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Atomatan salula na John Conway na 1970. Kowane sel mai rai ne ko matacce, kuma a kowane mataki yana duba maƙwabtansa takwas: matacce mai daidai uku yana rayuwa, mai rai mai biyu ko uku yana tsira, kuma duk sauran suna mutuwa. Wannan duk ƙa’idodin ne. Danna grid don ƙara sel.

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Maki na bazuwar suna sauka a murabba’i mai kwata na da’ira. Kason da ke sauka a ciki π/4 ne. Wannan shi ne ƙiyasin Monte Carlo a mafi sauƙi. Kuskuren yana raguwa ne kawai bisa tushen murabba’in yawan samfura, don haka kowane ƙarin lamba daidai yana ɗaukar samfura sau ɗari fiye da haka.

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Dokoki uku na Craig Reynolds daga 1987: rabuwa, daidaitawa da haɗuwa. Babu tsuntsun da ya san siffar garken, kuma babu shugaba.

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Wakilai 280 suna motsi na bazuwar a cikin akwati. Uku sun fara da kamuwa. Wakili da ya wuce kusa da wanda ya kamu zai iya kamuwa, kuma yana warkewa bayan kayyadadden lokaci. Za ka iya canza mutane nawa ke zama a gida. Danna Reset don amfani da shi. Wannan shi ne tsarin agent-based. Tsarin compartmental yana yin samfurin irin wannan motsi da ƙananan lissafin differential.

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Kowane pixel ƙwayar yashi ne. A kowane mataki ƙwaya tana faɗi idan sarari na ƙasa fanko ne, ko tana zamewa a kusurwa idan za ta iya. Tarin, gangara da zaftarewa suna fitowa daga wannan ƙa’ida ɗaya. Zana a kan canvas don ƙara ƙwayoyi.

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Hanya mai zagaye ta layi ɗaya, da aka zana a matsayin tsiri na lokaci: kowane jere lokaci ɗaya ne, sabo a ƙasa, kuma kowane ɗigo mai launi mota ne (ja ta tsaya, zinariya a hankali, kore a iyaka). Kowane direba yana ƙara gudu idan akwai wuri, yana birki ga motar da ke gaba, kuma wani lokaci yana rage gudu na bazuwar. Wannan shi ne dukan samfurin, daga Kai Nagel da Michael Schreckenberg (1992). Sama da yawan kusan 15%, cunkoso yana bayyana ba tare da dalilin waje ba kuma yana komawa baya a kan zirga-zirga.

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Tururuwa ɗari biyu suna barin gidan zinariya suna yawo. Kowanne yana ajiye pheromone yayin da yake motsi kuma yana juyawa zuwa mafi ƙarfin pheromone a gaba. Nau’i ɗaya yana kai wa gida, ɗayan yana kai wa abinci. Babu tururuwar da ta san inda komai yake, amma cikin minti ɗaya ƙungiyar ta shimfiɗa hanyoyi tsakanin gida da abincin ruwan hoda. Jean-Louis Deneubourg ya yi nazarin wannan a gwaje-gwajen tururuwarsa na 1990, kuma Marco Dorigo ya gina shi cikin algorithms ɗinsa na ant colony. Danna don jefa ƙarin abinci.

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Sinadarai biyu a faifai. Ɗaya ana ciyar da shi a daidaitaccen adadi. Ɗayan yana cinye shi, yana yin ƙari na kansa, kuma yana ruɓewa a hankali. Duka suna yaɗuwa, a gudu daban-daban. Turing (1952) ya nuna cewa irin wannan tsarin zai iya mayar da cakuda mai daidai zuwa tabo da ratsi. Wannan shi ne amsawar Gray–Scott, wanda John Pearson ya zana (1993). Ka canza saitunan sai ka sami tsarin murjani, sel masu rabuwa, zanen yatsu da tsutsotsi. Danna don ɗan tura shi.

