Menene fractal? Fractals a cikin yanayi

Sau da yawa abin da aka gano a cikin kimiyya sun iya canza rayuwarmu sosai. Alal misali, ƙwayar maganin alurar rigakafi na iya ceton mutane da dama, kuma ƙirƙirar makaman makamai ya kai ga kisan kai. A halin yanzu a jiya (a cikin tarihin tarihin) mutum yana "wutar lantarki", kuma yau ba zai iya tunanin rayuwarsa ba tare da shi ba. Duk da haka, akwai kuma irin wannan binciken, wanda, suka ce, kasancewa a cikin inuwa, kuma duk da cewa suna da wasu tasiri a rayuwarmu. Ɗaya daga cikin irin wannan binciken ya zama fractal. Yawancin mutane ba su taɓa jin labarin wannan ba kuma ba za su iya bayyana ma'anarta ba. A cikin wannan labarin za mu yi ƙoƙari mu fahimci batun abin da ke faruwa a fractal, la'akari da ma'anar wannan lokaci daga matsayin kimiyya da yanayin.

Sanya a Chaos

Domin ya fahimci abin da a fractal kamata a fara debriefing tare da matsayi na lissafi, amma kafin ya shiga cikin kimiyyar, mu ne kadan philosophize. Kowane mutum na da sha'awar yanayi, ta hanyar da ya san duniya da ke kewaye da shi. Sau da yawa a kokarinsa na ilimi, yana ƙoƙari yayi aiki tare da tunani a cikin shari'arsa. Saboda haka, yana nazarin hanyoyin da ke faruwa, yana ƙoƙarin lissafin dangantaka da kuma samun wasu ƙayyadaddun tsarin. Mafi girma cikin tunanin duniya suna shiga cikin warware matsalar. Da yake magana mai kyau, masana kimiyyarmu na neman alamu inda basu kasance, kuma kada su kasance. Duk da haka, ko da hargitsi, akwai dangantaka tsakanin waɗannan ko waɗannan abubuwan. Wannan shine haɗin da fractal yake. Alal misali, la'akari da rassan fashe da ke kwance a hanya. Idan ka dube shi a hankali, zamu ga cewa yana kama da itacen da dukkan rassansa da kusoshi. A nan wannan kama da wani ɓangaren sashi tare da duka ɗaya yana tabbatar da abin da ake kira ka'ida mai kama da juna. Fractals a cikin yanayin za a iya samun sau da yawa sau da yawa, saboda yawancin inorganic da Organic siffofin da aka kafa kamar wancan. Wannan shi ne girgije, da bawo na teku, da bawo na katantanwa, da kuma rawanin bishiyoyi, har ma da tsarin sigina. Wannan jerin za a iya ci gaba ba tare da iyaka ba. Duk waɗannan siffofin bazuwar sun bayyana fractal algorithm. A nan mun zo muyi la'akari da abin da fractal ya fito daga matsayin kimiyya daidai.

Wasu 'yan gaskiyar abubuwa

Kalmar "fractal" a cikin Latin an juya shi a matsayin "m", "rabu", "ƙaddarar", kuma game da abubuwan da ke cikin wannan lokaci, babu wani tsari kamar haka. Yawancin lokaci ana bi da shi a matsayin tsari mai kama da kai, ɓangare na duka, wanda aka sake ta ta hanyar tsari a matakin ƙananan ƙwayoyin. Wannan kalma buga a cikin seventies na karni na ashirin, Benoit Mandelbrot, wanda aka gane a matsayin uba na fractal lissafi. Yau, manufar fractal yana nuna alamar hoto na tsarin da, kamar girman ƙananan, zai zama kama da kanta. Duk da haka, tushen tushen ilimin ilmin lissafi don halittar wannan ka'idar ta dage farawa tun kafin haihuwar Mandelbrot kansa, amma ba zai iya cigaba ba har sai kwamfutar lantarki ya bayyana.

