Ukuqinisekisa iqiniso leNdalo

UGenesise 1: 1 - “Ekuqaleni uNkulunkulu wadala amazulu nomhlaba”

Uchungechunge 1 - Ikhodi Yendalo - Mathematics

Ingxenye 1 - I-Mandelbrot Equation - Ukukhazimula engqondweni kaNkulunkulu

Isingeniso

Indaba yeMathematics ivame ukuletha enye yezimpendulo ezimbili.

    1. Akunankinga, uma nje akuyona inkimbinkimbi futhi
    2. Angizithandi izibalo zalesi sizathu i-xxxxxx.

Kodwa-ke, noma ngabe kuyiphi impendulo ekuboneni kwegama elithi 'Mathematics' elikukhulayo, qiniseka ukuthi awudingi ukubala noma yiziphi izibalo ukuze ukwazi ukuqonda lobu bufakazi obuhle bokuthi uNkulunkulu ukhona.

Lo mbhalo uzozama ukuveza izizathu zokuqiniseka ukuthi uNkulunkulu ukhona ngempela, owadala zonke izinto, ngokungafani nathi ngokuba lapha ngengozi nje ngomqondo we-Evolution.

Ngakho-ke ngicela uqhubeke nalokhu kuhlolwa nami, ngoba simangalisa ngempela!

Mathematics

Lapho sibona umdwebo omuhle noma omuhle njengokuthi Mona Lisa, singakwazisa lokho, futhi simesabe umenzi wawo yize singeke sifise ukupenda ngale ndlela. Kunjalo nangeMathematics, kungenzeka sikuqonde kahle, kepha sisakwazi ukwazisa ubuhle bayo, ngoba muhle impela!

Yini iMathematics?

    • I-Mathematics isifundo sobudlelwano obuphakathi kwezinombolo.

Yini izinombolo?

    • Bachazwa kahle njenge- a umqondo ngobuningi.

Ziyini izinombolo ke?

    • Izinombolo ezibhaliwe akuzona izinombolo, kuyindlela esiveza ngayo umqondo wamanani ngezinhlobo ezibhaliwe nezibonakalayo.
    • Kumane kuyizimpawu zezinombolo.

Ngaphezu kwalokho, iphuzu elibalulekile okufanele ulikhumbule ukuthi yonke imithetho yezibalo conceptual.

    • Umqondo yinto emelwe engqondweni.

Isisekelo

Sonke sijwayelene ne umqondo kwethi “Isethi”. Ungase ube nesethi yamakhadi okudlala, noma isethi yezicucu ze-chess noma iqoqo lezingilazi zeWayini.

Ngakho-ke, singakwazi ukuqonda ukuthi le ncazelo:

I-SET: = iqoqo lezinto ezinempahla evamile echaziwe.

Ukufanekisa, ikhadi ngalinye lokudlala ngalinye liyinto esethiwe yamakhadi, futhi ngokufanayo isiqeshana se-chess ngasinye siyisici sayo yonke i-chess set. Ngokwengeziwe ingilazi yewayini kungenye yeqoqo lezingilazi zesimo esithile esinezakhiwo eziklanyelwe ukukhipha okungcono kakhulu ewayinini, njengokuhogela, nokubukeka.

Ngokufanayo, kwizibalo, iqoqo lezinombolo iqoqo lezinombolo ezinempahla ethile noma izakhiwo ezichaza lokho kusetha kodwa kungenzeka zingabi kwelinye iqoqo.

Isibonelo, thatha izinombolo ezilandelayo: 0, -2, 1, 2, -1, 3, -3, -½, ½.

Kulezo zinamba ezilandelayo

    • Isethi Engalungile: {-2, -1, -3, -½}
    • Ukusetha Okuvumayo: {1, 2, 3, ½}
    • Iqoqo lamafrakshini: {-½, ½}
    • Inani eliphelele lezinombolo: {1, 2, 3}

Futhi nokunye.

Enye yezinsizakalo ezinjalo isethi iMandelbrot:

Lokhu kusethi lwazo zonke izinombolo (c) formula Zn2 + c = Zn+1 no-Zn ihlala incane.

Kusungulwa izinombolo ingxenye ye-Mandelbrot set

Njengesibonelo, ukubheka ukuthi inombolo 1 iyingxenye yohlelo lweMandelbrot:

Uma u-c = 1 bese uqala nge-Zn = 0.