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Ka zuba yashi a kan tebur ƙwaya ɗaya a lokaci. Kowane murabba’i mai ƙwayoyi huɗu yana rushewa ya ba kowane maƙwabci ɗaya, kuma waɗannan za su iya rushewa su ma. Ƙwayoyin da suka faɗi daga gefe sun ɓace. Per Bak, Chao Tang da Kurt Wiesenfeld sun yi amfani da wannan samfurin a 1987 don nuna yadda tsari zai iya tsara kansa zuwa yanayin da ke bakin sauyi. Yawancin ƙwayoyi ba sa yin komai. Wasu kaɗan suna haifar da zaftarewa a duk tarin. Girman zaftarewa ba shi da wani girman da aka saba. Danna don jefa ƙwaya a wani wuri.

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Nau’o’in gida biyu, cyan da ruwan hoda, an sanya su na bazuwar. Gida yana gamsuwa idan isassun maƙwabtansa takwas nau’insa ne. Idan ba haka ba, yana ƙaura zuwa wani wuri fanko na bazuwar. Schelling (1971) ya yi wannan da tsabar kuɗi a allon chess. Ko da gidaje suna farin ciki su zama marasa rinjaye, har yanzu za ka sami rabuwa mai kaifi. Za ka iya canza kason maƙwabta masu kama da suke buƙata.

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Nauyi uku da dokar nauyi ta Newton. Jikuna biyu za su iya zagayawa har abada. Uku ba su da mafita ta daidai ta gaba ɗaya, kamar yadda Henri Poincaré ya nuna a shekarun 1890, kuma daga yawancin wuraren farawa jiki ɗaya ana jefar da shi. Zagayen siffar takwas yana ɗaya daga cikin mafitar maimaituwa masu tsayuwa da ba kasafai ba. Cris Moore ya same shi a 1993, kuma Alain Chenciner da Richard Montgomery sun tabbatar da wanzuwarsa a 2000. Farawar Pythagorean tana da jikuna uku a tsaye, masu nauyi 3, 4 da 5. Carl Burrau ya gabatar da shi a 1913. Karatun yana nuna yadda hanyar lamba take kiyaye jimillar makamashi. Mafita ta daidai za ta kiyaye shi daidai.

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Ƙasa marar komai tana shuka bishiyoyi a hankali. Walƙiya wani lokaci tana kunna wuta ga bishiya, kuma gobara tana yaɗuwa zuwa bishiyoyin da ke kusa kafin ta ƙare. Barbara Drossel da Franz Schwabl sun yi nazarin wannan samfurin a 1992. Daji ba ya taɓa daidaitawa, kuma gobara ta kowane girma tana ci gaba da rage shi, kamar tarin yashi. Danna bishiya don kunna ta.

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Kowane pixel spin ne mai nuni sama ko ƙasa. Kowanne yana karkata ya daidaita da maƙwabtansa huɗu, kuma zafi yana girgiza su daga layi. Ernst Ising ya warware layi mai girma ɗaya a 1925; Lars Onsager ya warware wannan grid mai lebur daidai a 1944 kuma ya sami zafin sauyi mai kaifi, kusan 2.27 a waɗannan raka’a. A ƙasansa, yankuna suna haɗuwa zuwa manyan domains kuma grid yana zama mai maganaɗisu. A samansa, tsarin yana kasancewa marar tsari. Za ka iya canza zafin yayin da yake gudana.

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Tekun kifi (cyan) da sharks (ruwan hoda). Kifi suna motsi na bazuwar kuma suna haihuwa. Sharks suna cin kifin da ke kusa, suna haihuwa a hankali, kuma suna mutuwa da yunwa idan sun daɗe ba su ci ba. A. K. Dewdney ya sa wa wannan duniyar suna Wa-Tor a 1984. Jadawalin da ke ƙasa yana nuna yawan biyun, kowanne a ma’aunin kansa. Kifi suna ƙaruwa, sharks suna biye, kifi suna rugujewa, sharks suna mutuwa da yunwa, kuma zagayen yana maimaituwa. Alfred Lotka da Vito Volterra sun sami irin wannan lilo daga lissafinsu a shekarun 1920. Anan yana fitowa daga wakilai ɗaiɗai.

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