9338b2o$9339bo23$7591bo$7592b o$7590b3o3$9308bobo$9308b2o$9309bo23$7561bo$7562bo$7560b3o3$9278bobo$
9278b2o$9279bo23$7531bo$7532bo$7530b3o3$9248bobo$9248b2o$9249bo23$
7501bo$7502bo$7500b3o3$9218bobo$9218b2o$9219bo23$7471bo$7472bo$7470b3o
3$9188bobo$9188b2o$9189bo23$7441bo$7442bo$7440b3o3$9158bobo$9158b2o$9159bo23$7411bo$7412bo$7410b3o3$9128bobo$9128b2o$9129bo23$7381bo$7382b o$7380b3o3$9098bobo$9098b2o$9099bo23$7351bo$7352bo$7350b3o3$9068bobo$
9068b2o$9069bo23$7321bo$7322bo$7320b3o3$9038bobo$9038b2o$9039bo23$
7291bo$7292bo$7290b3o3$9008bobo$9008b2o$9009bo23$7261bo$7262bo$7260b3o
3$8978bobo$8978b2o$8979bo23$7231bo$7232bo$7230b3o3$8948bobo$8948b2o$8949bo23$7201bo$7202bo$7200b3o3$8918bobo$8918b2o$8919bo23$7171bo$7172b o$7170b3o3$8888bobo$8888b2o$8889bo23$7141bo$7142bo$7140b3o3$8858bobo$
8858b2o$8859bo23$7111bo$7112bo$7110b3o3$8828bobo$8828b2o$8829bo23$
7081bo$7082bo$7080b3o3$8798bobo$8798b2o$8799bo23$7051bo$7052bo$7050b3o
3$8768bobo$8768b2o$8769bo23$7021bo$7022bo$7020b3o3$8738bobo$8738b2o$8739bo23$6991bo$6992bo$6990b3o3$8708bobo$8708b2o$8709bo23$6961bo$6962b o$6960b3o3$8678bobo$8678b2o$8679bo23$6931bo$6932bo$6930b3o3$8648bobo$
8648b2o$8649bo23$6901bo$6902bo$6900b3o3$8618bobo$8618b2o$8619bo23$
6871bo$6872bo$6870b3o3$8588bobo$8588b2o$8589bo23$6841bo$6842bo$6840b3o
3$8558bobo$8558b2o$8559bo23$6811bo$6812bo$6810b3o3$8528bobo$8528b2o$8529bo23$6781bo$6782bo$6780b3o3$8498bobo$8498b2o$8499bo23$6751bo$6752b o$6750b3o3$8468bobo$8468b2o$8469bo23$6721bo$6722bo$6720b3o3$8438bobo$
8438b2o$8439bo23$6691bo$6692bo$6690b3o3$8408bobo$8408b2o$8409bo23$
6661bo$6662bo$6660b3o3$8378bobo$8378b2o$8379bo23$6631bo$6632bo$6630b3o
3$8348bobo$8348b2o$8349bo23$6601bo$6602bo$6600b3o3$8318bobo$8318b2o$8319bo23$6571bo$6572bo$6570b3o3$8288bobo$8288b2o$8289bo23$6541bo$6542b o$6540b3o3$8258bobo$8258b2o$8259bo23$6511bo$6512bo$6510b3o3$8228bobo$
8228b2o$8229bo23$6481bo$6482bo$6480b3o3$8198bobo$8198b2o$8199bo23$
6451bo$6452bo$6450b3o3$8168bobo$8168b2o$8169bo23$6421bo$6422bo$6420b3o
3$8138bobo$8138b2o$8139bo23$6391bo$6392bo$6390b3o3$8108bobo$8108b2o$8109bo23$6361bo$6362bo$6360b3o3$8078bobo$8078b2o$8079bo23$6331bo$6332b o$6330b3o3$8048bobo$8048b2o$8049bo23$6301bo$6302bo$6300b3o3$8018bobo$
8018b2o$8019bo23$6271bo$6272bo$6270b3o3$7988bobo$7988b2o$7989bo23$
6241bo$6242bo$6240b3o3$7958bobo$7958b2o$7959bo23$6211bo$6212bo$6210b3o
3$7928bobo$7928b2o$7929bo23$6181bo$6182bo$6180b3o3$7898bobo$7898b2o$7899bo23$6151bo$6152bo$6150b3o3$7868bobo$7868b2o$7869bo23$6121bo$6122b o$6120b3o3$7838bobo$7838b2o$7839bo23$6091bo$6092bo$6090b3o3$7808bobo$
7808b2o$7809bo23$6061bo$6062bo$6060b3o3$7778bobo$7778b2o$7779bo23$
6031bo$6032bo$6030b3o3$7748bobo$7748b2o$7749bo23$6001bo$6002bo$6000b3o