Tarihin tarihi, ko yadda aka fara duka

A ƙarshen karni na 19 da 20, nazarin yanayin fractals shine episodic. Wannan shi ne saboda gaskiyar mathematicians sun fi so suyi nazarin abubuwa waɗanda za a iya nazari bisa ga ka'idodi da hanyoyi na gaba. A 1872, masanin lissafi na Jamus K. Weierstrass ya gina misali na aikin ci gaba wanda babu wani abu mai banbanci. Duk da haka, wannan aikin ya zama cikakkiyar abu mai wuyar fahimta. Nan gaba sai Swede Helge von Koch, wanda a shekara ta 1904 ya gina ginin da yake ci gaba, wanda babu inda yake da tango. Yana da kyau sauƙin zanawa, kuma kamar yadda ya fito, an nuna shi ta hanyar fractal. Ɗaya daga cikin bambance-bambancen wannan shafin an ambaci shi don girmama marubucinsa - "snowflake Koch". Bugu da ari, ra'ayin mai ba da shawara akan kamannin da aka tsara ya zama mai koyarwa na B. Mandelbrot, Faransanci Paul Levy. A shekara ta 1938 ya wallafa wata kasida mai suna "Flat da sararin samaniya da ɗakunan dake kunshe da sassa kamar duka." A ciki ya bayyana sabon nau'in - Cury C-Curve. Dukkanin lambobin da ke sama an danganta su da nau'i, kamar yadda fractals na geometric suke.

Dynamic, ko algebraic fractals

Wannan kundin ya ƙunshi Mandelbrot. Masu binciken farko na wannan jagoran sune masanan lissafin Faransa Pierre Fatou da Gaston Julia. A 1918, Julia ta wallafa wani takarda wanda ya danganci nazarin abubuwan da suka shafi ayyuka masu mahimmanci. A nan ya kwatanta iyalin fractals wanda ke da dangantaka da Mandelbrot. Duk da cewa wannan aikin ya girmama marubuci a tsakanin masana lissafi, an manta da sauri. Bayan rabin karni na baya, godiya ga kwakwalwa, aikin Julia ya sami rai na biyu. Kwamfuta sun ba da izini ga kowa da kowa cewa kyakkyawa da dukiya na duniya na fractals wanda zai iya "ganin" mathematicians, nuna su ta hanyar ayyuka. Mandelbrot shi ne farkon wanda ya yi amfani da kwamfutar don yin lissafi (irin wannan ƙara ba za a iya aiki tare da hannu ba), wanda ya ba da izinin gina hoto na waɗannan siffofi.

Mutumin da ke cikin sararin samaniya

Mandelbrot ya fara aikin kimiyya a cibiyar bincike na IBM. Yin nazarin yiwuwar watsa bayanai a kan nisa, masana kimiyya sun fuskanci gaskiyar babban asarar da ta tashi saboda tsangwama. Benoit yana neman hanyoyin magance matsalar. Dubi sakamakon ma'auni, ya kusantar da hankalin zuwa wani abu mai ban mamaki, wato: maɗauran hoto sunyi kama da juna a ma'auni daban-daban. An yi kama da hoto guda biyu na tsawon kwana guda, kuma har kwana bakwai ko sa'a ɗaya. Benois Mandelbrot kansa sau da yawa ya ce ba ya aiki tare da siffofin, amma wasa da hotuna. Wannan masanin kimiyya ya sãɓã a cikin tunani na siffar, ya fassara kowane matsala na algebra a cikin yankin geometric, inda amsar daidai yake a bayyane. Saboda haka ba abin mamaki ba cewa irin wannan mutum shi ne mai arziki a cikin sarari tattaunawa, da kuma haifi fractal lissafi. Bayan haka, fahimtar wannan adadi ba zai zo ba idan ka yi nazarin zane kuma ka yi tunani da ma'anar waɗannan bambance-bambance waɗanda suka tsara nauyin. Abubuwan fashewa ba su da abubuwa masu kama, amma suna da kamala a kowane sikelin.

