For general discussion about Conway's Game of Life.

### Re: Thread for basic questions

KittyTac wrote:
dvgrn wrote:
KittyTac wrote:How big is the entire rule table rulespace?

I think it's (2^512)^256 -- each possible MAP-rule bit can point to any of 256 different states.

Maybe someone else can think about it with more brain cells than I have to spare at the moment, and confirm or deny. In any case it's pretty definitely a Painfully Large Number.

According to the same logic, it would be (2^102)^256... which is so much smaller than the number for all the MAP rules that it's practically zero, but it's still so much bigger than any reasonable number that it might as well be infinity:

`Number of possible isotropic rule table definitions for 256 states: 31278561947875052547079635722750231802892527748163799362328001343507661088125841605669624882915053596205517501325699958937569480665865214040057071250664859895038844131255539174530769054190265821190818165613286641061948679909627254987393256830999228932559609958778116963444348680250540404045642744429048113046922443145971895635858742591368397521329300481522235772830067874521886442842358148330713291675418240387192369006829142858484989836707586315579185465004593744701615633688888760201557729484840904687218177934482656662773634489630144413647144583758819871828839655861968752576339094211532091084084425336626025926937163627805510528134410751392837648258322024528852391679359240615294548044250287772313872396630670387718879196400256700442069980137124992544073289630332711853279825416692811097320936351649717660029511627299374208649468260064005657392124001333339464075020424914319482979966892864519024042717002316819265633329917403624689120059997681712914057119960415150136377014821563057238516175063434192663319035046390017034517611684407235068081764642502260152048269294058826420535517579203149656837745972497426804154196208455969010469114466768451839637699031542760973450042403650791214782333098627849831372905938692628829513076924962000717729180919783524256162148220349950572708179002833563627362244176958163078608453050413897667613406041742852939615861084196996754097132270446470441864328179428029048375281431230086693187353928673151148242164519407062098918992969305012590186292772802448408360775474253836390252326871881322557584336408405418460821956124703839661302035872555245254727283980874841622965699417622839338385154319893972718769194084018974148729487906213009056557955620300580452110217450235001954351177021369074158612761552054197646246056930545381949015586409046719967522406768665228155493904186524168905825991106387095657585488240007785703795166287787693581378072053121549506070691578946145060370006543084370825423862519551737889065312590812943697199655508138931905386682576327798358208014935088020251957702558472749904723435141975622879136853948789797202439247984585724992572299435086432196258461176660275950264681528722301433631566456411418762770192821738509082783537508428847585856435029986110008379055272136235729313827273745628376498168103158605189190547551988253086527500433070012544852430973264173171132421266291554377316476719964153803753407853238124658485521870454976294311846516555339679639012699101463877538659512068910148174760216032354453702751171150435992279715672237301375739439119139597220939470960212010712224219019279025577135920237571658369584091823792337212991479072418463561550204918002254141049642868463477669722073673177515127181127109271466602066368974948626353058292001709838342131130823465253716647319109131077894295140522478108212772192766164765924873457635426118644659216129631944695939176087517392732073038692951189825188704352046213507473593058381905590488013972804385275198476293170444115439945562839659380602897557418057643384703561759684253562933017171436659665331291977987180836784990039861989259155299144045601340437461986050278211903897449684762190688880098665923188404512485786925884784593626363494465929540002515990204343263537844454960729295458451976897575358583636537175612591203195051080174832676683704480683219116076718120935855967843668139791310748751054128967653398430357529759073254546643603109532461294413871698359353856041293405501872453415084522871528062144800847161971399159908844098745777568225892528170726910497518466889634743659081793453502028440832239950605327950880218223759022623201894462665393877182711762095988006353188789811275597108385945420075251833193198685479349139083743553299411595437759239045777010564301142015047998856397996893983435404421316367949607816483985997168327612441190776195547554153646108633738349537545854714840823095975032093016578246701873285968981766324033923883029439339726233109147707543701204424838260092624718089049890170826094196462139002862170571009464244620905979832507037350778480911147657003230963692508949354775494635662202423306634037925601727806949730774849869098090417917257466250374200399873325114973143922953573172803550054286579406568708609198934318856052026795343990230836490959787943828859533185008846782837792586680593821871170199535405505153016960724712054643734789740763245584222645183940094764845080006687080839300198137188845304348219071056881965851710414167680318772194119606113829495460890169029384334676295010962397704145796146615372033972038313750706926410012812348613050307535679152560355821637169725567762855109608550996459390574132555823107196317468851801260020225716919341661165126292770744630317284557132745528851090680461392715883349357907373365360113007483400453865672977109776284134946100383592069940493020040703926503417756469344721702864785323692585447852938298400441690297025918072918101496620592368788109999517805474559747528645054267161634475046902699872190540028692557145911433498104655177397760275256678503398340693972621228206942615955512268456415234543237831248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dvgrn
Moderator

Posts: 5622
Joined: May 17th, 2009, 11:00 pm

### 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.
One big dirty Oro. Yeeeeeeeeee...

gameoflifemaniac

Posts: 726
Joined: January 22nd, 2017, 11:17 am
Location: There too

### Re: Thread for basic questions

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.

