├── README.md ├── gen.rb ├── plot.rb ├── self-description-set.hs └── self-description-set.png /README.md: -------------------------------------------------------------------------------- 1 | ![The self-description set](self-description-set.png) 2 | 3 | --- 4 | 5 | THIS IS 〝THE SELF-DESCRIPTION SET $A$〟 WHERE: 6 | 7 | $A = \lbrace (x, y) : x \in R \wedge y \in R \wedge (\lfloor x \rfloor, \lfloor y \rfloor) \in B \cup C \rbrace$ 8 | 9 | $B = \lbrace (x, y + 1) : x \in I(0, 240) \wedge y \in I(0, 59) \wedge g({\mathrm K}, 240 y + x, 2) = 1 \rbrace$ 10 | 11 | $C = \lbrace (x, -y - 1) : x \in I(0, 240) \wedge y \in I(0, 419) \wedge f(x, y) = 1 \rbrace$ 12 | 13 | $I(x, y) = \lbrace n \in Z : x \le n < y \rbrace$ 14 | 15 | $f(x, y) = g(g(2 {\mathrm F}, g({\mathrm K}, 4199 - 60 \lfloor \frac{y}{6} \rfloor - \lfloor \frac{x}{4} \rfloor, 10), 1048576), 4 {\mathrm mod}(y, 6) + {\mathrm mod}(x, 4), 2)$ 16 | 17 | $g(k, x, b) = {\mathrm mod}(\lfloor k b^{-x} \rfloor, b)$ 18 | 19 | ${\mathrm F} = 731024063570851866511465264858993450227206304418681785374039$ 20 | 21 | ${\mathrm K} =$ 22 | 23 | ``` 24 | 1431487833696853176700157431078133300807345625216694848607 25 | 270563208155416337169196351358980580604619006940957434879772 26 | 028845592243617643316119085595555875582798798158387973177961 27 | 695587578188817228313270884309874099454731913241985765682402 28 | 480224733096696517805958475042928066100949209924392429965610 29 | 551766692904047263776654396499838486398528392900895041691929 30 | 709953815043504772858511723069075303646254955446123264474132 31 | 399135568097499209716863422382789934101032731521846133868000 32 | 262329082771730906048784389387705912576097416771115812864994 33 | 198317336696101343690251839925474483575213942785063242683363 34 | 056895377315670280246764867791471907877623375038271649453182 35 | 854021185885389244374830321750777584790301153742853542800001 36 | 803212776995615125143244379356783669548607899860292215030468 37 | 372496357389687827338321380869009775183121027221622306000665 38 | 434108529937588506145256252374820685424106104653500265071429 39 | 499165977490516978768334029153298397589002274564473050238958 40 | 518723573172157176290043800440280395832035460552484762992067 41 | 849529493561574241307638065213995109640364226013296804961000 42 | 811321628352092513531339413313635921859713758236408663277002 43 | 386192216559126203984335509470259495329395180693003674481916 44 | 985784593729922914627462237255795851931055864600242532142318 45 | 674966768787359732406186007861171799850725223859636070231916 46 | 750293338790554961393908296465761510712256725042256150275961 47 | 853353038409593050154710454454971515086554776219129386191600 48 | 322844140670645385184627169239185326202513499888542720362735 49 | 998962021191766587885886375125283567616781242503845756516197 50 | 816876191710321803724279392085178759541805985378446786499999 51 | 355037854466378351524894055474084206664157675270124690002296 52 | 225319060857108132382273200584697384305825630469888977896432 53 | 560991543457042590254018585056927703776270596684379711927456 54 | 545078675187493947032274853673051855860122642712742370425853 55 | 963917860278944365922453978838483505214433388496878103399242 56 | 764407233837488918588883937087620092755170919027581059747658 57 | 687075260371020955132747315668285130611301948108509116362253 58 | 747034975626216146082065221763158722674864411736435609439600 59 | 721776130602651434691420627380848179973759206780190501532296 60 | 925802808790098781605594867546916690356299479523077404724197 61 | 946245726845183987376879398449418268922655335560612974635097 62 | 005543335638081982736279909805892964001894841686119109573543 63 | 090939336919368613186406945691544143703157025934407386944550 64 | 330246511216446769151033970189967336734074013033848520209515 65 | 918237997203937733562025438624853083446223743440168756571528 66 | 414728446749926603145457016114346065154181033867100753769439 67 | 041167254040774095432977057561464774698899066162660966140185 68 | 215017344545826901332797344178731597263993888151924585095949 69 | 592032310079010520371626665442224977109595506737417799566785 70 | 216348612593838405570128942169997754189060055948704116042801 71 | 127477452268451094379294013711634015451585382189606298412728 72 | 014051369018701118838401136494733540740703953356325628783371 73 | 453541118150965536789458775209803614635969806070635830661626 74 | 018796342020752673273787800692186347956204794348144022812339 75 | 370836117303786515553815606896168323272602756230677817295160 76 | 299954827997549085951896930123204362889275594738651705447020 77 | 323941639698395334192997012320910816923882486607439689115913 78 | 935065147563110191641773139452996426629926289613106847839879 79 | 497279568522406503816859003107052538587220753124221353664483 80 | 518844704860778218423384626452520064466203292073598028657804 81 | 094976489950291235455741425233569565297078253058387854773607 82 | 958742033328413164095843349303478827447502011163529338377924 83 | 282512905373355009689723648704956016318485168350690226970214 84 | 554064110121442985837293222421724842859785544597542309087676 85 | 231056127065035130412782484415460105782905072060734679328910 86 | 224234976659961653641143971374342378294563851212838452696539 87 | 440976148300104461171268854188854899938692788951901814055423 88 | 563988675580879375031500645546793494651069862529078359992872 89 | 398214042484623904682864685712734868941203696774466022261388 90 | 617800710778204106568476582538119303684144770652453644482942 91 | 378914919452119098364708800221922345010595494910106217845237 92 | 154021402181343119384299678932319414105519084205068519946232 93 | 617745756502372943664260390850946855181451132605067070064051 94 | 648518584235652757103867056333091068696069058723992812028933 95 | ``` 96 | 97 | --- 98 | 99 | ``` 100 | $ ruby gen.rb > self-description-set.hs 101 | $ runghc self-description-set.hs | ruby plot.rb 102 | ``` 103 | 104 | --- 105 | 106 | This was inspired by [Tupper's self-referential formula](https://en.wikipedia.org/wiki/Tupper%27s_self-referential_formula), made in 2009 [(Japanese article)](https://mametter.hatenablog.com/entry/20091106/p1). 107 | -------------------------------------------------------------------------------- /gen.rb: -------------------------------------------------------------------------------- 1 | bitmap = <