Thread for basic questions
- gameoflifemaniac
- Posts: 1242
- Joined: January 22nd, 2017, 11:17 am
- Location: There too
Re: Thread for basic questions
There are 1+2^2^9+3^3^9+4^4^9+5^5^9+...+254^254^9+255^255^9 range 1 rules.
I was so socially awkward in the past and it will haunt me for the rest of my life.
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b4o25bo$o29bo$b3o3b3o2bob2o2bob2o2bo3bobo$4bobo3bob2o2bob2o2bobo3bobo$
4bobo3bobo5bo5bo3bobo$o3bobo3bobo5bo6b4o$b3o3b3o2bo5bo9bobo$24b4o!
Re: Thread for basic questions
AUGGGGGH!gameoflifemaniac wrote:There are 1+2^2^9+3^3^9+4^4^9+5^5^9+...+254^254^9+255^255^9 range 1 rules.
Re: Thread for basic questions
It definitely doesn't have to be _that_ complicated. The maximum is 256 states, not 255, so it seems to me that the last term should be 256^256^9 if anything -- but that last term will include all the previous terms (i.e., a 256-state rule in which one of the states never happens to be chosen, is really a 255-state rule).KittyTac wrote:AUGGGGGH!gameoflifemaniac wrote:There are 1+2^2^9+3^3^9+4^4^9+5^5^9+...+254^254^9+255^255^9 range 1 rules.
That will happen 255 times, for the 255 different possible non-zero states that can be left out. (The zero state is a little strange and special, since we're guaranteed to have some of those states around the edges.) So in a practical sense, even with just one term instead of 255 terms, the formula is counting a lot of functionally equivalent rules as different. The question of how many rule tables there are seems a little bit different from how many rules there are.
(Now I have to go think again about whether the formula is really correct or not...)
EDIT: Yeah, it seems like (256^9)^256 is the number of different rule tables. Many of them produce rules that are functionally isomorphic to each other -- i.e., you could substitue all state S1 cells for state S2 cells, and then the pattern would behave exactly the same from then on with S2 always appearing where S1 did -- but they're still distinct rules.
So that's a mere 5550-digit number
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38448559958689582446977056492823062848927500337801248175571406455205640359363297329514829541070592676457967314688087605622316283099436819343890491013635088466499729825070976031210275483598854650564606111014665118125927723996499339432016213581444364821345016492704280888753836915090019089891021956471980034903237378400465979859826540187609718141492082898673816622337123245934288996076604339638524418394253023635460869167245612500247759155716272608571716958636926667805605753641932050068903767467165937176253315864988785133650181824849372103644977934119026825380749068108066872357582754400729634791720080164446537402135117661781469236359174184255596033792669086827411915986015838150656848431408992911771591624913941525780483938691571136538834822539584780911120126939399103070964745357217580167614907010324711156089416280463510336088047045004415745873169503686247087308031500178696881177302535389100298789242479384645073132351705737430484773132931574739815631252123422088074872372420202820360457330362118560631777500785925332990575820431004243688532105196903898543880465330550104758220492216377002140369482478254204390083473034586963001593132129378013492383581515627940015744644254953670143816119601465095726473112229478950729757709871425341485860918764648625881275487722015393560501796730878520888361812411650414282946262045476883178592995488364563880126578286951607355735992947731781538294875271574864043108188539109119918277016773246558167048666085193765160124264190947420400645854469508014776755883989972065875639618553446753825836144875262993424412684554556898756972714184734041991686692081821547127972614988059962571969025831790124999327826103472589043482166860944335563305313733753718974625930549278520594961590025279061819898430504890594651542030355356712920957135982522276103401297842683130400014844612945480945116470621327528087145999056500069274154450643588945060068255600120128885964595474682275618783873088243118219745124777903386837399811094658903562890136512940695482752032031808086815733887292852972336277631358557245113042785818028051234887370149420184820248600593508295242689017771401347522072896573378892123196299780401472964400022154953633543845395087356920833120210730705011855968171103867054322048889349241026647431540276824581324251471335305137613210452034008440330746299711661622469116156548292474296008218098552544333228771438814286275417774489280051686677036552028331663254360440592548720586690433130063140540114058064527982221082862164986576526942793763175079583002874559996712571073894078195183501370725252885453637960201238946868676704110226218852035688645870611182416843308352284639191207991983695852572958929112314976838541136669254081533813799126406405859720539994908516479854848301589373052500259590217147630533104470624038420535996537794398168556941689489640590025493737279963818741514851666330909146526690531131709880043528697041489213387210197441399336846028145341896358640909788006549837881428946105757595856448280368524742297818185817412680662660258958441387230755918575863934176465654300391746741973083621319557095445725462131414155911712013461673012726532528323680913900239598800737988323416624314219337539777582831138070457165646115997641224672692221125637111123732207977809418046079624113902168870945867329326278996425619089432645727236803104861591666361945805373249913689827164734590878498462786698283811077576686035697346883127932791702533774526352910857830279322367021165325386944768843132906644432143161038078918177112498627500208496202955180688087245450366196193864679352522944682019035419149105624897885390781969271541302191353712405440163953084005922519105018976327469686328255007397145963155262198675302949968271388691940362274767798076328607378638440486543891012727297778268255277026160910530357786644939919306653741443016100824786550126143125924489015012723962504052636184076541884054667789069600066921840220577878306346214272726027010242839821689530872073373999328339098568843763904574053249005460846820910932792707741310744602737806382175467523259723497880623436622585852541326384059959995143312091736735843249441506666014129572853323906202386567067638700947859246730291156601125272415511900919608531548328979621028717360314901833032365958594603475955686744170452409666419029111578818803036900869624373440575853216805793950656085549318966062263612496388862306204701273007349199949990079715873565509967880817971018426048058146068039800158577047061243337199803725265207339575928474688454010509360930063137390729226079007289045496751180410993944295642503355698510297924224644240753414126413706400103044149165908557074617237622080932446184169932297882164792564014718276494215637734995241343815930987865825647133828470637438944808041762845059451803399725505863858011570199292519794533344377559174398017366476326492384814758816154748041122844387670552125008043076417403088411607080337480550534303802771112912581428328885557869146753007103287223391486780332361239355963432012493496051285072027635618926443633387893019054756343722688074200391334446252106751133882642438547367391301229272298694451522040433810620207374283045600853922309924495353348734859731800287200050286615033184132697017296572340419013735770106600797612496359412588114138431619220641386838078912450881641429040837254213276369578953312144755186685359585141180598398368235739814200624474677442416064830195463694588605124744950362063529234545240378021620895676803531848237377551457882046712672355146932491169091236445252690403712024392627335056563543107562770803672059136162039931331357996511511072625851039832806754552212807873198131511296
Re: Thread for basic questions
And rule tables have nothing on range-2 rules. Kind of interesting that even a very limited section of the CA space has more rules than there are stars in the universe. It's incomprehensibly vast.