Julia - Mandelbrot

Ɗaya daga cikin zane-zane na wannan adadi shi ne fassarar fasalin saiti, wanda aka haife ta saboda ayyukan Gaston Julia kuma Mandelbrot ya canza shi. Gaston yayi ƙoƙari ya yi tunani game da yadda saitin yake kama da shi, wanda aka gina a kan wani tsari mai sauƙi, wanda aka rasa ta hanyar mayar da martani. Bari mu yi kokarin bayyana abin da aka fada da harshen ɗan adam, don haka, a kan yatsunsu. Ga wani nau'i mai mahimmanci, zamu yi amfani da dabarun don samun sabon darajar. Muna musanya shi a cikin tsari sannan mu sami wadannan. A sakamakon haka ne manyan yawan jerin. Domin wakiltar irin wannan tsari, ana buƙatar yin wannan aiki sau da yawa: daruruwan, dubban, miliyoyin. Wannan shi ne abin da Benoit yayi. Ya aiwatar da jerin kuma ya sauya sakamakon zuwa wani nau'in hoto. Daga bisani, sai ya zana siffar da aka samu (kowane launi ya dace da wasu lokuta). Wannan hoto mai suna "Mandelbrot Fractal".

L. Masana: sana'ar da aka halitta ta yanayi

Ka'idar fractals da sauri ya sami aikace-aikace m. Tun da yake yana da alaƙa da bayyanar hotunan kamannin kama da juna, wanda ya fara amfani da ka'idodi da algorithms don gina wadannan siffofin da ba a saba ba su ne masu fasaha. Na farko daga cikin wadannan shine mai tsara Lauren Carpenter na Pixar. Yin aiki a kan gabatar da samfurin jiragen sama, ya faru da shi don amfani da hoton duwatsu kamar baya. Yau, kusan kowane mai amfani da kwamfuta zai iya ɗaukar wannan aiki, kuma a cikin shekarun bakwai na karni na karshe kwakwalwa ba zai iya yin irin wannan matakai ba, saboda babu wasu masu gyara hotuna da aikace-aikace na 3D graphics a wannan lokacin. Sabili da haka Loren ya ɗauki littafin Mandelbrot "Fractals: Form, Accident and Dimension." A ciki, Benoit ya ba da misalai da dama, yana nuna cewa akwai fractals a cikin yanayi (fyva), ya bayyana irin nau'o'in su kuma yayi jayayya cewa suna iya bayyana su ta hanyar maganin ilmin lissafi. Masanin lissafi ya ambata wannan hujja a matsayin hujja don amfani da ka'idar da ya ci gaba da karɓuwa ga yawancin zargi daga abokan aiki. Sun yi jayayya cewa fractal - wannan hoto ne mai kyau, wanda ba shi da amfani, wanda shine samfurin aikin na'urorin lantarki. Masassaƙan ya yanke shawarar gwada wannan hanyar a aiki. Bayan nazarin littafin a hankali, mai gabatarwa a nan gaba ya fara neman hanyar aiwatar da jigilar fassarar kwamfuta a cikin na'urorin kwamfuta. Ya ɗauki shi ne kawai kwana uku don ganin hotunan yanayin tsaunuka a kan kwamfutarsa. Kuma a yau yau ana amfani da wannan tsarin. Kamar yadda ya bayyana, halittar fractals ba ya dauki lokaci mai tsawo da kuma kokarin.

Ginin maƙerin

Ka'idar da Lauren yayi amfani da shi mai sauƙi ne. Yana da su tsattsage fi girma lissafi siffofi cikin kananan abubuwa, da waɗannan - domin kama karami, da sauransu. Masassaƙan, ta amfani da magunguna masu yawa, ta rushe su cikin kananan yara 4, da sauransu, har sai da ya sami tsaunin dutse mai kyau. Saboda haka, ya zama zane-zane na farko da ya yi amfani da fractal algorithm a cikin na'urorin kwamfuta don gina image da ake bukata. A yau, ana amfani da wannan ka'idojin don daidaita nau'o'in siffofi daban-daban.