3$7718bobo$7718b2o$7719bo23$5971bo$5972bo$5970b3o3$7688bobo$7688b2o$7689bo23$5941bo$5942bo$5940b3o3$7658bobo$7658b2o$7659bo23$5911bo$5912b o$5910b3o3$7628bobo$7628b2o$7629bo23$5881bo$5882bo$5880b3o3$7598bobo$
7598b2o$7599bo23$5851bo$5852bo$5850b3o3$7568bobo$7568b2o$7569bo23$
5821bo$5822bo$5820b3o3$7538bobo$7538b2o$7539bo23$5791bo$5792bo$5790b3o
3$7508bobo$7508b2o$7509bo23$5761bo$5762bo$5760b3o3$7478bobo$7478b2o$7479bo23$5731bo$5732bo$5730b3o3$7448bobo$7448b2o$7449bo23$5701bo$5702b o$5700b3o3$7418bobo$7418b2o$7419bo23$5671bo$5672bo$5670b3o3$7388bobo$
7388b2o$7389bo23$5641bo$5642bo$5640b3o3$7358bobo$7358b2o$7359bo23$
5611bo$5612bo$5610b3o3$7328bobo$7328b2o$7329bo23$5581bo$5582bo$5580b3o
3$7298bobo$7298b2o$7299bo23$5551bo$5552bo$5550b3o3$7268bobo$7268b2o$7269bo23$5521bo$5522bo$5520b3o3$7238bobo$7238b2o$7239bo23$5491bo$5492b o$5490b3o3$7208bobo$7208b2o$7209bo23$5461bo$5462bo$5460b3o3$7178bobo$
7178b2o$7179bo23$5431bo$5432bo$5430b3o3$7148bobo$7148b2o$7149bo23$
5401bo$5402bo$5400b3o3$7118bobo$7118b2o$7119bo23$5371bo$5372bo$5370b3o
3$7088bobo$7088b2o$7089bo23$5341bo$5342bo$5340b3o3$7058bobo$7058b2o$7059bo23$5311bo$5312bo$5310b3o3$7028bobo$7028b2o$7029bo23$5281bo$5282b o$5280b3o3$6998bobo$6998b2o$6999bo23$5251bo$5252bo$5250b3o3$6968bobo$
6968b2o$6969bo23$5221bo$5222bo$5220b3o3$6938bobo$6938b2o$6939bo23$
5191bo$5192bo$5190b3o3$6908bobo$6908b2o$6909bo23$5161bo$5162bo$5160b3o
3$6878bobo$6878b2o$6879bo23$5131bo$5132bo$5130b3o3$6848bobo$6848b2o$6849bo23$5101bo$5102bo$5100b3o3$6818bobo$6818b2o$6819bo23$5071bo$5072b o$5070b3o3$6788bobo$6788b2o$6789bo23$5041bo$5042bo$5040b3o3$6758bobo$
6758b2o$6759bo23$5011bo$5012bo$5010b3o3$6728bobo$6728b2o$6729bo23$
4981bo$4982bo$4980b3o3$6698bobo$6698b2o$6699bo23$4951bo$4952bo$4950b3o
3$6668bobo$6668b2o$6669bo23$4921bo$4922bo$4920b3o3$6638bobo$6638b2o$6639bo23$4891bo$4892bo$4890b3o3$6608bobo$6608b2o$6609bo23$4861bo$4862b o$4860b3o3$6578bobo$6578b2o$6579bo23$4831bo$4832bo$4830b3o3$6548bobo$
6548b2o$6549bo23$4801bo$4802bo$4800b3o3$6518bobo$6518b2o$6519bo23$
4771bo$4772bo$4770b3o3$6488bobo$6488b2o$6489bo23$4741bo$4742bo$4740b3o
3$6458bobo$6458b2o$6459bo23$4711bo$4712bo$4710b3o3$6428bobo$6428b2o$6429bo23$4681bo$4682bo$4680b3o3$6398bobo$6398b2o$6399bo23$4651bo$4652b o$4650b3o3$6368bobo$6368b2o$6369bo23$4621bo$4622bo$4620b3o3$6338bobo$
6338b2o$6339bo23$4591bo$4592bo$4590b3o3$6308bobo$6308b2o$6309bo23$
4561bo$4562bo$4560b3o3$6278bobo$6278b2o$6279bo23$4531bo$4532bo$4530b3o
3$6248bobo$6248b2o$6249bo23$4501bo$4502bo$4500b3o3$6218bobo$6218b2o$6219bo23$4471bo$4472bo$4470b3o3$6188bobo$6188b2o$6189bo23$4441bo$4442b o$4440b3o3$6158bobo$6158b2o$6159bo23$4411bo$4412bo$4410b3o3$6128bobo$
6128b2o$6129bo23$4381bo$4382bo$4380b3o3$6098bobo$6098b2o$6099bo23$
