Ukuqinisekisa iNyaniso yendalo

IGenesis 1: 1 - "Ekuqaleni uThixo wadala amazulu nomhlaba"

Uthotho 1-Ikhowudi yokuDala- iMathematics

Inxalenye 1-Inqanaba leMandelbrot-Ukubonakalalisa kwingqondo kaThixo

intshayelelo

Isifundo seMathematics sidla ngokuzisa impendulo ibe nye kwezi zinto zimbini.

1. 1. Akukho ngxaki, ukuba ayiyingxaki kwaye
   2. Andizithandi i-maths ngenxa yesi sizathu i-xxxxxx.

Nangona kunjalo, nayiphi na impendulo ekubonayo igama 'iMathematics' ephakanyisiweyo kuwe, qiniseka ukuba awudingi ukubala naziphi na izibalo ukuze ube nokuqonda obu bungqina buhle bobukho bukaThixo.

Eli nqaku liza kuzama ukuhambisa izizathu zokuqiniseka ukuba ngokwenene ukhona uThixo, owadala zonke izinto, ngokuchasene nathi ukuba silapha ngamabona-ndenzile ngokungathi kunjalo ngakwimfundiso yendaleko.

Ke nceda uqhubeke noluviwo kunye nam, kuba luyamangalisa ngokwenene!

IMathematika

Xa sibona imizobo entle okanye ethandekayo efana ne-Mona Lisa, siyayibulela, simoyike umenzi wayo nangona singenakuze sifune ukupeyinta ngoluhlobo. Kukwanjalo neMathematics, sisenokungayiqondi kakuhle, kodwa sibuxabise ubuhle bayo, kuba intle ngokwenene!

Yintoni iMathematics?

• • IMathematics sisifundo sobudlelwane phakathi kwamanani.

Athini amanani?

• • Bacacelwe gca njenge a Ngcamango ngobungakanani.

Athini ke amanani?

• • Amanani ebhaliweyo ayizizo iinombolo, ziyindlela yokubonisa umbono wento ebhaliweyo nebonakalayo.
  • Yimifuziselo yamanani kuphela.

Ukongeza, ingongoma ephambili ekufuneka uyikhumbule kukuba yonke imithetho yezibalo yile ngcamango.

• • Ingqondo yinto ebekiwe engqondweni.

Isiseko

Sonke siqhelene no Ngcamango ye "Seti". Unokuba neeseti zamakhadi okudlala, okanye iseti yamaqhekeza chess okanye iseti yeiglasi zeewayini.

Ke ngoko, sinokuqonda ukuba le nkcazo:

I-SET: = ingqokelela yezinto ezinepropathi echaziweyo echaziweyo.

Ukwenza umzekelo, ikhadi ngalinye lokudlala liyinto eseti yamakhadi, kwaye ngokufanayo isiqwenga somlinganiso ngamnye sisiseko secandelo lonke le-chess. Ukongeza iglasi ye wayini yenye yeeseti zeglasi zendlela ethile enezinto ezikhutshelwe ukukhupha eyona intle kwi wayini, enje ngevumba, kunye nembonakalo.

Ngokufanayo, kwimathematics, iseti yamanani yingqokelela yamanani nepropathi ethile okanye iipropathi ezichaza isethi kodwa isenokungabikho kwenye ingqokelela.

Umzekelo, thabatha la manani alandelayo: 0, -2, 1, 2, -1, 3, -3, -½, ½.

Kula manani alandelayo yeyakho

• • Iseti engalunganga: {-2, -1, -3, -½}
  • Iseti efanelekileyo: {1, 2, 3, ½}
  • Iseti yamaqhezu: {-½, ½}
  • Inani elipheleleyo leNombolo lilonke: {1, 2, 3}

Kwaye nakanjalo.

Omnye weeseti zeMandelbrot:

Oku kusekwe kuwo onke amanani (c) kwifomula engu-Z_n² + c = Z_n+1 kunye no-Z_n ihlala incinci.

Ukusekwa kwamanani yinxalenye yeseti yeMandelbrot

Umzekelo, ukujonga ukuba inombolo 1 iyinxalenye yeseti yeMandelbrot:

Ukuba u-c = 1 uqalise ngo-Z_n = 0.

Ukutshintsha amanani la kule fomula siyifumana:

(Z) 0² + (c) 1 = 1. Ke ngoko uZ_n = 0 kunye no-1.

Okulandelayo kuthatha isiphumo se-1, ukubeka i-Z = 1 sifumana:

(Z) 1²+ (c) 1 = 2.