AUGGGGGH!

KittyTac

Posts: 533
Joined: December 21st, 2017, 9:58 am

### Re: Thread for basic questions

KittyTac wrote:
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.

AUGGGGGH!

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).

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

`38448559958689582446977056492823062848927500337801248175571406455205640359363297329514829541070592676457967314688087605622316283099436819343890491013635088466499729825070976031210275483598854650564606111014665118125927723996499339432016213581444364821345016492704280888753836915090019089891021956471980034903237378400465979859826540187609718141492082898673816622337123245934288996076604339638524418394253023635460869167245612500247759155716272608571716958636926667805605753641932050068903767467165937176253315864988785133650181824849372103644977934119026825380749068108066872357582754400729634791720080164446537402135117661781469236359174184255596033792669086827411915986015838150656848431408992911771591624913941525780483938691571136538834822539584780911120126939399103070964745357217580167614907010324711156089416280463510336088047045004415745873169503686247087308031500178696881177302535389100298789242479384645073132351705737430484773132931574739815631252123422088074872372420202820360457330362118560631777500785925332990575820431004243688532105196903898543880465330550104758220492216377002140369482478254204390083473034586963001593132129378013492383581515627940015744644254953670143816119601465095726473112229478950729757709871425341485860918764648625881275487722015393560501796730878520888361812411650414282946262045476883178592995488364563880126578286951607355735992947731781538294875271574864043108188539109119918277016773246558167048666085193765160124264190947420400645854469508014776755883989972065875639618553446753825836144875262993424412684554556898756972714184734041991686692081821547127972614988059962571969025831790124999327826103472589043482166860944335563305313733753718974625930549278520594961590025279061819898430504890594651542030355356712920957135982522276103401297842683130400014844612945480945116470621327528087145999056500069274154450643588945060068255600120128885964595474682275618783873088243118219745124777903386837399811094658903562890136512940695482752032031808086815733887292852972336277631358557245113042785818028051234887370149420184820248600593508295242689017771401347522072896573378892123196299780401472964400022154953633543845395087356920833120210730705011855968171103867054322048889349241026647431540276824581324251471335305137613210452034008440330746299711661622469116156548292474296008218098552544333228771438814286275417774489280051686677036552028331663254360440592548720586690433130063140540114058064527982221082862164986576526942793763175079583002874559996712571073894078195183501370725252885453637960201238946868676704110226218852035688645870611182416843308352284639191207991983695852572958929112314976838541136669254081533813799126406405859720539994908516479854848301589373052500259590217147630533104470624038420535996537794398168556941689489640590025493737279963818741514851666330909146526690531131709880043528697041489213387210197441399336846028145341896358640909788006549837881428946105757595856448280368524742297818185817412680662660258958441387230755918575863934176465654300391746741973083621319557095445725462131414155911712013461673012726532528323680913900239598800737988323416624314219337539777582831138070457165646115997641224672692221125637111123732207977809418046079624113902168870945867329326278996425619089432645727236803104861591666361945805373249913689827164734590878498462786698283811077576686035697346883127932791702533774526352910857830279322367021165325386944768843132906644432143161038078918177112498627500208496202955180688087245450366196193864679352522944682019035419149105624897885390781969271541302191353712405440163953084005922519105018976327469686328255007397145963155262198675302949968271388691940362274767798076328607378638440486543891012727297778268255277026160910530357786644939919306653741443016100824786550126143125924489015012723962504052636184076541884054667789069600066921840220577878306346214272726027010242839821689530872073373999328339098568843763904574053249005460846820910932792707741310744602737806382175467523259723497880623436622585852541326384059959995143312091736735843249441506666014129572853323906202386567067638700947859246730291156601125272415511900919608531548328979621028717360314901833032365958594603475955686744170452409666419029111578818803036900869624373440575853216805793950656085549318966062263612496388862306204701273007349199949990079715873565509967880817971018426048058146068039800158577047061243337199803725265207339575928474688454010509360930063137390729226079007289045496751180410993944295642503355698510297924224644240753414126413706400103044149165908557074617237622080932446184169932297882164792564014718276494215637734995241343815930987865825647133828470637438944808041762845059451803399725505863858011570199292519794533344377559174398017366476326492384814758816154748041122844387670552125008043076417403088411607080337480550534303802771112912581428328885557869146753007103287223391486780332361239355963432012493496051285072027635618926443633387893019054756343722688074200391334446252106751133882642438547367391301229272298694451522040433810620207374283045600853922309924495353348734859731800287200050286615033184132697017296572340419013735770106600797612496359412588114138431619220641386838078912450881641429040837254213276369578953312144755186685359585141180598398368235739814200624474677442416064830195463694588605124744950362063529234545240378021620895676803531848237377551457882046712672355146932491169091236445252690403712024392627335056563543107562770803672059136162039931331357996511511072625851039832806754552212807873198131511296`

... which is just infinitesimally small compared to that 7862-digit number I quoted earlier.

dvgrn
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### 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.