4351bo$4352bo$4350b3o3$6068bobo$6068b2o$6069bo23$4321bo$4322bo$4320b3o
3$6038bobo$6038b2o$6039bo23$4291bo$4292bo$4290b3o3$6008bobo$6008b2o$6009bo23$4261bo$4262bo$4260b3o3$5978bobo$5978b2o$5979bo23$4231bo$4232b o$4230b3o3$5948bobo$5948b2o$5949bo23$4201bo$4202bo$4200b3o3$5918bobo$
5918b2o$5919bo23$4171bo$4172bo$4170b3o3$5888bobo$5888b2o$5889bo23$
4141bo$4142bo$4140b3o3$5858bobo$5858b2o$5859bo23$4111bo$4112bo$4110b3o
3$5828bobo$5828b2o$5829bo23$4081bo$4082bo$4080b3o3$5798bobo$5798b2o$5799bo23$4051bo$4052bo$4050b3o3$5768bobo$5768b2o$5769bo23$4021bo$4022b o$4020b3o3$5738bobo$5738b2o$5739bo23$3991bo$3992bo$3990b3o3$5708bobo$
5708b2o$5709bo23$3961bo$3962bo$3960b3o3$5678bobo$5678b2o$5679bo23$
3931bo$3932bo$3930b3o3$5648bobo$5648b2o$5649bo23$3901bo$3902bo$3900b3o
3$5618bobo$5618b2o$5619bo23$3871bo$3872bo$3870b3o3$5588bobo$5588b2o$5589bo23$3841bo$3842bo$3840b3o3$5558bobo$5558b2o$5559bo23$3811bo$3812b o$3810b3o3$5528bobo$5528b2o$5529bo23$3781bo$3782bo$3780b3o3$5498bobo$
5498b2o$5499bo23$3751bo$3752bo$3750b3o3$5468bobo$5468b2o$5469bo23$
3721bo$3722bo$3720b3o3$5438bobo$5438b2o$5439bo23$3691bo$3692bo$3690b3o
3$5408bobo$5408b2o$5409bo23$3661bo$3662bo$3660b3o3$5378bobo$5378b2o$5379bo23$3631bo$3632bo$3630b3o3$5348bobo$5348b2o$5349bo23$3601bo$3602b o$3600b3o3$5318bobo$5318b2o$5319bo23$3571bo$3572bo$3570b3o3$5288bobo$
5288b2o$5289bo23$3541bo$3542bo$3540b3o3$5258bobo$5258b2o$5259bo23$
3511bo$3512bo$3510b3o3$5228bobo$5228b2o$5229bo23$3481bo$3482bo$3480b3o
3$5198bobo$5198b2o$5199bo23$3451bo$3452bo$3450b3o3$5168bobo$5168b2o$5169bo23$3421bo$3422bo$3420b3o3$5138bobo$5138b2o$5139bo23$3391bo$3392b o$3390b3o3$5108bobo$5108b2o$5109bo23$3361bo$3362bo$3360b3o3$5078bobo$
5078b2o$5079bo23$3331bo$3332bo$3330b3o3$5048bobo$5048b2o$5049bo23$
3301bo$3302bo$3300b3o3$5018bobo$5018b2o$5019bo23$3271bo$3272bo$3270b3o
3$4988bobo$4988b2o$4989bo23$3241bo$3242bo$3240b3o3$4958bobo$4958b2o$4959bo23$3211bo$3212bo$3210b3o3$4928bobo$4928b2o$4929bo23$3181bo$3182b o$3180b3o3$4898bobo$4898b2o$4899bo23$3151bo$3152bo$3150b3o3$4868bobo$
4868b2o$4869bo23$3121bo$3122bo$3120b3o3$4838bobo$4838b2o$4839bo23$
3091bo$3092bo$3090b3o3$4808bobo$4808b2o$4809bo23$3061bo$3062bo$3060b3o
3$4778bobo$4778b2o$4779bo23$3031bo$3032bo$3030b3o3$4748bobo$4748b2o$4749bo23$3001bo$3002bo$3000b3o3$4718bobo$4718b2o$4719bo23$2971bo$2972b o$2970b3o3$4688bobo$4688b2o$4689bo23$2941bo$2942bo$2940b3o3$4658bobo$
4658b2o$4659bo23$2911bo$2912bo$2910b3o3$4628bobo$4628b2o$4629bo23$
2881bo$2882bo$2880b3o3$4598bobo$4598b2o$4599bo23$2851bo$2852bo$2850b3o
3$4568bobo$4568b2o$4569bo23$2821bo$2822bo$2820b3o3$4538bobo$4538b2o$4539bo23$2791bo$2792bo$2790b3o3$4508bobo$4508b2o$4509bo23$2761bo$2762b o$2760b3o3$4478bobo$4478b2o$4479bo23$2731bo$2732bo$2730b3o3$4448bobo$