Okulandelayo kuthatha isiphumo se-2, ukubeka i-Z = 2 sifumana:

2²+1 = 5

Okulandelayo kuthatha isiphumo se-5, ukubeka i-Z = 5 sifumana:

5²+1 = 26

Okulandelayo kuthatha isiphumo se-26, ukubeka i-Z = 26 sifumana:

26²+1 = 677

Ke uZ_n= 0, 1, 2, 5, 26, 677,…

Singabona ke ukuba ixabiso le-c = 1 ngu hayi Inxalenye ye-Mandelbrot esekwe njengoko inani alihlali lincinci, eqinisweni ngokukhawuleza liye laba yi-677.

Ke, kunjalo c = -1 (Ukuthenga / Ukukhuphela) yinxalenye yeseti yeMandelbrot?

Impendulo emfutshane ngu-ewe, njengoko ulandela la manyathelo alandelayo xa elandelwa ngasentla sifumana ukulandelelana kwamanani.

Ukuqala kwakhona nge-Z_n = 0. Ukutshintsha la manani kule fomyula sifumana:

(Z) 0² (c) -1 = -1. Ke ngoko uZ_n = -1.

Okulandelayo ngokuthatha isiphumo -1, ukuseta Z = -1 sifumana:

-1² -1 = 0.

Okulandelayo kuthatha isiphumo se-0, ukubeka i-Z = 0 sifumana:

 0²-1 = -1

Okulandelayo ngokuthatha isiphumo -1, ukuseta Z = -1 sifumana:

-1² -1 = 0.

Okulandelayo kuthatha isiphumo se-0, ukubeka i-Z = 0 sifumana:

 0²-1 = -1

Isiphumo kukuba Z_n= 0, -1, 0, -1, 0, -1, 0, -1,….

Ke siyayibona loo nto c = -1 is Inxalenye ye-Mandelbrot esekwe njengoko ihlala ihlala incinci.

Kukho enye ngaphezulu Ngcamango Kufuneka sixoxe ngemvelaphi ngaphambi kokuba babone ubuhle.

Iseti ye-Mandelbrot ikwanamanani 'wokucinga'.

• • Isikweri senani 'elifikelelweyo' linani elingelilo.
  • Njengakwi i²= -1 apho ndiyinombolo yokucinga.

Ukubabona ngamehlo bacinga nge-axis engqameneyo yegrafu enamanani aNgekhoyo ukuya ku-zero ukuya kumanani aqinisekileyo. Emva koko i-Y axis ihamba ngokuthe nkqo ukusuka -i, -i ukuya kwi-zero (indawo enqamlezileyo ye-axis ezimbini) kwaye inyuka uye ku-i kunye no-i.

Umzobo 1: Ukubonisa amanani aqikelelweyoAmanye amanani kwiseti ye-Mandelbrot zii-0, -1, -2, ¼, ngelixa i-1, -3, ½ azikho. Amanani amaninzi kule seti abandakanya i, -i, ½i, - ½I, kodwa 2i, -2i awunguye.

Eso sisiphelo sazo zonke izibalo ezinzima.

Ngoku kulapho apho inomdla khona ngokwenene!

Iziphumo zale fomyula

Njengoko unokucinga ukubala kwaye emva koko ucebe onke amaxabiso avumelekileyo nesandla ngesandla kuya kuthatha ixesha elide.

Nangona kunjalo iikhompyuter zinokusetyenziswa kakuhle ukubala i-100 lamawaka, kunye nezigidi zexabiso kwaye emva koko ucwangcise iziphumo zale formula ngokubonakalayo kwigrafu.

Ukuchonga ngokulula ngamehlo amanqaku avumayo amakishwe kumnyama, amanqaku angasebenziyo aphawulwa ngombala obomvu, kwaye amanqaku asondeleyo kakhulu, kodwa engangqinelaniyo abhalwe ngatyheli.

Ukuba sisebenzisa inkqubo yekhompyuter ukwenza oko, sifumana ezi ziphumo zilandelayo ziboniswe ngezantsi.

(Ungayizamela ngokwakho ngeenkqubo ezahlukeneyo ze-intanethi ezinje ngezi zilandelayo:

1. 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

)

Umzobo wesi-2: Iziphumo zeMephu ye-Mandelbrot equation

Ukufunyanwa 1

Siqala ukubala amasebe aphuzi kwiibhola ezinkulu ezimnyama kwizinyo elikhulu elimnyama njengezimilo.

Kwisangqa esincinci esincinci esimnyama ngaphezulu kwendawo enkulu enezintso zomnyama sinee-3. Ukuba siqhubela kwisangqa esincinci esincinci kwicala lasekhohlo, sifumana amasebe ama-5.