- gameoflifemaniac
- Posts: 1242
- Joined: January 22nd, 2017, 11:17 am
- Location: There too
Re: Thread for basic questions
WRONG.dvgrn wrote: So that's a mere 5550-digit number
... which is just infinitesimally small compared to that 7862-digit number I quoted earlier.Code: Select all
38448559958689582446977056492823062848927500337801248175571406455205640359363297329514829541070592676457967314688087605622316283099436819343890491013635088466499729825070976031210275483598854650564606111014665118125927723996499339432016213581444364821345016492704280888753836915090019089891021956471980034903237378400465979859826540187609718141492082898673816622337123245934288996076604339638524418394253023635460869167245612500247759155716272608571716958636926667805605753641932050068903767467165937176253315864988785133650181824849372103644977934119026825380749068108066872357582754400729634791720080164446537402135117661781469236359174184255596033792669086827411915986015838150656848431408992911771591624913941525780483938691571136538834822539584780911120126939399103070964745357217580167614907010324711156089416280463510336088047045004415745873169503686247087308031500178696881177302535389100298789242479384645073132351705737430484773132931574739815631252123422088074872372420202820360457330362118560631777500785925332990575820431004243688532105196903898543880465330550104758220492216377002140369482478254204390083473034586963001593132129378013492383581515627940015744644254953670143816119601465095726473112229478950729757709871425341485860918764648625881275487722015393560501796730878520888361812411650414282946262045476883178592995488364563880126578286951607355735992947731781538294875271574864043108188539109119918277016773246558167048666085193765160124264190947420400645854469508014776755883989972065875639618553446753825836144875262993424412684554556898756972714184734041991686692081821547127972614988059962571969025831790124999327826103472589043482166860944335563305313733753718974625930549278520594961590025279061819898430504890594651542030355356712920957135982522276103401297842683130400014844612945480945116470621327528087145999056500069274154450643588945060068255600120128885964595474682275618783873088243118219745124777903386837399811094658903562890136512940695482752032031808086815733887292852972336277631358557245113042785818028051234887370149420184820248600593508295242689017771401347522072896573378892123196299780401472964400022154953633543845395087356920833120210730705011855968171103867054322048889349241026647431540276824581324251471335305137613210452034008440330746299711661622469116156548292474296008218098552544333228771438814286275417774489280051686677036552028331663254360440592548720586690433130063140540114058064527982221082862164986576526942793763175079583002874559996712571073894078195183501370725252885453637960201238946868676704110226218852035688645870611182416843308352284639191207991983695852572958929112314976838541136669254081533813799126406405859720539994908516479854848301589373052500259590217147630533104470624038420535996537794398168556941689489640590025493737279963818741514851666330909146526690531131709880043528697041489213387210197441399336846028145341896358640909788006549837881428946105757595856448280368524742297818185817412680662660258958441387230755918575863934176465654300391746741973083621319557095445725462131414155911712013461673012726532528323680913900239598800737988323416624314219337539777582831138070457165646115997641224672692221125637111123732207977809418046079624113902168870945867329326278996425619089432645727236803104861591666361945805373249913689827164734590878498462786698283811077576686035697346883127932791702533774526352910857830279322367021165325386944768843132906644432143161038078918177112498627500208496202955180688087245450366196193864679352522944682019035419149105624897885390781969271541302191353712405440163953084005922519105018976327469686328255007397145963155262198675302949968271388691940362274767798076328607378638440486543891012727297778268255277026160910530357786644939919306653741443016100824786550126143125924489015012723962504052636184076541884054667789069600066921840220577878306346214272726027010242839821689530872073373999328339098568843763904574053249005460846820910932792707741310744602737806382175467523259723497880623436622585852541326384059959995143312091736735843249441506666014129572853323906202386567067638700947859246730291156601125272415511900919608531548328979621028717360314901833032365958594603475955686744170452409666419029111578818803036900869624373440575853216805793950656085549318966062263612496388862306204701273007349199949990079715873565509967880817971018426048058146068039800158577047061243337199803725265207339575928474688454010509360930063137390729226079007289045496751180410993944295642503355698510297924224644240753414126413706400103044149165908557074617237622080932446184169932297882164792564014718276494215637734995241343815930987865825647133828470637438944808041762845059451803399725505863858011570199292519794533344377559174398017366476326492384814758816154748041122844387670552125008043076417403088411607080337480550534303802771112912581428328885557869146753007103287223391486780332361239355963432012493496051285072027635618926443633387893019054756343722688074200391334446252106751133882642438547367391301229272298694451522040433810620207374283045600853922309924495353348734859731800287200050286615033184132697017296572340419013735770106600797612496359412588114138431619220641386838078912450881641429040837254213276369578953312144755186685359585141180598398368235739814200624474677442416064830195463694588605124744950362063529234545240378021620895676803531848237377551457882046712672355146932491169091236445252690403712024392627335056563543107562770803672059136162039931331357996511511072625851039832806754552212807873198131511296
256^(256^9), not (256^256)^9.
I was so socially awkward in the past and it will haunt me for the rest of my life.
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b4o25bo$o29bo$b3o3b3o2bob2o2bob2o2bo3bobo$4bobo3bob2o2bob2o2bobo3bobo$
4bobo3bobo5bo5bo3bobo$o3bobo3bobo5bo6b4o$b3o3b3o2bo5bo9bobo$24b4o!