4448b2o$4449bo23$2701bo$2702bo$2700b3o3$4418bobo$4418b2o$4419bo23$
2671bo$2672bo$2670b3o3$4388bobo$4388b2o$4389bo23$2641bo$2642bo$2640b3o
3$4358bobo$4358b2o$4359bo23$2611bo$2612bo$2610b3o3$4328bobo$4328b2o$4329bo23$2581bo$2582bo$2580b3o3$4298bobo$4298b2o$4299bo23$2551bo$2552b o$2550b3o3$4268bobo$4268b2o$4269bo23$2521bo$2522bo$2520b3o3$4238bobo$
4238b2o$4239bo23$2491bo$2492bo$2490b3o3$4208bobo$4208b2o$4209bo23$
2461bo$2462bo$2460b3o3$4178bobo$4178b2o$4179bo23$2431bo$2432bo$2430b3o
3$4148bobo$4148b2o$4149bo23$2401bo$2402bo$2400b3o3$4118bobo$4118b2o$4119bo23$2371bo$2372bo$2370b3o3$4088bobo$4088b2o$4089bo23$2341bo$2342b o$2340b3o3$4058bobo$4058b2o$4059bo23$2311bo$2312bo$2310b3o3$4028bobo$
4028b2o$4029bo23$2281bo$2282bo$2280b3o3$3998bobo$3998b2o$3999bo23$
2251bo$2252bo$2250b3o3$3968bobo$3968b2o$3969bo23$2221bo$2222bo$2220b3o
3$3938bobo$3938b2o$3939bo23$2191bo$2192bo$2190b3o3$3908bobo$3908b2o$3909bo23$2161bo$2162bo$2160b3o3$3878bobo$3878b2o$3879bo23$2131bo$2132b o$2130b3o3$3848bobo$3848b2o$3849bo23$2101bo$2102bo$2100b3o3$3818bobo$
3818b2o$3819bo23$2071bo$2072bo$2070b3o3$3788bobo$3788b2o$3789bo23$
2041bo$2042bo$2040b3o3$3758bobo$3758b2o$3759bo23$2011bo$2012bo$2010b3o
3$3728bobo$3728b2o$3729bo23$1981bo$1982bo$1980b3o3$3698bobo$3698b2o$3699bo23$1951bo$1952bo$1950b3o3$3668bobo$3668b2o$3669bo23$1921bo$1922b o$1920b3o3$3638bobo$3638b2o$3639bo23$1891bo$1892bo$1890b3o3$3608bobo$
3608b2o$3609bo23$1861bo$1862bo$1860b3o3$3578bobo$3578b2o$3579bo23$
1831bo$1832bo$1830b3o3$3548bobo$3548b2o$3549bo23$1801bo$1802bo$1800b3o
3$3518bobo$3518b2o$3519bo23$1771bo$1772bo$1770b3o3$3488bobo$3488b2o$3489bo23$1741bo$1742bo$1740b3o3$3458bobo$3458b2o$3459bo23$1711bo$1712b o$1710b3o3$3428bobo$3428b2o$3429bo23$1681bo$1682bo$1680b3o3$3398bobo$
3398b2o$3399bo23$1651bo$1652bo$1650b3o3$3368bobo$3368b2o$3369bo23$
1621bo$1622bo$1620b3o3$3338bobo$3338b2o$3339bo23$1591bo$1592bo$1590b3o
3$3308bobo$3308b2o$3309bo23$1561bo$1562bo$1560b3o3$3278bobo$3278b2o$3279bo23$1531bo$1532bo$1530b3o3$3248bobo$3248b2o$3249bo23$1501bo$1502b o$1500b3o3$3218bobo$3218b2o$3219bo23$1471bo$1472bo$1470b3o3$3188bobo$
3188b2o$3189bo23$1441bo$1442bo$1440b3o3$3158bobo$3158b2o$3159bo23$
1411bo$1412bo$1410b3o3$3128bobo$3128b2o$3129bo23$1381bo$1382bo$1380b3o
3$3098bobo$3098b2o$3099bo23$1351bo$1352bo$1350b3o3$3068bobo$3068b2o$3069bo23$1321bo$1322bo$1320b3o3$3038bobo$3038b2o$3039bo23$1291bo$1292b o$1290b3o3$3008bobo$3008b2o$3009bo23$1261bo$1262bo$1260b3o3$2978bobo$
2978b2o$2979bo23$1231bo$1232bo$1230b3o3$2948bobo$2948b2o$2949bo23$
1201bo$1202bo$1200b3o3$2918bobo$2918b2o$2919bo23$1171bo$1172bo$1170b3o
3$2888bobo$2888b2o$2889bo23$1141bo$1142bo$1140b3o3$2858bobo$2858b2o$2859bo23$1111bo$1112bo$1110b3o3$2828bobo$2828b2o$2829bo23$1081bo$1082b o$1080b3o3$2798bobo$2798b2o$2799bo23$1051bo$1052bo$1050b3o3$2768bobo$