Ukushintsha lezi zinombolo kule formula esiyitholayo:

(Z) 02 + (c) 1 = 1. Ngakho-ke Zn = 0 no-1.

Okulandelayo kuthatha umphumela we-1, ukubeka i-Z = 1 esikutholayo:

(Z) 12+ (c) 1 = 2.

Okulandelayo kuthatha umphumela we-2, ukubeka i-Z = 2 esikutholayo:

22+1 = 5

Okulandelayo kuthatha umphumela we-5, ukubeka i-Z = 5 esikutholayo:

52+1 = 26

Okulandelayo kuthatha umphumela we-26, ukubeka i-Z = 26 esikutholayo:

262+1 = 677

Ngakho-ke Zn= 0, 1, 2, 5, 26, 677,…

Ngakho-ke singabona ukuthi inani le-c = 1 liyi hhayi ingxenye ye-Mandelbrot isethwe njengoba isibalo asihlali sincane, eqinisweni masinyane sesibe ngama-677.

Ngakho-ke, kuyinto c = -1 ingxenye isethi yeMandelbrot?

Impendulo emfishane inguyebo, njengoba kulandela izinyathelo ezifanayo njengoba kulandelwe ngenhla sithola ukulandelana kwezinombolo okulandelayo.

Kuqala futhi nge-Zn = 0. Ukubuyisela lezi zinombolo kule formula esiyitholayo:

(Z) 02 (c) -1 = -1. Ngakho-ke Zn = -1.

Okulandelayo kuthatha umphumela ka -1, kusethwa i-Z = -1 esikutholayo:

-12 -1 = 0.

Okulandelayo kuthatha umphumela we-0, ukubeka i-Z = 0 esikutholayo:

02-1 = -1

Okulandelayo kuthatha umphumela ka -1, kusethwa i-Z = -1 esikutholayo:

-12 -1 = 0.

Okulandelayo kuthatha umphumela we-0, ukubeka i-Z = 0 esikutholayo:

02-1 = -1

Umphumela uba ukuthi Zn= 0, -1, 0, -1, 0, -1, 0, -1,….

Ngakho-ke siyakubona lokho c = -1 is ingxenye isethi yeMandelbrot njengoba ihlala incane.

Kunokunye futhi umqondo sidinga ukuxoxa njengemuva ngaphambi kokubona ubuhle.

Isethi iMandelbrot nayo iqukethe izinombolo 'zokucabanga'.

    • Isikwele 'senombolo yokuqagela' siyinombolo engemihle.
    • Njengokuthi ku i2= -1 lapho ngiyinombolo yokucabanga.

Ukuzibona ngeso lengqondo zicabanga ngezinga le-x axis yegrafu enezinombolo ezingezinhle ngokusebenzisa zero kuya ezinombolweni ezivumayo. Lapho-ke izembe le-Y liya ngokuqondile lisuka ku-,, ii lidlula ku-zero (iphuzu lesiphikisi se-eksisi ezimbili) liye phezulu ku-½i naku i.

Umdwebo woku-1: Ukubonisa izinombolo ezifikayoKunezinye izinombolo eziseMandelbrot kusetshenziswe kungu-0, -1, -2, ¼, kanti u-1, -3, ½ awekho. Izinombolo eziningi kuleli seti zifaka i, -i, ½i, - ½I, kepha u-2i, u-2i awekho.

Lokho kungukuphela kwazo zonke izibalo eziyinkimbinkimbi.

Manje nakhu lapho kuthakazelisa khona impela!

Imiphumela yale formula

Njengoba ungacabanga ukubala bese uhlela wonke amanani avumelekile futhi angavumelekile ngesandla kungathatha isikhathi eside kakhulu.

Noma kunjalo amakhompyutha angasetshenziswa kahle ukubala izinkulungwane zama-100, ngisho nezigidi zamanani bese ahlela imiphumela yaleli formula ngegrafu.

Ukubona kalula ngamehlo amaphuzu avumelekile amakwe kumnyama, amaphuzu angavumelekile amakwe ngokubomvu, futhi amaphuzu asondele kakhulu, kepha hhayi avumelekile amakwe ngaphuzi.

Uma sisebenzisa uhlelo lwekhompyutha ukwenza lokho, sithola umphumela olandelayo oboniswe ngezansi.