Re: Thread for basic questions
Heh. Have you calculated the difference between those two rather large numbers?gameoflifemaniac wrote:WRONG.
256^(256^9), not (256^256)^9.
- Redstoneboi
- Posts: 429
- Joined: May 14th, 2018, 3:57 am
Re: Thread for basic questions
to account for state function switching, divide by factorial
let s = max states
let n = number of possible neighbors
(s^[s^n])/(s!)
which by substitution becomes
(256^[256^9])/(256!)
and I can’t calculate this
let s = max states
let n = number of possible neighbors
(s^[s^n])/(s!)
which by substitution becomes
(256^[256^9])/(256!)
and I can’t calculate this
c(>^w^<c)~*
This is 「Fluffy」
「Fluffy」is my sutando.
「Fluffy」has the ability to engineer r e p l i c a t o r s.
「Fluffy」likes to watch spaceship guns in Golly.
「Fluffy」knows Natsuki best girl.
This is 「Fluffy」
「Fluffy」is my sutando.
「Fluffy」has the ability to engineer r e p l i c a t o r s.
「Fluffy」likes to watch spaceship guns in Golly.
「Fluffy」knows Natsuki best girl.
Re: Thread for basic questions
Python can do it, though not terribly quickly. It's a 5043-digit number:Redstoneboi wrote:to account for state function switching, divide by factorial
let s = max states
let n = number of possible neighbors
(s^[s^n])/(s!)
which by substitution becomes
(256^[256^9])/(256!)
and I can’t calculate this
Code: Select all
44821360741006920927118125563344294069712618441345403098562857255809227239160043579760371886464596995489062274108744120199671762251468517721753419132979862379056953100468497385599593285559686138634035432205756236470775283882790175378123396983120793247149663296331150517544915673719501890339158202008041570762128564641914095283548440101107158073165558844344006117324199034608910304702943457842657623268037234276167642902877246877148973187197700009919097525078135810516499124934591510551141722914994756267817818446404637183464253121251345517642811185472338560896975045079227351075854551876046679813081975920731276030681726233101583481614300065209856122290708493750240170850166491339033131194951975843214384462875238344589029086429610311507821912016121274818017035383117393896405801826096649450701667324815003114219392417727247709992428533794821334638598303372122199984460499584494476048815413242387990236881323981327610991088342207527990697121304636721300423926050673623583992051738547124071865833572495808748464842960039679952507438565983596903271684726921402286358983372514110724436618616038627078171751571374981193481389239738018911847753040012042787717918908254528251383698867573135156939084331086758097907106095031547377278425617974502609591951482145610903954114723199175023668647127177171005078000230111841493293005098907252636413635633920751956022278837329406458663016725225858003022739549055062274361677955303156553396862455151776202367024537323175120553029177103272539450743286199138801302521724010186618263274929550795001141051128801614407279190360193127735430043687153224887844534769888437163665155800807463266843575103824059767284025940207275881960101519957916237708399875030372830269982631590567036289112792996676043853858411636406315981937522523463993396230828303434497509207051224667499492669294263050230559229676800568132382747151593579043989050178300829184643383595462517549306306474120786647700402892258487237997035359714591336600967370844334051004556584697268688966747575103026127402993600525260976910157191425375547783663028991220655494093577189810628207736824408765366252321547962537934163945058829871740990197017995479964655862858093533840154857599880559772822085707880357574223432953948114891117934451277005092303052452112158056476214906893587342030175547626651425026074833715152032952805169562075282179294553771261840060129307917562327518559447865560261869530619146796289605068773232280672043579212840213614934562130900927235803520092924949100933582669717418978032456490181287614496615337772202853561213724015646715694758940324144982567076229510224248921269187933597475519063663022757442713208129469622210659669536778045973317494731118990707967432774062244466075136722917025925009563913590052330611701222318368085100464973062147652246689225209600815677748233777662320645699744705636073421345796240053484790947490102494432936503470044285598487443191685499243787281532963627704292193424182943705360756645473340519414095571075906987921999994589589249185617638227290154466026945274766811106853096897936712824729657611432539798592716143987257658160530629482056080902245386837930231790704750654110781542255930924919874882282807461734345268621370264400363276081835323582898730664274722057146166965002489980037918333408523044028288630105000226961017101057911404439308945076014236700573803528075158097441596911890827780594707319154983659005344832899989561862660959130461722456610784770149431378576981345529022912974211559543506305874845139436429418602990811191514032095585427455050829742344137591691348336147594598106232787833354040920189543974857608087516319325230734952899760499184322016189412875490908364556014134221232189516514253131071953417743398305589250283949261639322480246103908899019192671003341114354426222279503260239379692002985820083691324001543770026121010659342635445175882283119028061806900247656062778452104695825791668229271089888239843678595833605360724031910208269201857832241519399456091000654999671882890157573953350680493959697423700920901526125561420840938619531572833243566141585750413363948101918633369088210553267837344133868481064157510091231648167146402765497018622521934157217722918252710260861762416803881844816281447193383020785507195544179097074683012618228156526573236865056979474673439761228079452790416346816424130437119160272875853115945840525610376098515206314549528779229566898655488992808412813208562567700649548920845247917159464920671204614608676010207017439945964053006478732190315269878558458539540181809600425140618593764715981322774361251735765127792981232516384702849531086986944407544314789200697349264961671890330493802893110038511078271458814149142021655319206993546999133764203804932225589425469230702521448316281442925721214305246932327940087990549046630745347388589661441788910366674227288837479995222348373760460096558952661701401872750873953119275134250746383544419899256714480402248874512152723381345337540041756915746027205111642496652868369791480941583725296478152527798879329044426981726565780911968075053031970793542854637797317255345847697294565655250581166197143757
Code: Select all
k = (256**256)**9
for i in range(1, 257):
k = k / i
print str(k) + "\n"
Re: Thread for basic questions
Is that bigger than the number of atoms in a human?dvgrn wrote:Python can do it, though not terribly quickly. It's a 5043-digit number:Redstoneboi wrote:to account for state function switching, divide by factorial
let s = max states
let n = number of possible neighbors
(s^[s^n])/(s!)