KittyTac

Posts: 533
Joined: December 21st, 2017, 9:58 am

### Re: Thread for basic questions

dvgrn wrote:So that's a mere 5550-digit number

`38448559958689582446977056492823062848927500337801248175571406455205640359363297329514829541070592676457967314688087605622316283099436819343890491013635088466499729825070976031210275483598854650564606111014665118125927723996499339432016213581444364821345016492704280888753836915090019089891021956471980034903237378400465979859826540187609718141492082898673816622337123245934288996076604339638524418394253023635460869167245612500247759155716272608571716958636926667805605753641932050068903767467165937176253315864988785133650181824849372103644977934119026825380749068108066872357582754400729634791720080164446537402135117661781469236359174184255596033792669086827411915986015838150656848431408992911771591624913941525780483938691571136538834822539584780911120126939399103070964745357217580167614907010324711156089416280463510336088047045004415745873169503686247087308031500178696881177302535389100298789242479384645073132351705737430484773132931574739815631252123422088074872372420202820360457330362118560631777500785925332990575820431004243688532105196903898543880465330550104758220492216377002140369482478254204390083473034586963001593132129378013492383581515627940015744644254953670143816119601465095726473112229478950729757709871425341485860918764648625881275487722015393560501796730878520888361812411650414282946262045476883178592995488364563880126578286951607355735992947731781538294875271574864043108188539109119918277016773246558167048666085193765160124264190947420400645854469508014776755883989972065875639618553446753825836144875262993424412684554556898756972714184734041991686692081821547127972614988059962571969025831790124999327826103472589043482166860944335563305313733753718974625930549278520594961590025279061819898430504890594651542030355356712920957135982522276103401297842683130400014844612945480945116470621327528087145999056500069274154450643588945060068255600120128885964595474682275618783873088243118219745124777903386837399811094658903562890136512940695482752032031808086815733887292852972336277631358557245113042785818028051234887370149420184820248600593508295242689017771401347522072896573378892123196299780401472964400022154953633543845395087356920833120210730705011855968171103867054322048889349241026647431540276824581324251471335305137613210452034008440330746299711661622469116156548292474296008218098552544333228771438814286275417774489280051686677036552028331663254360440592548720586690433130063140540114058064527982221082862164986576526942793763175079583002874559996712571073894078195183501370725252885453637960201238946868676704110226218852035688645870611182416843308352284639191207991983695852572958929112314976838541136669254081533813799126406405859720539994908516479854848301589373052500259590217147630533104470624038420535996537794398168556941689489640590025493737279963818741514851666330909146526690531131709880043528697041489213387210197441399336846028145341896358640909788006549837881428946105757595856448280368524742297818185817412680662660258958441387230755918575863934176465654300391746741973083621319557095445725462131414155911712013461673012726532528323680913900239598800737988323416624314219337539777582831138070457165646115997641224672692221125637111123732207977809418046079624113902168870945867329326278996425619089432645727236803104861591666361945805373249913689827164734590878498462786698283811077576686035697346883127932791702533774526352910857830279322367021165325386944768843132906644432143161038078918177112498627500208496202955180688087245450366196193864679352522944682019035419149105624897885390781969271541302191353712405440163953084005922519105018976327469686328255007397145963155262198675302949968271388691940362274767798076328607378638440486543891012727297778268255277026160910530357786644939919306653741443016100824786550126143125924489015012723962504052636184076541884054667789069600066921840220577878306346214272726027010242839821689530872073373999328339098568843763904574053249005460846820910932792707741310744602737806382175467523259723497880623436622585852541326384059959995143312091736735843249441506666014129572853323906202386567067638700947859246730291156601125272415511900919608531548328979621028717360314901833032365958594603475955686744170452409666419029111578818803036900869624373440575853216805793950656085549318966062263612496388862306204701273007349199949990079715873565509967880817971018426048058146068039800158577047061243337199803725265207339575928474688454010509360930063137390729226079007289045496751180410993944295642503355698510297924224644240753414126413706400103044149165908557074617237622080932446184169932297882164792564014718276494215637734995241343815930987865825647133828470637438944808041762845059451803399725505863858011570199292519794533344377559174398017366476326492384814758816154748041122844387670552125008043076417403088411607080337480550534303802771112912581428328885557869146753007103287223391486780332361239355963432012493496051285072027635618926443633387893019054756343722688074200391334446252106751133882642438547367391301229272298694451522040433810620207374283045600853922309924495353348734859731800287200050286615033184132697017296572340419013735770106600797612496359412588114138431619220641386838078912450881641429040837254213276369578953312144755186685359585141180598398368235739814200624474677442416064830195463694588605124744950362063529234545240378021620895676803531848237377551457882046712672355146932491169091236445252690403712024392627335056563543107562770803672059136162039931331357996511511072625851039832806754552212807873198131511296`

... which is just infinitesimally small compared to that 7862-digit number I quoted earlier.