(Ungakuzama ngokwakho ngezinhlelo ezahlukahlukene ze-inthanethi ezinjengokulandelayo:

    1. http://math.hws.edu/eck/js/mandelbrot/MB.html
    2. https://sciencedemos.org.uk/mandelbrot.php
    3. http://www.jakebakermaths.org.uk/maths/mandelbrot/canvasmandelbrotv12.html
    4. http://davidbau.com/mandelbrot/
    5. https://fractalfoundation.org/resources/fractal-software/
    6. https://www.youtube.com/watch?v=PD2XgQOyCCk

)

Umdwebo 2: Umphumela Wokwenza Imephu ye-Mandelbrot equation

Ukutholwa 1

Siqala ukubala amagatsha aphuzi kumabhola amnyama amnyama esikweni esikhulu esimnyama esinjengesimo.

Esiqongweni esikhulu esincane esimnyama ngaphezulu kwendawo enkulu ebunjiwe yezinso esimnyama sinamagatsha ama-3. Uma siqhubekela kumbuthano omncane olandelayo ngakwesobunxele, sithola amagatsha ama-5.

Elikhulu kakhulu ngakwesobunxele linama-7, njalonjalo, 9, 11, 13, njll, zonke izinombolo ezingathandeki ekuthini infinity.

Umdwebo 3: Amagatsha

Ukutholwa 2

Manje, ukuya ngakwesokunene sesimo sezinso esimnyama kusuka phezulu iyazi ukubala. Sithola u-4, 5, 6, 7, 8, 9, 10, nangaphezulu njengokubala kwamagatsha ngaphezulu kwamabhola amnyama amakhulu.

Ukutholwa 3

Kepha asikaqedi. Ukuya kwesobunxele kusuka phezulu, umbuthano omkhulu omnyama kusuka phezulu phakathi kwemibuthano yegatsha engu-3 no-5 unamagatsha ayi-8, isamba samagatsha asuka kwimibuthano ngapha nangapha! Futhi phakathi kuka-5 no-7 umbuthano omncane omnyama unama-12, njalonjalo.

Izibalo ezifanayo zitholakala ziya ngakwesokudla. Ngakho-ke, ibhola elikhulu kunawo wonke phakathi kuka-3 no-4 linamagatsha ayi-7, kuthi phakathi kuka-4 no-5 kube namagatsha ayi-9 nokunye.

Umdwebo 4: Amagatsha angenza nezibalo!

Ukutholwa 4

Ngaphezu kwalokho, lezi zinhlaka zingakhula ngokuqhubekayo, futhi bobunjwa obufanayo bazophinda.

Umdwebo 5: Iphethini efanayo iphindwe kaningi

Icashazi elincane elimnyama ngakwesobunxele komugqa omnyama liya ngakwesobunxele, uma likhuliswe isithombe esifanayo njengoba sibona lapha. Kuyinto engqondo emangalisa ngempela.

Ukutholwa 5

Phakathi kwesimo senhliziyo esikhudlwana nendilinga emnyama enamathiselwe ngakwesobunxele yindawo ebukeka njengesigodi saseSeahorse ukuthola amajamo amahle abonwa lapho.

Umdwebo wesithupha: IsiGodi Sama-Seahorses!

Ukushintsha okubomvu kube luhlaza okwesibhakabhaka nokuphuzi kube mhlophe ngokuhluka okulula, lapho sisondeza kakhulu, sibona amaphethini amahle nokuphindaphindeka okuningi kwephethini eyisisekelo yezinso elimnyama elimiswe ngebhola elinamathiselwe ngakwesobunxele.

Umdwebo 7: Seahorse in closeup

Ukungena endaweni emhlophe egqamile siyabona:

Umdwebo 8: Imininingwane yeWhite whorl enkabeni yeSeahorse

Futhi ukusondeza ngokwengeziwe endaweni ephakathi nendawo sithola okulandelayo:

Umdwebo 9: Sondeza ngokweqile!

Ukungena futhi ngaphezulu sithola enye imilo yethu eyisisekelo:

Umdwebo 10: Leso sakhiwo futhi

Uma sisondeza kokunye kokuvunguza, sithola okulandelayo:

Umdwebo 11: Ukuqondisa Ngokulawula

Futhi enkabeni ye-whirl sithola okulandelayo:

Umdwebo 12: Ngabe amehlo ami nawo ahamba emvunguza?

Ukusondeza futhi phezulu kwesinye sezimpikiswano ezimbili sithola lezi zithombe ezimbili ezilandelayo ezihlanganisa enye futhi eyokuqala ukwakheka kwezinso neMandelbrot.