2768b2o$2769bo23$1021bo$1022bo$1020b3o3$2738bobo$2738b2o$2739bo23$991b
o$992bo$990b3o3$2708bobo$2708b2o$2709bo23$961bo$962bo$960b3o3$2678bobo$2678b2o$2679bo23$931bo$932bo$930b3o3$2648bobo$2648b2o$2649bo23$901bo$902bo$900b3o3$2618bobo$2618b2o$2619bo23$871bo$872bo$870b3o3$2588bobo$
2588b2o$2589bo23$841bo$842bo$840b3o3$2558bobo$2558b2o$2559bo23$811bo$812bo$810b3o3$2528bobo$2528b2o$2529bo23$781bo$782bo$780b3o3$2498bobo$
2498b2o$2499bo23$751bo$752bo$750b3o3$2468bobo$2468b2o$2469bo23$721bo$722bo$720b3o3$2438bobo$2438b2o$2439bo23$691bo$692bo$690b3o3$2408bobo$
2408b2o$2409bo23$661bo$662bo$660b3o3$2378bobo$2378b2o$2379bo23$631bo$632bo$630b3o3$2348bobo$2348b2o$2349bo23$601bo$602bo$600b3o3$2318bobo$
2318b2o$2319bo23$571bo$572bo$570b3o3$2288bobo$2288b2o$2289bo23$541bo$542bo$540b3o3$2258bobo$2258b2o$2259bo23$511bo$512bo$510b3o3$2228bobo$
2228b2o$2229bo23$481bo$482bo$480b3o3$2198bobo$2198b2o$2199bo23$451bo$452bo$450b3o3$2168bobo$2168b2o$2169bo23$421bo$422bo$420b3o3$2138bobo$
2138b2o$2139bo23$391bo$392bo$390b3o3$2108bobo$2108b2o$2109bo23$361bo$362bo$360b3o3$2078bobo$2078b2o$2079bo23$331bo$332bo$330b3o3$2048bobo$
2048b2o$2049bo23$301bo$302bo$300b3o3$2018bobo$2018b2o$2019bo23$271bo$272bo$270b3o3$1988bobo$1988b2o$1989bo23$241bo$242bo$240b3o3$1958bobo$
1958b2o$1959bo23$211bo$212bo$210b3o3$1928bobo$1928b2o$1929bo23$181bo$182bo$180b3o3$1898bobo$1898b2o$1899bo23$151bo$152bo$150b3o3$1868bobo$
1868b2o$1869bo23$121bo$122bo$120b3o3$1838bobo$1838b2o$1839bo23$91bo$92bo$90b3o3$1808bobo$1808b2o$1809bo23$61bo$62bo$60b3o3$1778bobo$1778b
2o$1779bo23$31bo$32bo$30b3o3$1748bobo$1748b2o$1749bo23$bo$2bo$3o3$1718bobo$1718b2o$1719bo!  Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace! BlinkerSpawn Posts: 1977 Joined: November 8th, 2014, 8:48 pm Location: Getting a snacker from R-Bee's ### Re: Discussion thread for infinite growth patterns muzik wrote:Should we come up with a name for this family/class of patterns? My suggestion is Extendo. Looks reminiscent of an elbow ladder to me. LifeWiki: Like Wikipedia but with more spaceships. [citation needed] gameoflifemaniac Posts: 1216 Joined: January 22nd, 2017, 11:17 am Location: There too ### Re: Discussion thread for infinite growth patterns You could make a cubic-growth pattern in a other cellular automaton (in 2D!) with a puffer creating dots which grow like a spacefiller some number of generations after emitting. I was so socially awkward in the past and it will haunt me for the rest of my life. Code: Select all b4o25bo$o29bo$b3o3b3o2bob2o2bob2o2bo3bobo$4bobo3bob2o2bob2o2bobo3bobo$4bobo3bobo5bo5bo3bobo$o3bobo3bobo5bo6b4o$b3o3b3o2bo5bo9bobo$24b4o!