WRONG.
256^(256^9), not (256^256)^9.
One big dirty Oro. Yeeeeeeeeee...

gameoflifemaniac

Posts: 726
Joined: January 22nd, 2017, 11:17 am
Location: There too

### Re: Thread for basic questions

gameoflifemaniac wrote:WRONG.
256^(256^9), not (256^256)^9.

Heh. Have you calculated the difference between those two rather large numbers?

dvgrn
Moderator

Posts: 5622
Joined: May 17th, 2009, 11:00 pm

### 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
c(>^w^<c)~*
This is Fluffy the cat.
Fluffy wants to discover new things that everyone likes.
Fluffy likes to watch spaceship guns in Golly.
Fluffy knows Natsuki best girl.

Redstoneboi

Posts: 335
Joined: May 14th, 2018, 3:57 am

### Re: Thread for basic questions

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

Python can do it, though not terribly quickly. It's a 5043-digit number:

`44821360741006920927118125563344294069712618441345403098562857255809227239160043579760371886464596995489062274108744120199671762251468517721753419132979862379056953100468497385599593285559686138634035432205756236470775283882790175378123396983120793247149663296331150517544915673719501890339158202008041570762128564641914095283548440101107158073165558844344006117324199034608910304702943457842657623268037234276167642902877246877148973187197700009919097525078135810516499124934591510551141722914994756267817818446404637183464253121251345517642811185472338560896975045079227351075854551876046679813081975920731276030681726233101583481614300065209856122290708493750240170850166491339033131194951975843214384462875238344589029086429610311507821912016121274818017035383117393896405801826096649450701667324815003114219392417727247709992428533794821334638598303372122199984460499584494476048815413242387990236881323981327610991088342207527990697121304636721300423926050673623583992051738547124071865833572495808748464842960039679952507438565983596903271684726921402286358983372514110724436618616038627078171751571374981193481389239738018911847753040012042787717918908254528251383698867573135156939084331086758097907106095031547377278425617974502609591951482145610903954114723199175023668647127177171005078000230111841493293005098907252636413635633920751956022278837329406458663016725225858003022739549055062274361677955303156553396862455151776202367024537323175120553029177103272539450743286199138801302521724010186618263274929550795001141051128801614407279190360193127735430043687153224887844534769888437163665155800807463266843575103824059767284025940207275881960101519957916237708399875030372830269982631590567036289112792996676043853858411636406315981937522523463993396230828303434497509207051224667499492669294263050230559229676800568132382747151593579043989050178300829184643383595462517549306306474120786647700402892258487237997035359714591336600967370844334051004556584697268688966747575103026127402993600525260976910157191425375547783663028991220655494093577189810628207736824408765366252321547962537934163945058829871740990197017995479964655862858093533840154857599880559772822085707880357574223432953948114891117934451277005092303052452112158056476214906893587342030175547626651425026074833715152032952805169562075282179294553771261840060129307917562327518559447865560261869530619146796289605068773232280672043579212840213614934562130900927235803520092924949100933582669717418978032456490181287614496615337772202853561213724015646715694758940324144982567076229510224248921269187933597475519063663022757442713208129469622210659669536778045973317494731118990707967432774062244466075136722917025925009563913590052330611701222318368085100464973062147652246689225209600815677748233777662320645699744705636073421345796240053484790947490102494432936503470044285598487443191685499243787281532963627704292193424182943705360756645473340519414095571075906987921999994589589249185617638227290154466026945274766811106853096897936712824729657611432539798592716143987257658160530629482056080902245386837930231790704750654110781542255930924919874882282807461734345268621370264400363276081835323582898730664274722057146166965002489980037918333408523044028288630105000226961017101057911404439308945076014236700573803528075158097441596911890827780594707319154983659005344832899989561862660959130461722456610784770149431378576981345529022912974211559543506305874845139436429418602990811191514032095585427455050829742344137591691348336147594598106232787833354040920189543974857608087516319325230734952899760499184322016189412875490908364556014134221232189516514253131071953417743398305589250283949261639322480246103908899019192671003341114354426222279503260239379692002985820083691324001543770026121010659342635445175882283119028061806900247656062778452104695825791668229271089888239843678595833605360724031910208269201857832241519399456091000654999671882890157573953350680493959697423700920901526125561420840938619531572833243566141585750413363948101918633369088210553267837344133868481064157510091231648167146402765497018622521934157217722918252710260861762416803881844816281447193383020785507195544179097074683012618228156526573236865056979474673439761228079452790416346816424130437119160272875853115945840525610376098515206314549528779229566898655488992808412813208562567700649548920845247917159464920671204614608676010207017439945964053006478732190315269878558458539540181809600425140618593764715981322774361251735765127792981232516384702849531086986944407544314789200697349264961671890330493802893110038511078271458814149142021655319206993546999133764203804932225589425469230702521448316281442925721214305246932327940087990549046630745347388589661441788910366674227288837479995222348373760460096558952661701401872750873953119275134250746383544419899256714480402248874512152723381345337540041756915746027205111642496652868369791480941583725296478152527798879329044426981726565780911968075053031970793542854637797317255345847697294565655250581166197143757`