which by substitution becomes
(256^[256^9])/(256!)
and I can’t calculate this
Code: Select all
44821360741006920927118125563344294069712618441345403098562857255809227239160043579760371886464596995489062274108744120199671762251468517721753419132979862379056953100468497385599593285559686138634035432205756236470775283882790175378123396983120793247149663296331150517544915673719501890339158202008041570762128564641914095283548440101107158073165558844344006117324199034608910304702943457842657623268037234276167642902877246877148973187197700009919097525078135810516499124934591510551141722914994756267817818446404637183464253121251345517642811185472338560896975045079227351075854551876046679813081975920731276030681726233101583481614300065209856122290708493750240170850166491339033131194951975843214384462875238344589029086429610311507821912016121274818017035383117393896405801826096649450701667324815003114219392417727247709992428533794821334638598303372122199984460499584494476048815413242387990236881323981327610991088342207527990697121304636721300423926050673623583992051738547124071865833572495808748464842960039679952507438565983596903271684726921402286358983372514110724436618616038627078171751571374981193481389239738018911847753040012042787717918908254528251383698867573135156939084331086758097907106095031547377278425617974502609591951482145610903954114723199175023668647127177171005078000230111841493293005098907252636413635633920751956022278837329406458663016725225858003022739549055062274361677955303156553396862455151776202367024537323175120553029177103272539450743286199138801302521724010186618263274929550795001141051128801614407279190360193127735430043687153224887844534769888437163665155800807463266843575103824059767284025940207275881960101519957916237708399875030372830269982631590567036289112792996676043853858411636406315981937522523463993396230828303434497509207051224667499492669294263050230559229676800568132382747151593579043989050178300829184643383595462517549306306474120786647700402892258487237997035359714591336600967370844334051004556584697268688966747575103026127402993600525260976910157191425375547783663028991220655494093577189810628207736824408765366252321547962537934163945058829871740990197017995479964655862858093533840154857599880559772822085707880357574223432953948114891117934451277005092303052452112158056476214906893587342030175547626651425026074833715152032952805169562075282179294553771261840060129307917562327518559447865560261869530619146796289605068773232280672043579212840213614934562130900927235803520092924949100933582669717418978032456490181287614496615337772202853561213724015646715694758940324144982567076229510224248921269187933597475519063663022757442713208129469622210659669536778045973317494731118990707967432774062244466075136722917025925009563913590052330611701222318368085100464973062147652246689225209600815677748233777662320645699744705636073421345796240053484790947490102494432936503470044285598487443191685499243787281532963627704292193424182943705360756645473340519414095571075906987921999994589589249185617638227290154466026945274766811106853096897936712824729657611432539798592716143987257658160530629482056080902245386837930231790704750654110781542255930924919874882282807461734345268621370264400363276081835323582898730664274722057146166965002489980037918333408523044028288630105000226961017101057911404439308945076014236700573803528075158097441596911890827780594707319154983659005344832899989561862660959130461722456610784770149431378576981345529022912974211559543506305874845139436429418602990811191514032095585427455050829742344137591691348336147594598106232787833354040920189543974857608087516319325230734952899760499184322016189412875490908364556014134221232189516514253131071953417743398305589250283949261639322480246103908899019192671003341114354426222279503260239379692002985820083691324001543770026121010659342635445175882283119028061806900247656062778452104695825791668229271089888239843678595833605360724031910208269201857832241519399456091000654999671882890157573953350680493959697423700920901526125561420840938619531572833243566141585750413363948101918633369088210553267837344133868481064157510091231648167146402765497018622521934157217722918252710260861762416803881844816281447193383020785507195544179097074683012618228156526573236865056979474673439761228079452790416346816424130437119160272875853115945840525610376098515206314549528779229566898655488992808412813208562567700649548920845247917159464920671204614608676010207017439945964053006478732190315269878558458539540181809600425140618593764715981322774361251735765127792981232516384702849531086986944407544314789200697349264961671890330493802893110038511078271458814149142021655319206993546999133764203804932225589425469230702521448316281442925721214305246932327940087990549046630745347388589661441788910366674227288837479995222348373760460096558952661701401872750873953119275134250746383544419899256714480402248874512152723381345337540041756915746027205111642496652868369791480941583725296478152527798879329044426981726565780911968075053031970793542854637797317255345847697294565655250581166197143757
But that certainly can't be an accurate formula. Doesn't even come out to an integer, really. The above code ends up doing integer division, because I definitely didn't care about anything after the decimal point.Code: Select all
k = (256**256)**9 for i in range(1, 257): k = k / i print str(k) + "\n"
Re: Thread for basic questions
Not quite sure if that's a serious question. "Yes" hardly seems to be an adequate answer. If you divide that number by the number of atoms in a human, you'll still have well over a 5000-digit number left.KittyTac wrote:Is that bigger than the number of atoms in a human?
If you packed the observable universe chock full of protons (which is a very bad idea, by the way, don't really do that) and if each proton was really its own universe, and you packed all those universes completely full of neutrons (only slightly safer), and each of those neutrons was its own universe, and you packed each of _those_ universes full of electrons (really bad idea again), and then counted all the electrons in all the sub-sub-universes inside the sub-universes inside our known universe...
-- well, you'd still have a long way to go. You wouldn't have gotten to a five-hundred-digit number yet, let alone a five-thousand-digit number.
-
- Posts: 795
- Joined: May 30th, 2016, 8:47 pm
- Location: Milky Way Galaxy: Planet Earth
Re: Thread for basic questions
What about photons? If you had that many photons, all of them having a wavelength of the observable universe, would they pack so tightly a universe-sized kugelblitz would form?dvgrn wrote:You wouldn't have gotten to a five-hundred-digit number yet, let alone a five-thousand-digit number.
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!