Gamedziner
Posts: 795
Joined: May 30th, 2016, 8:47 pm
Location: Milky Way Galaxy: Planet Earth

### Re: Discussion thread for infinite growth patterns

I wonder: Could it be used as a sort of "detection system" for eaters?

Code: Select all

x = 81, y = 96, rule = LifeHistory
58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27. A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A$4.2A18$4.2A$4.2A2.2A$8.2A!  gameoflifemaniac Posts: 1216 Joined: January 22nd, 2017, 11:17 am Location: There too ### Re: Discussion thread for infinite growth patterns What do you mean? I was so socially awkward in the past and it will haunt me for the rest of my life. Code: Select all b4o25bo$o29bo$b3o3b3o2bob2o2bob2o2bo3bobo$4bobo3bob2o2bob2o2bobo3bobo$4bobo3bobo5bo5bo3bobo$o3bobo3bobo5bo6b4o$b3o3b3o2bo5bo9bobo$24b4o!

gmc_nxtman
Posts: 1150
Joined: May 26th, 2015, 7:20 pm

### Re: Discussion thread for infinite growth patterns

gameoflifemaniac wrote:You could make a cubic-growth pattern in a other cellular automaton (in 2D!) with a puffer creating dots which grow like a spacefiller some number of generations after emitting.
The fact that it's 2D can be proven to make cubic growth impossible. In this example, the spacefillers would merely collide at some point in time, taking away the quadratic aspect. The only way for cubic growth is to somehow have infinite clearance for each spacefiller, which isn't possible if they all grow in the same two dimensions.

