I-fractal yinto yejometri enokuthi ihlulwe ibe ngamacandelo, nganye ifana nento yokuqala. Iifractals zineenkcukacha ezingapheliyo kwaye zihlala zifana kwaye zilinganiswe. Kwiimeko ezininzi, iifractals zinokuveliswa ngeepatheni eziphindaphindiweyo, iinkqubo eziphindaphindayo okanye eziphindaphindayo.
Kweli nqaku siza kukuxelela yonke into ofuna ukuyazi malunga fractals, iimpawu zabo kunye nokubaluleka.
Iipropati zeefractals
Iimpawu eziphambili ezibonisa i-fractals zifana nokuzifanisa, ubunzima obungapheliyo kunye nobukhulu.
ukufana
Ukuzifanisa kuxa inxalenye yomfanekiso okanye ulwandlalo lunokubonwa njengomfanekiso wento yonke, kumlinganiselo omncinci.
ubunzima obungenasiphelo
Ibhekisa kwinto yokuba inkqubo yokwenziwa kwegrafu iphindaphindwa. Oku kuthetha ukuba xa inkqubo isenziwa, inkqubo ebisenziwa ngaphambili ngokwayo ifunyenwe iyinkqubo engaphantsi kwenkqubo yayo.
Kuyafaneleka ukuba kuqatshelwe ukuba kwimeko yokwakhiwa okuphindaphindiweyo kwe-fractal echazwe ngokwemathematika, inkqubo eya kuphunyezwa ayinasiphelo, nto leyo ephumela kwisakhiwo esinzima esingenasiphelo.
Ubukhulu
Ngokungafaniyo nejometri ye-Euclidean, imilinganiselo yeefractals ayingomanani apheleleyo. Kweli sebe lemathematika, amanqaku anomlinganiselo onguziro, imigca inomlinganiselo omnye, umphezulu unemilinganiselo emibini, kwaye imiqulu inemilinganiselo emithathu. Kwimeko ye-fractal dimension, le yi-fractal quantity ebonisa indlela isakhiwo esisithatha ngayo isithuba esisiquletheyo.
imizekelo yeefractals
Iifractals zokuqala ezaphononongwayo yayiyiCantor set, ikhephu lekhephu laseKoch, kunye nonxantathu weSierpinski. I-Fractals inokufumaneka ngejometri okanye i-stochastically ngokusebenzisa iinkqubo zokuphindaphinda kwaye inokuthatha iimpawu zeentlobo ezahlukeneyo zeemilo ezifunyenwe kwindalo.
Iifractals zikhona kuyo yonke indawo. Kukho izinto ezininzi zendalo ezithathwa njengee-fractals zendalo ngenxa yokuziphatha okanye ukwakheka kwazo, kodwa ezi ziintlobo ezinomda zeefractals, ezizohlula kuhlobo lwemathematika oludalwe lunxibelelwano oluphindaphindayo. Imizekelo yezi ngamafu nemithi.
Iimpawu eziphambili
Igama elithi "fractal" livela kwi-Latin fractus, elithetha "ukuqhekeka", "ukuqhekeka", okanye nje "ukuqhekeka" okanye "ukuqhekeka", kwaye ifaneleka kakuhle kwizinto ezinomlinganiselo we-fractional. Eli gama layilwa nguBenoît Mandelbrot ngo-1977 kwaye lavela kwincwadi yakhe ethi Fractal Geometry of Nature. Uphononongo lwezinto eziqhekekileyo ludla ngokubizwa ngokuba yifractal geometry.
I-fractal yiseti yemathematika enokonwabela ukufana nayo nangasiphi na isikali, kwaye imilinganiselo yayo ayizizo ii- integers, okanye ukuba bekunjalo, bezingayi kuba zii- integers eziqhelekileyo. Inyani yokuba iyafana nayo ithetha ukuba into eqhekezayo ayixhomekeke kumntu obukeleyo, oko kukuthi, ukuba sithatha uhlobo oluthile lwe-fractal, sinokuqinisekisa ukuba xa sisondeza kabini, umzobo uyafana nowokuqala. Ukuba sisondeza nge-factor ye-1000, siqinisekisa iimpawu ezifanayo, ngoko ke ukuba sandisa n, iploti iyafana, ngoko ke inxalenye iyafana nayo yonke.