`k = (256**256)**9for i in range(1, 257):   k = k / i   print str(k) + "\n"`

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.

dvgrn
Moderator

Posts: 5622
Joined: May 17th, 2009, 11:00 pm

### Re: Thread for basic questions

dvgrn wrote:
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

Python can do it, though not terribly quickly. It's a 5043-digit number:

`44821360741006920927118125563344294069712618441345403098562857255809227239160043579760371886464596995489062274108744120199671762251468517721753419132979862379056953100468497385599593285559686138634035432205756236470775283882790175378123396983120793247149663296331150517544915673719501890339158202008041570762128564641914095283548440101107158073165558844344006117324199034608910304702943457842657623268037234276167642902877246877148973187197700009919097525078135810516499124934591510551141722914994756267817818446404637183464253121251345517642811185472338560896975045079227351075854551876046679813081975920731276030681726233101583481614300065209856122290708493750240170850166491339033131194951975843214384462875238344589029086429610311507821912016121274818017035383117393896405801826096649450701667324815003114219392417727247709992428533794821334638598303372122199984460499584494476048815413242387990236881323981327610991088342207527990697121304636721300423926050673623583992051738547124071865833572495808748464842960039679952507438565983596903271684726921402286358983372514110724436618616038627078171751571374981193481389239738018911847753040012042787717918908254528251383698867573135156939084331086758097907106095031547377278425617974502609591951482145610903954114723199175023668647127177171005078000230111841493293005098907252636413635633920751956022278837329406458663016725225858003022739549055062274361677955303156553396862455151776202367024537323175120553029177103272539450743286199138801302521724010186618263274929550795001141051128801614407279190360193127735430043687153224887844534769888437163665155800807463266843575103824059767284025940207275881960101519957916237708399875030372830269982631590567036289112792996676043853858411636406315981937522523463993396230828303434497509207051224667499492669294263050230559229676800568132382747151593579043989050178300829184643383595462517549306306474120786647700402892258487237997035359714591336600967370844334051004556584697268688966747575103026127402993600525260976910157191425375547783663028991220655494093577189810628207736824408765366252321547962537934163945058829871740990197017995479964655862858093533840154857599880559772822085707880357574223432953948114891117934451277005092303052452112158056476214906893587342030175547626651425026074833715152032952805169562075282179294553771261840060129307917562327518559447865560261869530619146796289605068773232280672043579212840213614934562130900927235803520092924949100933582669717418978032456490181287614496615337772202853561213724015646715694758940324144982567076229510224248921269187933597475519063663022757442713208129469622210659669536778045973317494731118990707967432774062244466075136722917025925009563913590052330611701222318368085100464973062147652246689225209600815677748233777662320645699744705636073421345796240053484790947490102494432936503470044285598487443191685499243787281532963627704292193424182943705360756645473340519414095571075906987921999994589589249185617638227290154466026945274766811106853096897936712824729657611432539798592716143987257658160530629482056080902245386837930231790704750654110781542255930924919874882282807461734345268621370264400363276081835323582898730664274722057146166965002489980037918333408523044028288630105000226961017101057911404439308945076014236700573803528075158097441596911890827780594707319154983659005344832899989561862660959130461722456610784770149431378576981345529022912974211559543506305874845139436429418602990811191514032095585427455050829742344137591691348336147594598106232787833354040920189543974857608087516319325230734952899760499184322016189412875490908364556014134221232189516514253131071953417743398305589250283949261639322480246103908899019192671003341114354426222279503260239379692002985820083691324001543770026121010659342635445175882283119028061806900247656062778452104695825791668229271089888239843678595833605360724031910208269201857832241519399456091000654999671882890157573953350680493959697423700920901526125561420840938619531572833243566141585750413363948101918633369088210553267837344133868481064157510091231648167146402765497018622521934157217722918252710260861762416803881844816281447193383020785507195544179097074683012618228156526573236865056979474673439761228079452790416346816424130437119160272875853115945840525610376098515206314549528779229566898655488992808412813208562567700649548920845247917159464920671204614608676010207017439945964053006478732190315269878558458539540181809600425140618593764715981322774361251735765127792981232516384702849531086986944407544314789200697349264961671890330493802893110038511078271458814149142021655319206993546999133764203804932225589425469230702521448316281442925721214305246932327940087990549046630745347388589661441788910366674227288837479995222348373760460096558952661701401872750873953119275134250746383544419899256714480402248874512152723381345337540041756915746027205111642496652868369791480941583725296478152527798879329044426981726565780911968075053031970793542854637797317255345847697294565655250581166197143757`

`k = (256**256)**9for i in range(1, 257):   k = k / i   print str(k) + "\n"`

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.