Elikhulu likhulu ngasekhohlo linesi-7, njalo njalo, 9, 11, 13, njl, onke amanani angaqhelekanga kwinto engaqhelekanga.

Umzobo 3: Amasebe

Ukufunyanwa 2

Ngoku, uye ngasekunene kobume bezintso ezimnyama ukusuka phezulu iyazi ukubala. Sifumana i-4, 5, 6, 7, 8, 9, 10, nangaphezulu njengokubalwa kwamasebe aphezulu kweyona bhola imnyama.

Ukufunyanwa 3

Kodwa okwangoku asikagqibi. Ukuya ngasekhohlo ukusuka phezulu, esona sangqa sikhulu simnyama ukusuka phezulu phakathi kwendawo ezi-3 ukuya kwezi-5 kwisebe elinamasebe asi-8, inani lamasebe avela kwizangqa ngapha nangapha! Kwaye phakathi kwesi-5 nesi-7 isangqa esincinci esimnyama sine-12, njalo njalo.

Izibalo ezifanayo zifunyanwa zisiya ngasekunene. Ke, eyona bhola inkulu phakathi kwe-3 ne-4 inamasebe asi-7, kwaye phakathi kwe-4 ne-5 inamasebe ayi-9 njalo njalo.

Umzobo wesi-4: Amasebe anokwenza nezibalo!

Ukufunyanwa 4

Ngapha koko, ezi milo zinokukhula ngokuqhubekayo, kwaye iimilo ezifanayo ziya kuphinda.

Umzobo 5: Ipateni efanayo iphindaphindwa ngokungenasiphelo

Ichaphaza elincinci elimnyama kwicala lasekhohlo lomgca omnyama liya ngasekhohlo, ukuba likhulisiwe umfanekiso ofanayo njengoko sibona apha. Kusengqondweni ngokwenene.

Ukufunyanwa 5

Phakathi kobume bentliziyo obukhulu kunye nesangqa esimnyama esincamathele kwicala lasekhohlo yindawo ekhangeleka ngathi yintlambo yeSeahorse malunga neemilo ezintle ezibonwe apho.

Umzobo 6: Intili yeelwandle!

Ukutshintsha ubomvu kube luhlaza okwesibhakabhaka kunye nobutyheli ukuze kube mhlophe ngokuchaseneyo, xa sisondela kufutshane, sibona iipateni ezintle kunye nokuphindaphinda okungaphezulu kwepateni esisiseko yeentso ezimnyama-zenziwe ngebhola eqhotyoshelweyo ngasekhohlo.

Umzobo wesi-7: I-Seahorse ngokusondeleyo

Ukungena kwindawo emhlophe eqaqambileyo sibona:

Umzobo wesi-8: Iinkcukacha zeWhite whorl embindini weSeahorse

Kwaye ukusondeza ngakumbi nangakumbi kwindawo yeziko sifumana oku kulandelayo:

Umzobo 9: Ukusondeza ngaphezulu!

Ukungena ngakumbi nangakumbi sifumana enye yeesimo zethu ezisisiseko:

Umzobo 10: Ubume bayo kwakhona

Ukuba sisondeza kwenye yeembalasane, sifumana oku kulandelayo:

Umzobo 11: UkuLawulwa kokuLawulwa

Kwiziko le-whirl sifumana oku kulandelayo:

Umzobo 12: Ngaba imehlo lam lihamba kukuntywila?

Ukusondeza ngakumbi kwenye yeziqhwithi zimbini sifumana le mifanekiso mibini ibandakanya enye ukuqala kweMandelbrot imilo yezintso kunye nebhola.

Umzobo 13: Xa kanye wawucinga ukuba ubonile okokugqibela kolo bumnyama!

Umzobo 14: Ewe, ubuyile kwakhona, ujikelezwe yipatheni entle

Ukufunyanwa 6

Ukubuyela kumfanekiso wethu wokuqala weMandelbrot esetiweyo kwaye siguqukele 'entlanjeni' esekunene kwicala lesimo sentliziyo enkulu kunye nokusondeza sibona imilo efana nendlovu, esiya kuyibiza ngegama lendlovu.

Umzobo 15: Intili yeNdlovu

Xa sisondeza, sifumana enye iseti yemihle kodwa eyahlukileyo ephindaphindayo yeemilo ngolu hlobo lulandelayo:

Umzobo 16: Landela umhlambi. Hup ezimbini, ezintathu, ezine, Matshi Elephant.

Singaqhubeka siqhubeke.

Ukufunyanwa 7

Ke, yintoni ebangela ubuhle kwezi Fractals zisuka kwi-Mandelbrot equation?