muzik
Posts: 3925
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Discussion thread for infinite growth patterns

But could you have rakes of rakes of rakes of rakes all the way down as long as you don't use perfectly linear growth patterns?
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Kazyan
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### Re: Discussion thread for infinite growth patterns

muzik wrote:But could you have rakes of rakes of rakes of rakes all the way down as long as you don't use perfectly linear growth patterns?
If you engineered the rakes to have less-than-linear growth, maybe, but you could never arrange them in a way that surpasses quadratic growth.

Here's a more intuitive way of thinking about it: the fastest that a pattern can expand in space is c/2, in both directions. The bounding box of the pattern, then, can increase quadratically at best. If the population increases faster-than-quadratically, then at some point, the number of ON cells will have to surpass the number of cells in the bounding box! This is clearly no good.
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Kiran
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### Re: Discussion thread for infinite growth patterns

Gamedziner wrote:2. Why is cubic growth impossible in 2D space?
Look at this rule:

Code: Select all

x = 49, y = 26, rule = B12345678/S012345678
20b3o3b3o$19bo2bo3bo2bo$4o18bo3bo18b4o$o3bo17bo3bo17bo3bo$o8bo12bo3bo
12bo8bo$bo2bo2b2o2bo25bo2b2o2bo2bo$6bo5bo7b3o3b3o7bo5bo$6bo5bo8bo5bo8b o5bo$6bo5bo8b7o8bo5bo$bo2bo2b2o2bo2b2o4bo7bo4b2o2bo2b2o2bo2bo$o8bo3b2o
4b11o4b2o3bo8bo$o3bo9b2o17b2o9bo3bo$4o11b19o11b4o$16bobo11bobo$19b11o$19bo9bo$20b9o$24bo$20b3o3b3o$22bo3bo2$21b3ob3o$21b3ob3o$20bob2ob2obo$20b3o3b3o$21bo5bo!

Any pattern grows at least as fast in this rule as in any other rule (barring B0).
It should be easy to see that the pattern I pasted grows quadratically, with population at time t being 4t^2+O(t).
EDIT:
The slowest growing known infinite growth pattern is currently Sawmill, and the slowest growing superlinear growth is also Sawmill.
The question is, can we build something even slower?
My thought is a large group of rakes going south and leaving a trail of recursive filters (along with the east-going spaceships, which must be synthesized), and each filter creating a switch engine going west when the first glider reaches it (similar to t log(log(t)) growth).
This would be slower than t log****(t) for any number of *'s.
What function would this be?
Are there any easier ways to construct something slower than Sawmill?
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calcyman
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### Re: Discussion thread for infinite growth patterns

Great idea, Kiran!

The growth rate would be O(t alpha(t)), where alpha is the famous Inverse Ackermann Function.
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Kiran
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### Re: Discussion thread for infinite growth patterns

Is there any fundamental limit on how slow something can grow?
For example, would it be possible to create something that grows slower than the inverse Graham's Function?
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calcyman
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### Re: Discussion thread for infinite growth patterns

Yes, there is a limit to how slow a finite pattern can grow.

More formally, let p(t) be the population of the pattern at time t, and P(t) = max{p(s) : s <= t} be the maximum population encountered up to time t.

Then either P(t) is eventually constant, or is omega(BB^-1(t)) -- that is to say, it asymptotically dominates the busy beaver function.

Proof: Suppose otherwise. Then we can program a Turing machine to take an integer n as input, run the super-slow-growing pattern until its population exceeds n, and output the time t at which it does so. This would be able to compute an uncomputable function; contradiction.
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Apple Bottom
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### Re: Discussion thread for infinite growth patterns

calcyman wrote:Yes, there is a limit to how slow a finite pattern can grow.

More formally, let p(t) be the population of the pattern at time t, and P(t) = max{p(s) : s <= t} be the maximum population encountered up to time t.

Then either P(t) is eventually constant, or is omega(BB^-1(t)) -- that is to say, it asymptotically dominates the busy beaver function.