Umdwebo 13: Lapho ucabanga ukuthi usubonile okokugcina kwalesosimo esimnyama!

Umdwebo 14: Yebo, ubuyile futhi, uzungezwe yiphathini ehlukile

Ukutholwa 6

Ukubuyela esithombeni sethu sokuqala seMandelbrot esethelwe bese siphendukela 'esigodini' ngakwesokunene sokwakheka kwenhliziyo enkulu nokusondeza lapho sibona ukwakheka okunjengendlovu, esizoyiqamba ngokuthi isigodi sendlovu.

Umdwebo 15: Isigodi Sendlovu

Njengoba sisondeza, sithola enye iqoqo lezimo ezinhle kodwa eziphindaphindayo zokubumba ngokulandelayo:

Umdwebo 16: Landela uMhlambi. Hup ezimbili, ezintathu, ezine, imashi Elephant.

Singaqhubeka siqhubeke.

Ukutholwa 7

Ngakho-ke, yini ebangela ubuhle kula ma-Fractals kusuka ku-Mandelbrot equation?

Yebo, ikhompyutha kungenzeka ukuthi isebenzise uhlelo lombala olwenziwe ngumuntu, kepha amaphethini imibala ayiqokomisayo angumphumela wefomula yezibalo ebilokhu ikhona. Ngeke ivele, noma iguquke.

Ubuhle buyingxenye yezibalo, njengoba kunjalo nangobunzima.

Ukutholwa 8

Kungenzeka ukuthi uqaphele igama elilodwa liqhubeka libonakala. Ligama lelo "Umqondo".

  • Umqondo awunqabile ngokwemvelo.
  • Umqondo ukhona kuphela ezingqondweni zethu.

Ukutholwa 9

Lokhu kuphakamisa imibuzo elandelayo ezingqondweni zabantu abacabangayo.

Imithetho yezibalo ivelaphi?

    • Ukuba ngumqondo, kungavela kuphela komunye umqondo, okumele kube kobuhlakani obuphezulu kunokwethu ukuze kuvumeleke endaweni yonke.

Ingabe imithetho yezibalo yavela? Uma kunjalo, babengakwenza kanjani?

    • Izinto ezingalawuleki azikwazi ukuvela njengoba zingezona ezomzimba.

Ngabe abantu basungula noma badala le mithetho yeMaths?

    • Cha, iMithetho yezibalo yayikhona ngaphambi kwabantu.

Ingabe bavela endaweni yonke?

    • Cha, into yoku-oda ayikwazanga ukuvela ngengozi engahleliwe. Umkhathi awunangqondo.

Isiphetho kuphela esingafinyelela kuso ukuthi bekufanele zivela emcabangweni wokuba mkhulu kakhulu kunomuntu. Umuntu okuwukuphela kokuba aqhamuke ngakho ngenxa yalokho kufanele abe ngumenzi wendawo yonke, yingakho evela kuNkulunkulu.

Imithetho yezibalo yile:

    • umcabango,
    • jikelele,
    • ongenelele,
    • izinto ezihlukile.

Zingavela kuphela kuNkulunkulu ngoba:

    • Imicabango kaNkulunkulu ingumbono (u-Isaya 55: 9)
    • UZimu wadala umkhathi (UGenesisi 1: 1)
    • UNkulunkulu akaguquki (Isaya 43: 10b)
    • UNkulunkulu wazi yonke indalo yasezulwini, akukho okushodayo (u-Isaya 40: 26)

iziphetho

    1. Kulokhu kuhlolwa kafushane kwama-fractals kanye ne-Mandelbrot equation sibubonile ubuhle nokuhleleka okuhle kwezibalo nokuklanywa kwendawo yonke.
    2. Lokhu kusinika ukubukisisa engqondweni kaNkulunkulu, okuqukethe ngokusobala ukuhleleka, ubuhle nezinhlobonhlobo ezingenamkhawulo futhi kuwubufakazi bomqondo ohlakaniphe kakhulu kunabantu.
    3. Kubonisa nothando lwayo ukuthi wasinika ubuhlakani ukuze sikwazi ukuthola futhi (omunye umqondo!) Wazise lezi zinto.

Ngakho-ke, masibonise lowo mqondo wokwazisa ngalokho amdalele ngakho futhi njengomdali.

Imiklomelo:

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