Ewe, ikhompyuter inokuthi isebenzise isikimu sombala esenziwe ngumntu, kodwa iipateni eziboniswa yimibala sisiphumo sefomula yemathematics ehlala ihleli ikho. Ayinakuvela, okanye itshintshe.

Ubuhle bunomdla kwezibalo, njengoko kunjalo nangobunzima.

Ukufunyanwa 8

Usenokuba uqaphele ukuba igama elinye lihlala libonakala. Elo lizwi "Umbono".

• Umxholo awunakuqondwa kwindalo.
• Umxholo ukhoyo ezingqondweni zethu.

Ukufunyanwa 9

Oku kuphakamisa le mibuzo ilandelayo kwiingqondo zabantu abacinga.

Ivela phi imithetho yemathematics?

• • Ukuba ingumbono, banokuvela kuphela ngengqondo enye, ekufuneka bekrelekrele ngakumbi kunesethu ukuba isebenze kwindalo iphela.

Ngaba imithetho yemathematics yavela? Ukuba kunjalo, banokwenza njani?

• • Izinto ezingavakaliyo azikwazi ukuvela njengoko zinjalo ngokwasemzimbeni.

Ngaba abantu bayile okanye bayila le mithetho yeMathematics?

• • Hayi, imithetho yeMathematics yayikhona ngaphambi kwabantu.

Ngaba zivela kwindalo iphela?

• • Hayi, into ye-odolo ayinakuvela ngamathuba angenamda. Indawo yonke ayinangqondo.

Isiphelo esinokufikelela kuso kukuba babezokuvela kwingqondo yokuba bakhulu kakhulu emntwini. Ekuphela kwento abanokuthi bavele kuyo ngenxa yoko kufanele ukuba ibe ngumyili wehlabathi, ke ngoko liphuma kuThixo.

Imithetho yemathematics yile:

• • concepts,
  • jikelele
  • ongenamntu,
  • izinto ezingabalulekanga.

Banokuvela kuphela kuThixo kuba:

• • Iingcamango zikaThixo ziyinyani (Isaya 55: 9)
  • UThixo wadala indalo yonke (Genesis 1: 1)
  • UThixo akaguquki (Isaya 43: 10b)
  • UThixo uyazi yonke indalo yasezulwini, akukho nto ilahlekileyo (u-Isaya 40: 26)

izigqibo

1. 1. Kolu vavanyo lufutshane lwee-fractals kunye ne-Mandelbrot equation sibubonile ubuhle kunye nokulandelelana okungaphakathi kwiMathematics kunye nokuyilwa kwendalo.
   2. Oku kusinika umbono engqondweni kaThixo, ngokucacileyo enolungelelwano, ubuhle kunye nobuhle obungenasiphelo kwaye ubungqina bokuba nengqondo ekrelekrele ngakumbi kunabantu.
   3. Ikwabonisa uthando lwakhe kuba wasinika ubukrelekrele ukuze sikwazi ukufumanisa kwaye (enye ingcinga!) Siyazixabisa ezi zinto.

Masibonise ke loo nto yokuxabisa uxabiso ngezinto azidalileyo nezithi zimdalele.

Izibongozo:

Ndinombulelo ongazenzisiyo ngenkxaso enikezwe yividiyo yeYouTube "Ikhowudi efihlakeleyo yokuDalwa" kwiCustoms Series kaCornerstone Television Network.

Ukusetyenziswa ngokuchanekileyo: Eminye yemifanekiso esetyenzisiweyo inokuba ingabinamalungelo okushicilela, ukusetyenziswa kwayo okungasoloko kugunyaziswa ngumnini welungelo lokushicilela. Senza ezi zinto zifumaneke kumzamo wethu wokuqhubela phambili ukuqonda ngemicimbi yezenzululwazi nezenkolo, njl njl. Sikholelwa ukuba oku kuzisa ukusetyenziswa ngokuchanekileyo kwazo naziphi na izinto ezinamalungelo okushicilela njengoko kubonelelwe kwicandelo lama-107 lomthetho wamalungelo obunini baseMelika. Ngokuhambelana nesihloko se-17 se-USC Icandelo le-107, izinto ezikule ndawo zenziwe ukuba zifumaneke ngaphandle kwenzuzo kwabo bavakalisa umdla wokufumana nokujonga izinto zophando kunye neenjongo zemfundo. Ukuba unqwenela ukusebenzisa izinto ezinamalungelo okushicilela ezingaphaya kokusetyenziswa ngokufanelekileyo, kufuneka ufumane imvume kumnini welungelo lokushicilela.

ITadua

Amanqaku nguTadua.