Is that bigger than the number of atoms in a human?

KittyTac

Posts: 533
Joined: December 21st, 2017, 9:58 am

### Re: Thread for basic questions

KittyTac wrote:Is that bigger than the number of atoms in a human?

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.

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.

dvgrn
Moderator

Posts: 5622
Joined: May 17th, 2009, 11:00 pm

### Re: Thread for basic questions

dvgrn wrote:You wouldn't have gotten to a five-hundred-digit number yet, let alone a five-thousand-digit number.

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?
`x = 81, y = 96, rule = LifeHistory58.2A\$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!`
Gamedziner

Posts: 709
Joined: May 30th, 2016, 8:47 pm
Location: Milky Way Galaxy: Planet Earth

### Re: Thread for basic questions

dvgrn wrote:
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

Python can do it, though not terribly quickly. It's a 5043-digit number:

`44821360741006920927118125563344294069712618441345403098562857255809227239160043579760371886464596995489062274108744120199671762251468517721753419132979862379056953100468497385599593285559686138634035432205756236470775283882790175378123396983120793247149663296331150517544915673719501890339158202008041570762128564641914095283548440101107158073165558844344006117324199034608910304702943457842657623268037234276167642902877246877148973187197700009919097525078135810516499124934591510551141722914994756267817818446404637183464253121251345517642811185472338560896975045079227351075854551876046679813081975920731276030681726233101583481614300065209856122290708493750240170850166491339033131194951975843214384462875238344589029086429610311507821912016121274818017035383117393896405801826096649450701667324815003114219392417727247709992428533794821334638598303372122199984460499584494476048815413242387990236881323981327610991088342207527990697121304636721300423926050673623583992051738547124071865833572495808748464842960039679952507438565983596903271684726921402286358983372514110724436618616038627078171751571374981193481389239738018911847753040012042787717918908254528251383698867573135156939084331086758097907106095031547377278425617974502609591951482145610903954114723199175023668647127177171005078000230111841493293005098907252636413635633920751956022278837329406458663016725225858003022739549055062274361677955303156553396862455151776202367024537323175120553029177103272539450743286199138801302521724010186618263274929550795001141051128801614407279190360193127735430043687153224887844534769888437163665155800807463266843575103824059767284025940207275881960101519957916237708399875030372830269982631590567036289112792996676043853858411636406315981937522523463993396230828303434497509207051224667499492669294263050230559229676800568132382747151593579043989050178300829184643383595462517549306306474120786647700402892258487237997035359714591336600967370844334051004556584697268688966747575103026127402993600525260976910157191425375547783663028991220655494093577189810628207736824408765366252321547962537934163945058829871740990197017995479964655862858093533840154857599880559772822085707880357574223432953948114891117934451277005092303052452112158056476214906893587342030175547626651425026074833715152032952805169562075282179294553771261840060129307917562327518559447865560261869530619146796289605068773232280672043579212840213614934562130900927235803520092924949100933582669717418978032456490181287614496615337772202853561213724015646715694758940324144982567076229510224248921269187933597475519063663022757442713208129469622210659669536778045973317494731118990707967432774062244466075136722917025925009563913590052330611701222318368085100464973062147652246689225209600815677748233777662320645699744705636073421345796240053484790947490102494432936503470044285598487443191685499243787281532963627704292193424182943705360756645473340519414095571075906987921999994589589249185617638227290154466026945274766811106853096897936712824729657611432539798592716143987257658160530629482056080902245386837930231790704750654110781542255930924919874882282807461734345268621370264400363276081835323582898730664274722057146166965002489980037918333408523044028288630105000226961017101057911404439308945076014236700573803528075158097441596911890827780594707319154983659005344832899989561862660959130461722456610784770149431378576981345529022912974211559543506305874845139436429418602990811191514032095585427455050829742344137591691348336147594598106232787833354040920189543974857608087516319325230734952899760499184322016189412875490908364556014134221232189516514253131071953417743398305589250283949261639322480246103908899019192671003341114354426222279503260239379692002985820083691324001543770026121010659342635445175882283119028061806900247656062778452104695825791668229271089888239843678595833605360724031910208269201857832241519399456091000654999671882890157573953350680493959697423700920901526125561420840938619531572833243566141585750413363948101918633369088210553267837344133868481064157510091231648167146402765497018622521934157217722918252710260861762416803881844816281447193383020785507195544179097074683012618228156526573236865056979474673439761228079452790416346816424130437119160272875853115945840525610376098515206314549528779229566898655488992808412813208562567700649548920845247917159464920671204614608676010207017439945964053006478732190315269878558458539540181809600425140618593764715981322774361251735765127792981232516384702849531086986944407544314789200697349264961671890330493802893110038511078271458814149142021655319206993546999133764203804932225589425469230702521448316281442925721214305246932327940087990549046630745347388589661441788910366674227288837479995222348373760460096558952661701401872750873953119275134250746383544419899256714480402248874512152723381345337540041756915746027205111642496652868369791480941583725296478152527798879329044426981726565780911968075053031970793542854637797317255345847697294565655250581166197143757`

