I-fractal yinto yejometri engahlukaniswa ibe izingxenye, ngayinye ifane nento yokuqala. Ama-Fractals anemininingwane engapheli futhi avame ukufana nawo futhi afakwe isikali. Ezimweni eziningi, ama-fractals zingakhiqizwa amaphethini aphindaphindayo, izinqubo eziphindaphindayo noma eziphindaphindayo.
Kulesi sihloko sizokutshela konke okudingeka ukwazi mayelana nama-fractals, izici zawo nokubaluleka kwawo.
Izakhiwo zama-fractals
Izici eziyinhloko ezibonisa ama-fractals ukuzifanisa, ubunkimbinkimbi obungapheli kanye nobukhulu.
ukufana kwakho
Ukuzifanisa kulapho ingxenye yomfanekiso noma uhlaka lungabonakala njengomfanekiso walo lonke, esikalini esincane.
ubunkimbinkimbi obungapheli
Kubhekisela eqinisweni lokuthi inqubo yokwakheka kwegrafu iyaphindaphinda. Lokhu kusho ukuthi uma inqubo yenziwa, inqubo eyake yaqalwa ngokwayo itholakala iyinqubo engaphansi kwenqubo yayo.
Kuyaphawuleka ukuthi esimweni sokwakhiwa okuphindaphindiwe kwe-fractal echazwe ngokwezibalo, uhlelo oluzokwenziwa alunamkhawulo, okuholela esakhiweni esiyinkimbinkimbi ngokungapheli.
Ubukhulu
Ngokungafani nejometri ye-Euclidean, Ubukhulu bama-fractals akuwona ngempela amanani aphelele. Kuleli gatsha lezibalo, amaphuzu anobukhulu obuyiziro, imigqa inobukhulu obubodwa, indawo engaphezulu inobukhulu obubili, kanti amavolumu anobukhulu obuthathu. Esimeni se-fractal dimension, leli linani eliyiqhezu elimelela ukuthi isakhiwo sithatha kahle kangakanani isikhala esisiqukethe.
izibonelo zama-fractals
Ama-fractals okuqala afundwa kwakuyisethi ye-Cantor, i-snowflake yase-Koch, kanye nonxantathu we-Sierpinski. Ama-Fractals angatholwa ngokwejometri noma ngokwe-stochastically ngokusebenzisa izinqubo eziphindaphindayo futhi angathatha izici zezinhlobo ezahlukene zomumo ezitholakala emvelweni.
Ama-Fractals akhona yonke indawo. Kunezinto eziningi zemvelo ezibhekwa njengama-fractals emvelo ngenxa yokuziphatha noma ukwakheka kwazo, kodwa lezi izinhlobo ezinomkhawulo zama-fractals, eziwahlukanisa nohlobo lwezibalo oludalwe ukuxhumana okuphindaphindayo. Izibonelo zalokhu amafu nezihlahla.
Izici eziyinhloko
Igama elithi "fractal" livela kwelesiLatini elithi fractus, elisho "ukuhlukana", "ukuphuka", noma nje "ukuphuka" noma "ukuphuka", futhi lifaneleka kahle ezintweni ezinobukhulu obuncane. Leli gama laqanjwa uBenoît Mandelbrot ngo-1977 futhi lavela encwadini yakhe ethi Fractal Geometry of Nature. Ukutadisha izinto ezihlakazekile kuvame ukubizwa ngokuthi i-fractal geometry.
I-fractal isethi yezibalo engajabulela ukuzifanisa kunoma yisiphi isikali, futhi ubukhulu bayo akuwona izinombolo eziphelele, noma uma bekunjalo, bekungeke kube izinombolo ezijwayelekile. Iqiniso lokuthi liyafana lisho ukuthi into eyi-fractal ayincikile kumbukeli uqobo, okungukuthi, uma sithatha uhlobo oluthile lwe-fractal, singaqinisekisa ukuthi uma sisondeza kabili, umdwebo uyafana nowokuqala. Uma sisondeza nge-factory ye-1000, siqinisekisa izakhiwo ezifanayo, ngakho-ke uma sandisa u-n, isakhiwo siyefana, ngakho ingxenye ifana nayo yonke.