Re: Thread for basic questions
Plugged this into one of my bots that evaluates arbitrary JavaScript.dvgrn wrote:Python can do it, though not terribly quickly. It's a 5043-digit number:Redstoneboi wrote:to account for state function switching, divide by factorial
let s = max states
let n = number of possible neighbors
(s^[s^n])/(s!)
which by substitution becomes
(256^[256^9])/(256!)
and I can’t calculate this
Code: Select all
44821360741006920927118125563344294069712618441345403098562857255809227239160043579760371886464596995489062274108744120199671762251468517721753419132979862379056953100468497385599593285559686138634035432205756236470775283882790175378123396983120793247149663296331150517544915673719501890339158202008041570762128564641914095283548440101107158073165558844344006117324199034608910304702943457842657623268037234276167642902877246877148973187197700009919097525078135810516499124934591510551141722914994756267817818446404637183464253121251345517642811185472338560896975045079227351075854551876046679813081975920731276030681726233101583481614300065209856122290708493750240170850166491339033131194951975843214384462875238344589029086429610311507821912016121274818017035383117393896405801826096649450701667324815003114219392417727247709992428533794821334638598303372122199984460499584494476048815413242387990236881323981327610991088342207527990697121304636721300423926050673623583992051738547124071865833572495808748464842960039679952507438565983596903271684726921402286358983372514110724436618616038627078171751571374981193481389239738018911847753040012042787717918908254528251383698867573135156939084331086758097907106095031547377278425617974502609591951482145610903954114723199175023668647127177171005078000230111841493293005098907252636413635633920751956022278837329406458663016725225858003022739549055062274361677955303156553396862455151776202367024537323175120553029177103272539450743286199138801302521724010186618263274929550795001141051128801614407279190360193127735430043687153224887844534769888437163665155800807463266843575103824059767284025940207275881960101519957916237708399875030372830269982631590567036289112792996676043853858411636406315981937522523463993396230828303434497509207051224667499492669294263050230559229676800568132382747151593579043989050178300829184643383595462517549306306474120786647700402892258487237997035359714591336600967370844334051004556584697268688966747575103026127402993600525260976910157191425375547783663028991220655494093577189810628207736824408765366252321547962537934163945058829871740990197017995479964655862858093533840154857599880559772822085707880357574223432953948114891117934451277005092303052452112158056476214906893587342030175547626651425026074833715152032952805169562075282179294553771261840060129307917562327518559447865560261869530619146796289605068773232280672043579212840213614934562130900927235803520092924949100933582669717418978032456490181287614496615337772202853561213724015646715694758940324144982567076229510224248921269187933597475519063663022757442713208129469622210659669536778045973317494731118990707967432774062244466075136722917025925009563913590052330611701222318368085100464973062147652246689225209600815677748233777662320645699744705636073421345796240053484790947490102494432936503470044285598487443191685499243787281532963627704292193424182943705360756645473340519414095571075906987921999994589589249185617638227290154466026945274766811106853096897936712824729657611432539798592716143987257658160530629482056080902245386837930231790704750654110781542255930924919874882282807461734345268621370264400363276081835323582898730664274722057146166965002489980037918333408523044028288630105000226961017101057911404439308945076014236700573803528075158097441596911890827780594707319154983659005344832899989561862660959130461722456610784770149431378576981345529022912974211559543506305874845139436429418602990811191514032095585427455050829742344137591691348336147594598106232787833354040920189543974857608087516319325230734952899760499184322016189412875490908364556014134221232189516514253131071953417743398305589250283949261639322480246103908899019192671003341114354426222279503260239379692002985820083691324001543770026121010659342635445175882283119028061806900247656062778452104695825791668229271089888239843678595833605360724031910208269201857832241519399456091000654999671882890157573953350680493959697423700920901526125561420840938619531572833243566141585750413363948101918633369088210553267837344133868481064157510091231648167146402765497018622521934157217722918252710260861762416803881844816281447193383020785507195544179097074683012618228156526573236865056979474673439761228079452790416346816424130437119160272875853115945840525610376098515206314549528779229566898655488992808412813208562567700649548920845247917159464920671204614608676010207017439945964053006478732190315269878558458539540181809600425140618593764715981322774361251735765127792981232516384702849531086986944407544314789200697349264961671890330493802893110038511078271458814149142021655319206993546999133764203804932225589425469230702521448316281442925721214305246932327940087990549046630745347388589661441788910366674227288837479995222348373760460096558952661701401872750873953119275134250746383544419899256714480402248874512152723381345337540041756915746027205111642496652868369791480941583725296478152527798879329044426981726565780911968075053031970793542854637797317255345847697294565655250581166197143757
But that certainly can't be an accurate formula. Doesn't even come out to an integer, really. The above code ends up doing integer division, because I definitely didn't care about anything after the decimal point.Code: Select all
k = (256**256)**9 for i in range(1, 257): k = k / i print str(k) + "\n"
Re: Thread for basic questions
Ouch. That kind of stumps my brain.dvgrn wrote:Not quite sure if that's a serious question. "Yes" hardly seems to be an adequate answer. If you divide that number by the number of atoms in a human, you'll still have well over a 5000-digit number left.KittyTac wrote:Is that bigger than the number of atoms in a human?
If you packed the observable universe chock full of protons (which is a very bad idea, by the way, don't really do that) and if each proton was really its own universe, and you packed all those universes completely full of neutrons (only slightly safer), and each of those neutrons was its own universe, and you packed each of _those_ universes full of electrons (really bad idea again), and then counted all the electrons in all the sub-sub-universes inside the sub-universes inside our known universe...
-- well, you'd still have a long way to go. You wouldn't have gotten to a five-hundred-digit number yet, let alone a five-thousand-digit number.
Re: Thread for basic questions
Photons are bosons, not fermions like protons, neutrons and electrons, and as such they don't have the same limitation on packing. In other words, quantum mechanics imposes no limit on how many photons can be in one place.Gamedziner wrote:What about photons? If you had that many photons, all of them having a wavelength of the observable universe, would they pack so tightly a universe-sized kugelblitz would form?dvgrn wrote:You wouldn't have gotten to a five-hundred-digit number yet, let alone a five-thousand-digit number.