Ingqokelela okanye into kuthiwa yifractal xa isiba nkulu ngokungenasizathu njengoko isikali sesixhobo sokulinganisa sincipha. Kukho izinto ezininzi eziqhelekileyo ezithathwa njengendalo ngenxa yesakhiwo okanye ukuziphatha kwazo.Nokuba asibazi. Amafu, iintaba, amanxweme, imithi, kunye nemilambo zonke ziziqhekeza zendalo, nangona zinesiphelo kwaye ke azilunganga, ngokungafaniyo neefractals zemathematika ezonwabela infinity kwaye zifanelekile.
Fractals kunye nesayensi
Ubugcisa beFractal bunxulumene ngokusondeleyo nezibalo, ngakumbi ijometri, kuba, njengoko igama layo libonisa, isebenzisa ingqikelelo yeefractals. I-Fractals isekelwe ukuphindaphinda rhoqo ipateni yejometri ehambelanayo, oko kukuthi, inxalenye ilingana nayo yonke.
Xa ukwakhiwa unxantathu we-Sierpinski, ukusuka kunxantathu olinganayo, thatha i-midpoint yayo, wenze unxantathu omtsha olinganayo, kwaye uphelise indawo enye. Yenza okufanayo ngonxantathu ngamnye oseleyo, njalo njalo, ngoko kuthathwa njenge-fractal. UBenoit Mandelbrot, owafumanisa iindlela zezibalo ezaziwa ngokuba ziifractals, usweleke ngenxa yomhlaza eneminyaka engama-85. UMandelbrot, ummi waseFransi nowaseMelika, wavelisa iifractals njengendlela yemathematika yokuqonda ubunzima obungenasiphelo bendalo.
Ukujongana nolwahlulo ukusuka ngokubanzi ukuya kwizinto ezikhethekileyo, sinokuzihlula zibe ziindidi ezimbini ezibanzi: i-fractals ye-deterministic (leyo inokuthi ibe yi-algebraic okanye i-geometric) kunye ne-non-deterministic fractals (eyaziwa nangokuthi i-stochastic fractals).
I-Linear fractals zezo zakhiwe njengoko izikali zihluka, oko kukuthi, ziyafana kuzo zonke izikali. Ngakwelinye icala, iifractals ezingezizo isiphumo sokugqwetheka okuntsokothileyo, okanye njengoko igama licebisa, ukusebenzisa igama kwimathematika enesiphithiphithi, ugqweso olungenamgca.
Ubomi bemihla ngemihla
Ubuninzi bezinto zezibalo nezendalo azinamgca. Kwimathematika, ukuzifanisa, ngamanye amaxesha kubizwa ngokuba kukufana, yipropathi yento (ebizwa ngokuba yinto efanayo) apho yonke iyafana ngokuchanekileyo okanye iphantse ifane nenxalenye enye, umzekelo xa iyonke inento enye enye nangaphezulu kwimilo yamalungu ayo.
I-fractal ibonakaliswe ngomjikelezo othande ukungapheli njenge yongeza iinkcukacha ezincinci nezincinci ngokuphindaphinda okulandelelanayo. Nangona kunjalo, eli gosa alidibanisi naliphi na ixesha lemithintelo yesangqa esijikeleza unxantathu wokuqala. Amafu, iintaba, iinkqubo zokujikeleza kwegazi, unxweme, okanye amahlwantsi ekhephu zonke ziingceba zendalo. Oku kumelwa kuqikelelo ngenxa yokuba iipropati zezinto ezifanelekileyo, njengeenkcukacha ezingapheliyo, zilinganiselwe kwindalo.
Ijometri yeFractal izama ukwenza imodeli kwaye ichaze izinto ezininzi zendalo kunye novavanyo lwesayensi, kwaye kwiminyaka nje embalwa iye yaba yimpumelelo. isixhobo esisetyenziswa ngoosonzululwazi, oogqirha, amagcisa, izazi ngentlalontle, izazi ngezoqoqosho, izazinzulu ngemozulu, iimvumi, izazinzulu ngekhompyutha., Njl
Ndiyathemba ukuba ngolu lwazi unokufunda ngakumbi malunga neefractals kunye neempawu zabo.