`k = (256**256)**9for i in range(1, 257):   k = k / i   print str(k) + "\n"`

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.

Plugged this into one of my bots that evaluates arbitrary JavaScript.
A91355C7-CC18-40DB-9E60-05EAEBD473F3.jpeg (119.5 KiB) Viewed 3408 times

wwei23

Posts: 935
Joined: May 22nd, 2017, 6:14 pm
Location: The (Life?) Universe

### Re: Thread for basic questions

dvgrn wrote:
KittyTac wrote:Is that bigger than the number of atoms in a human?

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.

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.

Ouch. That kind of stumps my brain.

KittyTac

Posts: 533
Joined: December 21st, 2017, 9:58 am

### Re: Thread for basic questions

Gamedziner wrote:
dvgrn wrote:You wouldn't have gotten to a five-hundred-digit number yet, let alone a five-thousand-digit number.

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?

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.

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 latest version of the 5S Project contains over 47,000 spaceships. Tabulated pages up to period 160 are available on the LifeWiki.
wildmyron

Posts: 1110
Joined: August 9th, 2013, 12:45 am

### Re: Thread for basic questions

dvgrn wrote:Python can do it, though not terribly quickly. It's a 5043-digit number:

`44821360741006920927118125563344294069712618441345403098562857255809227239160043579760371886464596995489062274108744120199671762251468517721753419132979862379056953100468497385599593285559686138634035432205756236470775283882790175378123396983120793247149663296331150517544915673719501890339158202008041570762128564641914095283548440101107158073165558844344006117324199034608910304702943457842657623268037234276167642902877246877148973187197700009919097525078135810516499124934591510551141722914994756267817818446404637183464253121251345517642811185472338560896975045079227351075854551876046679813081975920731276030681726233101583481614300065209856122290708493750240170850166491339033131194951975843214384462875238344589029086429610311507821912016121274818017035383117393896405801826096649450701667324815003114219392417727247709992428533794821334638598303372122199984460499584494476048815413242387990236881323981327610991088342207527990697121304636721300423926050673623583992051738547124071865833572495808748464842960039679952507438565983596903271684726921402286358983372514110724436618616038627078171751571374981193481389239738018911847753040012042787717918908254528251383698867573135156939084331086758097907106095031547377278425617974502609591951482145610903954114723199175023668647127177171005078000230111841493293005098907252636413635633920751956022278837329406458663016725225858003022739549055062274361677955303156553396862455151776202367024537323175120553029177103272539450743286199138801302521724010186618263274929550795001141051128801614407279190360193127735430043687153224887844534769888437163665155800807463266843575103824059767284025940207275881960101519957916237708399875030372830269982631590567036289112792996676043853858411636406315981937522523463993396230828303434497509207051224667499492669294263050230559229676800568132382747151593579043989050178300829184643383595462517549306306474120786647700402892258487237997035359714591336600967370844334051004556584697268688966747575103026127402993600525260976910157191425375547783663028991220655494093577189810628207736824408765366252321547962537934163945058829871740990197017995479964655862858093533840154857599880559772822085707880357574223432953948114891117934451277005092303052452112158056476214906893587342030175547626651425026074833715152032952805169562075282179294553771261840060129307917562327518559447865560261869530619146796289605068773232280672043579212840213614934562130900927235803520092924949100933582669717418978032456490181287614496615337772202853561213724015646715694758940324144982567076229510224248921269187933597475519063663022757442713208129469622210659669536778045973317494731118990707967432774062244466075136722917025925009563913590052330611701222318368085100464973062147652246689225209600815677748233777662320645699744705636073421345796240053484790947490102494432936503470044285598487443191685499243787281532963627704292193424182943705360756645473340519414095571075906987921999994589589249185617638227290154466026945274766811106853096897936712824729657611432539798592716143987257658160530629482056080902245386837930231790704750654110781542255930924919874882282807461734345268621370264400363276081835323582898730664274722057146166965002489980037918333408523044028288630105000226961017101057911404439308945076014236700573803528075158097441596911890827780594707319154983659005344832899989561862660959130461722456610784770149431378576981345529022912974211559543506305874845139436429418602990811191514032095585427455050829742344137591691348336147594598106232787833354040920189543974857608087516319325230734952899760499184322016189412875490908364556014134221232189516514253131071953417743398305589250283949261639322480246103908899019192671003341114354426222279503260239379692002985820083691324001543770026121010659342635445175882283119028061806900247656062778452104695825791668229271089888239843678595833605360724031910208269201857832241519399456091000654999671882890157573953350680493959697423700920901526125561420840938619531572833243566141585750413363948101918633369088210553267837344133868481064157510091231648167146402765497018622521934157217722918252710260861762416803881844816281447193383020785507195544179097074683012618228156526573236865056979474673439761228079452790416346816424130437119160272875853115945840525610376098515206314549528779229566898655488992808412813208562567700649548920845247917159464920671204614608676010207017439945964053006478732190315269878558458539540181809600425140618593764715981322774361251735765127792981232516384702849531086986944407544314789200697349264961671890330493802893110038511078271458814149142021655319206993546999133764203804932225589425469230702521448316281442925721214305246932327940087990549046630745347388589661441788910366674227288837479995222348373760460096558952661701401872750873953119275134250746383544419899256714480402248874512152723381345337540041756915746027205111642496652868369791480941583725296478152527798879329044426981726565780911968075053031970793542854637797317255345847697294565655250581166197143757`