Even without actually working out what order of magnitude the equivalent mass of 1 Exp 5000 ultra low energy photons is, I think we can safely say it's well in excess of that required to create a kugelblitz the size of the observable universe.
The 5S project (Smallest Spaceships Supporting Specific Speeds) is now maintained by AforAmpere. The latest collection is hosted on GitHub and contains well over 1,000,000 spaceships.
Semi-active here - recovering from a severe case of LWTDS.
Semi-active here - recovering from a severe case of LWTDS.
- gameoflifemaniac
- Posts: 1242
- Joined: January 22nd, 2017, 11:17 am
- Location: There too
Re: Thread for basic questions
GAHHHHHHHHHHH!dvgrn wrote: Python can do it, though not terribly quickly. It's a 5043-digit number:
Code: Select all
44821360741006920927118125563344294069712618441345403098562857255809227239160043579760371886464596995489062274108744120199671762251468517721753419132979862379056953100468497385599593285559686138634035432205756236470775283882790175378123396983120793247149663296331150517544915673719501890339158202008041570762128564641914095283548440101107158073165558844344006117324199034608910304702943457842657623268037234276167642902877246877148973187197700009919097525078135810516499124934591510551141722914994756267817818446404637183464253121251345517642811185472338560896975045079227351075854551876046679813081975920731276030681726233101583481614300065209856122290708493750240170850166491339033131194951975843214384462875238344589029086429610311507821912016121274818017035383117393896405801826096649450701667324815003114219392417727247709992428533794821334638598303372122199984460499584494476048815413242387990236881323981327610991088342207527990697121304636721300423926050673623583992051738547124071865833572495808748464842960039679952507438565983596903271684726921402286358983372514110724436618616038627078171751571374981193481389239738018911847753040012042787717918908254528251383698867573135156939084331086758097907106095031547377278425617974502609591951482145610903954114723199175023668647127177171005078000230111841493293005098907252636413635633920751956022278837329406458663016725225858003022739549055062274361677955303156553396862455151776202367024537323175120553029177103272539450743286199138801302521724010186618263274929550795001141051128801614407279190360193127735430043687153224887844534769888437163665155800807463266843575103824059767284025940207275881960101519957916237708399875030372830269982631590567036289112792996676043853858411636406315981937522523463993396230828303434497509207051224667499492669294263050230559229676800568132382747151593579043989050178300829184643383595462517549306306474120786647700402892258487237997035359714591336600967370844334051004556584697268688966747575103026127402993600525260976910157191425375547783663028991220655494093577189810628207736824408765366252321547962537934163945058829871740990197017995479964655862858093533840154857599880559772822085707880357574223432953948114891117934451277005092303052452112158056476214906893587342030175547626651425026074833715152032952805169562075282179294553771261840060129307917562327518559447865560261869530619146796289605068773232280672043579212840213614934562130900927235803520092924949100933582669717418978032456490181287614496615337772202853561213724015646715694758940324144982567076229510224248921269187933597475519063663022757442713208129469622210659669536778045973317494731118990707967432774062244466075136722917025925009563913590052330611701222318368085100464973062147652246689225209600815677748233777662320645699744705636073421345796240053484790947490102494432936503470044285598487443191685499243787281532963627704292193424182943705360756645473340519414095571075906987921999994589589249185617638227290154466026945274766811106853096897936712824729657611432539798592716143987257658160530629482056080902245386837930231790704750654110781542255930924919874882282807461734345268621370264400363276081835323582898730664274722057146166965002489980037918333408523044028288630105000226961017101057911404439308945076014236700573803528075158097441596911890827780594707319154983659005344832899989561862660959130461722456610784770149431378576981345529022912974211559543506305874845139436429418602990811191514032095585427455050829742344137591691348336147594598106232787833354040920189543974857608087516319325230734952899760499184322016189412875490908364556014134221232189516514253131071953417743398305589250283949261639322480246103908899019192671003341114354426222279503260239379692002985820083691324001543770026121010659342635445175882283119028061806900247656062778452104695825791668229271089888239843678595833605360724031910208269201857832241519399456091000654999671882890157573953350680493959697423700920901526125561420840938619531572833243566141585750413363948101918633369088210553267837344133868481064157510091231648167146402765497018622521934157217722918252710260861762416803881844816281447193383020785507195544179097074683012618228156526573236865056979474673439761228079452790416346816424130437119160272875853115945840525610376098515206314549528779229566898655488992808412813208562567700649548920845247917159464920671204614608676010207017439945964053006478732190315269878558458539540181809600425140618593764715981322774361251735765127792981232516384702849531086986944407544314789200697349264961671890330493802893110038511078271458814149142021655319206993546999133764203804932225589425469230702521448316281442925721214305246932327940087990549046630745347388589661441788910366674227288837479995222348373760460096558952661701401872750873953119275134250746383544419899256714480402248874512152723381345337540041756915746027205111642496652868369791480941583725296478152527798879329044426981726565780911968075053031970793542854637797317255345847697294565655250581166197143757
But that certainly can't be an accurate formula. Doesn't even come out to an integer, really. The above code ends up doing integer division, because I definitely didn't care about anything after the decimal point.Code: Select all
k = (256**256)**9 for i in range(1, 257): k = k / i print str(k) + "\n"
256^(256^9), not (256^256)^9!!!
(256^256)^9 is 3.844855995870422 × 10^5548, but 256^(256^9) is 10^(1.1372591694895835 × 10^22).
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!
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Re: Thread for basic questions
Even so, the point still stands that 256^(256^9)/256! cannot possibly be correct, on account of not even being a natural number.gameoflifemaniac wrote:256^(256^9), not (256^256)^9!!!
(256^256)^9 is 3.844855995870422 × 10^5548, but 256^(256^9) is 10^(1.1372591694895835 × 10^22).
(You may also want to reconsider the number of exclamanation marks you're using.)
If you speak, your speech must be better than your silence would have been. — Arabian proverb
Catagolue: Apple Bottom • Life Wiki: Apple Bottom • Twitter: @_AppleBottom_
Proud member of the Pattern Raiders!
Catagolue: Apple Bottom • Life Wiki: Apple Bottom • Twitter: @_AppleBottom_
Proud member of the Pattern Raiders!