Proof: Suppose otherwise. Then we can program a Turing machine to take an integer n as input, run the super-slow-growing pattern until its population exceeds n, and output the time t at which it does so. This would be able to compute an uncomputable function; contradiction.
Would a pattern be possible where the minimum population of any future generation grows slower than BB^-1?

That is to say -- fix a pattern, and let p(t) again be the population at time t. For any generation, t, define mp(t) := min { p(s) | s >= t }. Can mp(t) exhibit growth below BB^-1 without being (eventually) constant?

The idea here is that the above proof won't work in this case, because the Turing machine considered cannot ever know whether the population will eventually fall below a certain bound again.

Then again I'm no mathematician. Is there an (immediate, obvious) reason why mp must be eventually constant or omega(BB^1)? Or could a pattern with uncomputably slow growth exist using this different definition of "growth"?
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### Re: Discussion thread for infinite growth patterns

Kiran wrote:Is there any fundamental limit on how slow something can grow?
For example, would it be possible to create something that grows slower than the inverse Graham's Function?
Compared to population, it is much easier to find a fundamental limit on how fast bounding area may grow. It is easily shown that no pattern can remain inside a bounding area (of any shape) containing A cells for more than 2^A generations without becoming periodic. Therefore, an upper bound for A at any time t is 2^t (assuming a finite starting pattern and that A is larger than it was at t=0, which is true in the limit for any pattern that does not become periodic), and therefore A(t) >= log2(t) assuming the same conditions. This is sufficient to prove that bounding area grows no slower than O(log t).

This works for common forms of bounding area such as bounding box and historical envelope, but fails if bounding area can change in a fashion that breaks certain Life symmetries (I'm not sure exactly which ones). An example of this is defining bounding area to be the area of all cells within a range-2 Moore neighborhood of a live cell. In this case, two gliders heading in different directions is a simple counterexample.

If I'm right, this shows that nothing can have a bounding box that grows slower than the inverse Graham's Function (or even O(log t)).
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x₁=ηx
V*_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

calcyman
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### Re: Discussion thread for infinite growth patterns

Apple Bottom wrote:Or could a pattern with uncomputably slow growth exist using this different definition of "growth"?

Consider a pattern which contains a stack of bounded-population register machines, {M1, M2, M3, M4, ..., Mk}. Now, each Mi simulates all possible i-state Turing machines simultaneously (a concept known as 'dovetailing'). Whenever one of the i-state Turing machines halts, Mi destroys all of the subsequent register machines in the stack and creates a new M(i+1).

The mp(t) of this pattern is bounded above by a constant multiple of BB^-1(t). Specifically, at some time bounded below by BB(n), the machine Mn will perform its final stack destruction and reduce the population of the pattern to no more than Kn, where K is the maximum population of any register machine. The first n machines will continue to exist forever, so the population will never dip below kn, where k is the minimum population of any register machine.
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Apple Bottom
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### Re: Discussion thread for infinite growth patterns

calcyman wrote:Yes, your intuition is correct.

Consider a pattern which contains a stack of bounded-population register machines, {M1, M2, M3, M4, ..., Mk}. Now, each Mi simulates all possible i-state Turing machines simultaneously (a concept known as 'dovetailing'). Whenever one of the i-state Turing machines halts, Mi destroys all of the subsequent register machines in the stack and creates a new M(i+1).

The mp(t) of this pattern is bounded above by a constant multiple of BB^-1(t). Specifically, at some time bounded below by BB(n), the machine Mn will perform its final stack destruction and reduce the population of the pattern to no more than Kn, where K is the maximum population of any register machine. The first n machines will continue to exist forever, so the population will never dip below kn, where k is the minimum population of any register machine.
This is one of those occasions where I wish the forums here had a "kudos" function. Thanks for the explanation, this is fascinating!
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calcyman
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### Re: Discussion thread for infinite growth patterns

Apple Bottom wrote:This is one of those occasions where I wish the forums here had a "kudos" function. Thanks for the explanation, this is fascinating!
I'm glad you agree! Of course, this is the least I could do in return for the generous CPU cycles you've donated to Catagolue (it's rather scarily satisfying that the total electricity cost expended exceeds my current capital!).
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