Na farko zane-zanen 3D a fractal algorithm

Bayan 'yan shekaru bayan haka, Lauren ya yi amfani da aikinsa a cikin babban tsari - shirin mai suna Vol Libre wanda aka nuna a Siggraph a 1980. Wannan bidiyo ta gigice mutane da dama, kuma an kirkiro mahaliccinsa don aiki a Lucasfilm. A nan mai gudanarwa ya iya ganewa har ya kai, ya kirkiro shimfidar wurare uku (dukan duniya) don fim din "Star Trek" mai cikakken lokaci. Duk wani shirin zamani ("Fractals") ko aikace-aikacen don ƙirƙirar siffofi uku (Terragen, View, Bryce) yana amfani da wannan algorithm don yin samfurin launi da surfaces.

Tom Beddard

A baya, masanin kimiyyar laser, yanzu mai sarrafa hoto da kuma mai zane-zane, Beddard ya tsara jerin jerin siffofin lissafin ƙasa mai mahimmanci, wanda ya kira Faberge fractals. A waje, suna kama da ƙyallen kayan ado na wani baƙar fata na Rasha, tare da irin wannan tsari mai ban sha'awa. Beddard ya yi amfani da tsarin samfurin don ƙirƙirar nuni na dijital na model. Abubuwan da aka samo sunyi mamaki da kyau. Kodayake mutane da yawa sun ƙi yin amfani da kayan aikin hannu tare da shirin kwamfuta, ya kamata a gane cewa siffofin da aka samo su na da kyau sosai. Abu mai ban mamaki shi ne cewa kowa zai iya gina irin wannan fractal ta yin amfani da ɗakin karatu na yanar gizon yanar gizon yanar gizo. Yana ba ka damar ganowa a halin yanzu lokuta daban-daban fractal.

Fractals a cikin yanayi

Mutane da yawa ba su kula ba, amma waɗannan ban mamaki ne a ko'ina. An halicci yanayi daga siffofin kama da kai, ba mu lura da shi ba. Ya isa mu duba ta hanyar gilashin gilashi a jikin mu ko ganye na itace, kuma za mu ga fractals. Ko kai, alal misali, abarba ko ma da wutsiyar tsuntsaye - sun ƙunshi siffofin kama da juna. Hanyoyin broccoli mai suna Romanescu suna da ban mamaki da gaske, saboda ana iya kiransu mu'ujizar yanayi.

Dakatar da wasanni

Ya nuna cewa fractals ba kawai lissafin lissafi ba ne, zasu iya zama sauti. Don haka, mai kida Jonathan Colton ya rubuta waƙa ta yin amfani da algorithms na fractal. Ya bayar da hujjar cewa, irin wannan karin waƙa yayi dace da halitta jituwa. Mai rikida ya wallafa duk ayyukansa a ƙarƙashin CreativeCommons Attribution - Lasisi na Kasuwanci, wanda ke ba da kyauta kyauta, kwashe, canja wurin ayyukan wasu mutane.

Alamar-fractal

Wannan samfurin ya samo aikace-aikace maras kyau. A kan asali, an kirkiro kayan aiki don nazarin kasuwar kasuwa ta kasuwar, kuma a sakamakon haka, an yi amfani da shi a kasuwar Forex. Yanzu mai nuna alama-fractal yana kan duk tallace-tallace ciniki kuma an yi amfani dashi a cikin kayan ciniki, wanda ake kira farashin farashin. Ci gaba da wannan fasaha Bill Williams. Kamar yadda marubucin ya faɗi akan abin da ya saba, wannan algorithm shine hade da dama "kyandir", inda tsakiyar ya nuna iyakar ko, a cikin maƙasudin, matsanancin matsayi.

A ƙarshe

Don haka muka dubi abin da ke faruwa a fractal. Ya bayyana cewa a cikin rikici da ke kewaye da mu, a gaskiya, akwai nau'i-nau'i masu kyau. Yanayin shi ne mashahuri mafi kyau, mai tsara ginin da injiniya. Ana shirya shi sosai a hankali, kuma idan baza mu iya samun doka ba, wannan ba yana nufin cewa babu shi. Watakila kana bukatar ka nemo shi a kan sikelin daban-daban. Za mu iya cewa da tabbaci cewa fractals adana mafi yawa asirin da muke da shi yanzu don gano.