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Re: Thread for basic questions
- Regards,
Bamboonium
I'm not good at Conway's Game of Life. I just like scribbling and seeing what happens.
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Re: Thread for basic questions
Hello, and welcome!
What you've found is the pulsar -- definitely a beautiful oscillator.
If you want to share patterns more-easily in the future, by the way, Golly happens to make it really simple: look toward the top of the screen and you'll notice the row of buttons that contains a pencil icon, an eyedropper, a dashed rectangle, a hand, and two magnifying glasses. Click on the dashed rectangle (it's a selection tool) and click+drag across the board until your pattern is selected, then simply hit ctrl+C -- that'll copy a "run-length encoded" form of the pattern (an "RLE") to your clipboard.
Here's what selecting it looks like:
And this is what ends up on my clipboard after hitting ctrl+C:
Notice that that text is in its own little box -- you can get that by writing the BBCode tags "
What you've found is the pulsar -- definitely a beautiful oscillator.
If you want to share patterns more-easily in the future, by the way, Golly happens to make it really simple: look toward the top of the screen and you'll notice the row of buttons that contains a pencil icon, an eyedropper, a dashed rectangle, a hand, and two magnifying glasses. Click on the dashed rectangle (it's a selection tool) and click+drag across the board until your pattern is selected, then simply hit ctrl+C -- that'll copy a "run-length encoded" form of the pattern (an "RLE") to your clipboard.
Here's what selecting it looks like:
And this is what ends up on my clipboard after hitting ctrl+C:
Code: Select all
x = 17, y = 15, rule = B3/S23
$4b2o5b2o$5b2o3b2o$2bo2bobobobo2bo$2b3ob2ob2ob3o$3bobobobobobo$4b3o3b
3o2$4b3o3b3o$3bobobobobobo$2b3ob2ob2ob3o$2bo2bobobobo2bo$5b2o3b2o$4b2o
5b2o!
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[ /code]" (but remove the spaces!) and pasting your pattern right in the middle of the two. The "show in viewer" link pops up if there's an RLE pattern detected inside the code-block, and users can click it to see the pattern in real time on their own screens :)
--
You may be interested in the pulsar's bigger cousins, by the way -- what's neat is that its sort-of quadrants can be split up and duplicated and rearranged in a bunch of different ways. Here's a [wiki]quasar[/wiki]:[code]x = 29, y = 29, rule = B3/S23
10b3o3b3o2$8bo4bobo4bo$8bo4bobo4bo$8bo4bobo4bo$10b3o3b3o2$8b3o7b3o$2b
3o2bo4bo3bo4bo2b3o$7bo4bo3bo4bo$o4bobo4bo3bo4bobo4bo$o4bo17bo4bo$o4bo
2b3o7b3o2bo4bo$2b3o19b3o2$2b3o19b3o$o4bo2b3o7b3o2bo4bo$o4bo17bo4bo$o4b
obo4bo3bo4bobo4bo$7bo4bo3bo4bo$2b3o2bo4bo3bo4bo2b3o$8b3o7b3o2$10b3o3b
3o$8bo4bobo4bo$8bo4bobo4bo$8bo4bobo4bo2$10b3o3b3o!
Last edited by M. I. Wright on September 24th, 2018, 10:49 pm, edited 1 time in total.
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Re: Thread for basic questions
Thank you for the insight ! I Will make sure to use this function next time it is applicable. I will also look into working with quasars!
Also, I would like to know how to import this BBcode into Golly. The run in browser function works fine, but I would like to do further experimentation on it in in Golly.
[Edit] Nevermind, I figured out that it Is the copy clipboard function under the file menu.
Regards,
Bamboonium
Also, I would like to know how to import this BBcode into Golly. The run in browser function works fine, but I would like to do further experimentation on it in in Golly.
[Edit] Nevermind, I figured out that it Is the copy clipboard function under the file menu.
Regards,
Bamboonium
I'm not good at Conway's Game of Life. I just like scribbling and seeing what happens.
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Re: Thread for basic questions
Is there some sort of mathematical equation or method for finding patterns that don't die over time or are all of the known ones just the result of millions of hours of experimenting?
Regards,
Bamboonium
Regards,
Bamboonium
I'm not good at Conway's Game of Life. I just like scribbling and seeing what happens.
Re: Thread for basic questions
"Millions of (CPU) hours of experimenting" is a good summary of how a lot of oscillators and other persistent objects have been found (Catagolue, and its predecessors).Bamboonium wrote:Is there some sort of mathematical equation or method for finding patterns that don't die over time or are all of the known ones just the result of millions of hours of experimenting?
However, a lot of "engineered" patterns that don't die over time are more the result of careful assembly than random experimentation. Once you have a few key reactions, like the Snark reflector catalyst or Herschel conduits, you can use them to build signal loops and more complicated circuits that are guaranteed not to die off.
Re: Thread for basic questions
Is a rule table metacell possible?
Re: Thread for basic questions
Scary thought. You mean, a Life metacell with programmable elements that can support variables and permutation symmetry and 256 states and nearly unlimited numbers of rule lines?KittyTac wrote:Is a rule table metacell possible?
It's certainly theoretically possible, but to be able to support a memory storage area big enough to hold the maximum number of rule lines, it would have to be so big and have such a high period that even StreamLife couldn't run it.
Of course, Golly can't run a rule table with the maximum number of rule lines on any existing computer, either. So if you set some very specific limitations, like no variables, symmetry=none only, and maximum of a thousand rule lines, then it's ... well, still extraordinarily impractical, since every cell would have to include its own rule-table processing circuitry, but ultimately just another kind of specialized Life computer.