`k = (256**256)**9for i in range(1, 257):   k = k / i   print str(k) + "\n"`

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.

GAHHHHHHHHHHH!
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).
One big dirty Oro. Yeeeeeeeeee...

gameoflifemaniac

Posts: 726
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### Re: Thread for basic questions

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).

Even so, the point still stands that 256^(256^9)/256! cannot possibly be correct, on account of not even being a natural number.

(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_

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Apple Bottom

Posts: 1023
Joined: July 27th, 2015, 2:06 pm

### Re: Thread for basic questions

How the "score" of a soup in apgsearch calculated?
Sarp

Posts: 192
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### Re: Thread for basic questions

Weird Golly Thing.JPG (268.2 KiB) Viewed 3172 times
So I found this patter that turns into what I think is a three period repeater. Can anybody tell me what this is or if it is just a common repeater? An image showing the pattern and what it turns into is attached.

- Regards,
Bamboonium
I'm not good at Conway's Game of Life. I just like scribbling and seeing what happens.
Bamboonium

Posts: 11
Joined: September 24th, 2018, 8:05 pm
Location: Hell, Michigan

### 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:
`x = 17, y = 15, rule = B3/S23\$4b2o5b2o\$5b2o3b2o\$2bo2bobobobo2bo\$2b3ob2ob2ob3o\$3bobobobobobo\$4b3o3b3o2\$4b3o3b3o\$3bobobobobobo\$2b3ob2ob2ob3o\$2bo2bobobobo2bo\$5b2o3b2o\$4b2o5b2o!`

Notice that that text is in its own little box -- you can get that by writing the BBCode tags "[code ][ /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 quasar:
`x = 29, y = 29, rule = B3/S2310b3o3b3o2\$8bo4bobo4bo\$8bo4bobo4bo\$8bo4bobo4bo\$10b3o3b3o2\$8b3o7b3o\$2b3o2bo4bo3bo4bo2b3o\$7bo4bo3bo4bo\$o4bobo4bo3bo4bobo4bo\$o4bo17bo4bo\$o4bo2b3o7b3o2bo4bo\$2b3o19b3o2\$2b3o19b3o\$o4bo2b3o7b3o2bo4bo\$o4bo17bo4bo\$o4bobo4bo3bo4bobo4bo\$7bo4bo3bo4bo\$2b3o2bo4bo3bo4bo2b3o\$8b3o7b3o2\$10b3o3b3o\$8bo4bobo4bo\$8bo4bobo4bo\$8bo4bobo4bo2\$10b3o3b3o!`
Last edited by M. I. Wright on September 24th, 2018, 10:49 pm, edited 1 time in total.
gamer54657 wrote:God save us all.
God save humanity.

hgkhjfgh

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M. I. Wright

Posts: 371
Joined: June 13th, 2015, 12:04 pm

### 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.
 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.
Bamboonium

Posts: 11
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Location: Hell, Michigan

### 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
I'm not good at Conway's Game of Life. I just like scribbling and seeing what happens.
Bamboonium

Posts: 11
Joined: September 24th, 2018, 8:05 pm
Location: Hell, Michigan

### Re: Thread for basic questions

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?

"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).

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.

dvgrn
Moderator

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### Re: Thread for basic questions

Is a rule table metacell possible?

KittyTac

Posts: 533
Joined: December 21st, 2017, 9:58 am

### Re: Thread for basic questions

KittyTac wrote:Is a rule table metacell possible?

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?

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.

dvgrn
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