Iqoqo noma into kuthiwa i-fractal uma iba nkulu ngokunqumela njengoba isikali sensimbi yokulinganisa sincipha. Kunezinto eziningi ezijwayelekile ezithathwa njengezemvelo ngenxa yesakhiwo noma ukuziphatha kwazo.Noma singabazi. Amafu, izintaba, ugu, izihlahla, kanye nemifula konke kungama-fractals emvelo, noma anomkhawulo ngakho-ke awalungile, ngokungafani nama-fractals ezibalo ajabulela infinity futhi alungile.
Ama-Fractals nesayensi
Ubuciko be-Fractal buhlobene eduze nezibalo, ikakhulukazi i-geometry, njengoba, njengoba igama layo liphakamisa, isebenzisa umqondo wama-fractals. Ama-Fractals asekelwe ekuphindaphindweni okungaguquki kwephethini yejometri ezihlotshaniswa nayo, okungukuthi, ingxenye ilingana nayo yonke.
Lapho wakha unxantathu we-Sierpinski, ukusuka kunxantathu olinganayo, thatha indawo ephakathi nendawo, wakhe unxantathu omusha olinganayo, bese ususa ophakathi nendawo. Bese wenza okufanayo ngonxantathu ngamunye osele, nokunye, ngakho-ke kubhekwa njenge-fractal. U-Benoit Mandelbrot, owathola izimo zezibalo ezaziwa ngokuthi ama-fractals, ubulawe umdlavuza eneminyaka engu-85. UMandelbrot, isakhamuzi saseFrance nesaseMelika, wenze ama-fractals njengendlela yezibalo yokuqonda ubunkimbinkimbi obungapheli bemvelo.
Ukuze sibhekane nokuhlukaniswa kusuka kokujwayelekile kuye kokukhethekile, singawahlukanisa abe izigaba ezimbili ezibanzi: ama-deterministic fractals (okungase kube i-algebraic noma i-geometric) nama-non-deterministic fractals (owaziwa nangokuthi ama-stochastic fractals).
Ama-Linear fractals yilawo akhiwa njengoba izikali zihluka, okungukuthi, afana kuzo zonke izikali. Ngakolunye uhlangothi, ama-Nonlinear fractals, umphumela wokuhlanekezelwa okuyinkimbinkimbi, noma njengoba igama liphakamisa, ukusebenzisa igama kuzibalo ezinesiphithiphithi, ukuhlanekezela okungaqondile.
Impilo yansuku zonke
Izinto eziningi zezibalo nezemvelo azikho emgqeni. Kumathematika, ukuzifanisa, ngezinye izikhathi okubizwa ngokuthi ukuzifanisa, kuyimpahla yento (ebizwa ngokuthi into ezifanisayo) lapho yonke ifana ncamashi noma icishe ifane nengxenye efanayo, isibonelo uma yonke inokufana eyodwa noma ngaphezulu ekumeni kwezingxenye zayo.
I-fractal ibonakala ngomjikelezo ovame ukungapheli njenge engeza imininingwane emincane nemincane ngokuphindaphinda okulandelanayo. Nokho, leli jika alidluleli nganoma isiphi isikhathi sendilinga ezungeza unxantathu wokuqala. Amafu, izintaba, amasistimu wokujikeleza kwegazi, ugu, noma amakhekheba eqhwa wonke ama-fractals emvelo. Lokhu kumelwa kuyahlawumbisela ngoba izakhiwo zezinto ezikahle, njengemininingwane engapheli, zinomkhawulo ngemvelo.
I-Fractal geometry izama ukumodela futhi ichaze izinto eziningi zemvelo nokuhlola kwesayensi, futhi eminyakeni embalwa nje sekuye kwaba ithuluzi lemikhakha eminingi elisetshenziswa ososayensi, odokotela, abaculi, izazi zezenhlalo, osomnotho, izazi zezulu, abaculi, ososayensi bamakhompyutha, Njll
Ngithemba ukuthi ngalolu lwazi ungafunda kabanzi mayelana nama-fractals nezici zawo.