Re: Thread for basic questions
A impressively basic question: how GUYTU6J find those waves?GUYTU6J wrote:Could such pattern be added into Lifewiki along with those block-laying waves and clean waves ?Code: Select all
x = 3356, y = 1088, rule = B3/S23 3o$o2bo$ob2o$4b2o5bo$4b2o4b3o$10bob2o$4b2o8bo$4b2o8b2o4b3o$10bo9bo2bo$ 14b2o8bo$11bo2bo7bobo6bo$8bo11bo3bo4b2ob2o$19bob5o6b2o$17bo3b2o9bobo6b o$17bobo13b2o5bobo$29b4o2b2o2b2ob2o$27b3obo7b2obo8bo$27b2o11bo2bobo4bo bo4b2o$40b3o2bo3bo2bo$37b2o6bo4bobo14bo$6bo30b2o11b2o8b3o5bo$6bo44b2ob 3o3b3o4bo$2b2o2b3o38b2o11bo16bo$2b2o3b2o6b2o30b2o12bo3bo5bo4bobo$o3bob obo8bo43bo3bo4b3o5bo$o3b5o3b2o43b2o3bo2bo8bo$2bob4o4bo2bob2o7bo30b2o 12b3o12b3o$10b2o6bo4bob2o45b4o4b3o3b3o$10b5o2bo5bob2o10bo29b2o4b2o6bo 2b3o$12bobob2o5bobob2o8bo29b2o12bo3bo5bo3bob2o$20b2o3bo2bo5b2o46bob2o 5bo3bo2bo$19bo2b6o5b3o12bo28b2o4bo7bo$26bo10b2o6b2obo28b2o13b2ob2o5b2o 3bo$22bo7b2o2bo3bo53b3o6b8o$29bo2bo2b3o5b2o13bo28b2o12bo3bobo$7b2o21bo 2bo10b2ob2o7b3o28b2o13b2obo2bo4bo$7b2o31b2o2b2ob2o5bob2o45b2o6b2obob3o $o30bobo5bobo4bo7bo2bo9bobo27b2o12bo3bobobo$17b2o21bobo11b2ob2o7bo2bo 22b2o3b2o13b2obo$9bo7b2o22b3o6bo4bobo6b3o47bo2bo4b3o2bo$9bo32b2o5bob2o 3bo7bo2bo9b2o24bo3b2o10b2ob2obob2o$9bo17b2o21bo14bobo2bo2bo3b3o22bo4b 2o14b3o2b2o6bo$27b2o23bo6bo5b3o2bo3bobo26bo23b3o3bo3bo$18b3o31b2o5bob 2o12bobo3bo6bo24b2o2b2o10bobob2o3bo$37b2o21b2o8bo4b2o2bo2bo4b2o23bo4b 2o15b2o2bo$29bo7b2o23bo6bo6bo4b3o2bo2bo23b2o22b2o3bo2b3o$29bo32bo6bobo bo3bo3b3obob5o31b2o2b2o11bo2b5o$29bo17b2o14bo6b2o10b2obo3bo2bo4b3o23b 2o2b2o11bo7bo$47b2o23bo6b2o3bo7bo3bo26bo9bo13bo8bo$38b3o31bo6b3ob3obo 4bo2bobo2bo34bob2o9bo2b3ob3o$57b2o14b2obo8b3o4bo3b2ob3o5b2o23bobo3bo3b o7b4o4bo$49bo7b2o23b4ob3ob2o3b2o2b3o3bob2o23bo12bo6bob3o$2b2o45bo32b7o 2b5obob2o4bob2obo31bobo2bobobob4o8b3o$2b2o45bo17b2o17bo12b3o3bo3bobo5b o24bobo3bo3b3o2b2ob6o2bo$67b2o22b2obo2b2o2b2o5bo3bo3bob2o23bo13b3obo3b 3o$12b2o44b3o32bob3o7bob3o2bo3bo3bo31b3o2b3obo14b2o$12b2o63b2o23bob2ob obob4o4bobo5b2o23b3o7b3o5bo2b2ob2o$69bo7b2o23bob2ob2o3bo3bo2b3o4bo36bo 2b6obo3bo$22b2o45bo32bo3bo12b3o4bo2b2o32bo7bob2o8bo2bo$22b2o45bo17b2o 26b3o4bob2o5bo6bo24bo9b2o8bo2b2o$87b2o22b3ob3obo3bob2o3bo6b2o24bo5bo9b 3obo4bo$5b2o25b2o44b3o42b2o4b2o5b2ob2o25b2o6b5obo2b2o9b2o$4bo2bo24b2o 63b2o21bob2ob2o3bo2bo3bo3bo7bo23b7o3bo6bo2b4o$4bobo82bo7b2o22b2o3b2o2b 2obob4obo6b2o24bob4o11bo2bo3b2o$5bo9b2o25b2o45bo40b2o2bo3b2o7bo3bo38bo 3bob3o$14bo2bo24b2o45bo17b2o22b2o3b2o3bob2o2bob2o9bo22b7o4b3ob2o3b4o$ 14bobo90b2o23bo3b2o3bob4ob3o7bobo22bo10b3ob3o2bo3bo$o14bo9b2o25b2o44b 3o40bo15b2o9bo26b2ob2o4b2ob2o$24bo2bo24b2o63b2o22bo4b2o4b2o3bob3o7bo 22bo2bo2bo10bo4b2o$9bo14bobo82bo7b2o23bo3bo4b3ob2o11b3o21bobo10bo4bob 2ob2o$9bo15bo9b2o25b2o45bo33bo7bo4bobo8bo2bo7bo25b2obobo5b3o$9bo24bo2b o24b2o45bo17b2o23b6o8bo3b2o5bobo22b3o3bo9b2o$34bobo90b2o23b3o6b4o3bo 10bo22b2o11b3obo3b4o$18b3o14bo9b2o25b2o44b3o40bo4b2o8bo3bo34bob3o2b2ob o2bo$44bo2bo24b2o63b2o23b3ob2o8bobobo6b3o22b2o8b2o4bo$29bo14bobo82bo7b 2o24bo7b2obobo3bo6b3o23bo9b5obo4bo$29bo15bo9b2o25b2o45bo41bo2b5o6b2o 36bobo2b2o2b2ob3o$29bo24bo2bo24b2o45bo17b2o23b3o13b3o7bo23b2o9bo2b3o$ 54bobo90b2o32b2obobob2o7b3o24bo9b2o3bo3bobo$38b3o14bo9b2o25b2o44b3o40b 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