Kuzindikira Choonadi cha Zachilengedwe

Genesis 1: 1 - "Pachiyambi Mulungu Adalenga Zakumwamba ndi Dziko Lapansi '

Mndandanda 1 - Code ya Chilengedwe - Masamu

Gawo 1 - Kukula kwa Mandelbrot - Kuwala pang'ono m'malingaliro a Mulungu

Introduction

Mutu wa Masamu umabweretsa yankho limodzi mwanjira ziwiri.

1. 1. Palibe vuto, bola sizovuta kwambiri komanso
   2. Sindikonda masamu pazifukwa izi xxxxxx.

Komabe, mulimonse momwe anthu angagwiritsire ntchito liwu la 'Mathematics' mwa inu, dziwani kuti simuyenera kuwerengera masamu kuti mumvetse umboni wokongola wopezeka kuti Mulungu alipo.

Nkhaniyi iyesetsa kupereka zifukwa zokhulupirira kuti kulidi Mulungu, amene adalenga zonse, osati ife mwangozi chabe monga chonena chiphunzitso cha chisinthiko.

Chifukwa chake chonde pitilizani mayeso awa ndi ine, chifukwa ndi odabwitsa!

masamu

Tikaona penti yokongola kapena yokopa monga ya Mona Lisa, timatha kuyiyamika, komanso kukhala ndi chidwi ndi omwe adatipanga ngakhale sitingafune kupenda utoto wotere. Zilinso ndi Masamu, mwina sitingazimvetse, koma timayamikirabe kukongola kwake, chifukwa kulidi kokongola!

Masamu ndi chiyani?

• • Masamu ndi kuphunzira pa ubale pakati pa ziwerengero.

Manambala ndi chiyani?

• • Amafotokozedwa bwino kwambiri ngati a lingaliro zochuluka.

Manambala ndi chiyani ndiye?

• • Manambala olembedwa si manambala, ndi momwe timafotokozera tanthauzo la manambala polemba ndi mawonekedwe.
  • Zangoyimira ziwerengero.

Kuphatikiza apo, mfundo yofunika kukumbukira ndikuti malamulo onse a masamu ndi malingaliro.

• • Lingaliro ndi kanthu kena kamalingaliro.

Maziko

Tonse tikudziwa lingaliro za "Seti". Mutha kukhala ndi makadi osewerera, kapena zidutswa za chess kapena magalasi a Wine.

Chifukwa chake, titha kumvetsetsa kuti tanthauzo lake:

SET: = mndandanda wa zinthu zomwe zili ndi katundu wamba.

Mwachitsanzo, khadi yamasewera aliyense payokha ndi gawo la makadi onse, momwemonso gawo lililonse la chess ndi gawo lazinthu zonse za chess. Kuphatikiza apo galasi la vinyo ndi amodzi mwa magalasi okhala ndi mawonekedwe enaake omwe ali ndi zinthu zomwe zimapangidwa kuti zizitulutsa zabwino kuchokera ku vinyo, monga fungo, komanso mawonekedwe.

Momwemonso, m'masamu, manambala ndi mndandanda wa zinthu zomwe zili ndi katundu kapena katundu yemwe amatanthauzira zomwe sizikupezeka koma sizingakhale pagulu lina.

Mwachitsanzo, tengani manambala otsatirawa: 0, -2, 1, 2, -1, 3, -3, -½, ½.

Mwa manambala otsatirawa ndi a

• • Zoipa Zoyipa: {-2, -1, -3, -½}
  • Chowonadi Chabwino: {1, 2, 3, ½}
  • Zigawo Zosanjidwa: {-½, ½}
  • Chiwerengero Chokwanira: {1, 2, 3}

Ndi zina zotero.

Chimodzi mwazomwezi ndi ma Mandelbrot:

Ili ndiye dongosolo la manambala onse (c) momwe formula Z_n² + c = Z_n+1 ndi Z_n amakhalabe ocheperako.

Kukhazikitsa manambala gawo la Mandelbrot

Mwachitsanzo, kuwunika ngati nambala 1 ndi gawo la Mandelbrot:

Ngati c = 1 ndiye kuyamba ndi Z_n = 0.

Kusintha manambala munjira iyi yomwe timapeza:

(Z) 0² + (c) 1 = 1. Chifukwa chake Z_n = 0 ndi 1.

Pambuyo potengera zotsatira za 1, kukhazikitsa Z = 1 tikupeza:

(Z) 1²+ (c) 1 = 2.

Pambuyo potengera zotsatira za 2, kukhazikitsa Z = 2 tikupeza:

2²+ 1 = 5

Pambuyo potengera zotsatira za 5, kukhazikitsa Z = 5 tikupeza:

5²+ 1 = 26

Pambuyo potengera zotsatira za 26, kukhazikitsa Z = 26 tikupeza:

26²+ 1 = 677

Chifukwa chake Z_n= 0, 1, 2, 5, 26, 677,…

Titha kuwona kuti mtengo wa c = 1 ndi osati gawo la Mandelbrot lakhazikitsidwa popeza chiwerengero sichikhala chochepa, kwenikweni mwachangu chakhala 677.

Chifukwa chake, ndi c = -1 gawo la Mandelbrot?

Yankho lalifupi ndilakuti inde, potsatira njira zomwezo monga tawatsata pamwambapa timapeza zotsatizana za manambala.

Kuyambanso ndi Z_n = 0. Kuchotsa manambala mu fomuyi timapeza:

(Z) 0² (c) -1 = -1. Chifukwa chake Z_n = -1.

Chotsatira potenga zotsatira za -1, kukhazikitsa Z = -1 tikupeza:

-1² -1 = 0.

Pambuyo potengera zotsatira za 0, kukhazikitsa Z = 0 tikupeza:

 0²-1 = -1

Chotsatira potenga zotsatira za -1, kukhazikitsa Z = -1 tikupeza:

-1² -1 = 0.

Pambuyo potengera zotsatira za 0, kukhazikitsa Z = 0 tikupeza:

 0²-1 = -1

Zotsatira zake ndikuti Z_n= 0, -1, 0, -1, 0, -1, 0, -1,….

Chifukwa chake titha kuwona c = -1 is gawo la Mandelbrot lokhalamo nthawi zonse limakhala laling'ono.

Palinso ina lingaliro tiyenera kukambirana ngati maziko tisanawone kukongola.

Seti ya Mandelbrot ilinso ndi manambala 'oyerekeza'.

• • Kukula kwa 'nambala yolingalira' ndi nambala yolakwika.
  • Monga mu i²= -1 kumene ndili nambala yolingalira.

Kuti muwone m'maganizo mwawo akuganiza za axis yopingasa ya graph yomwe ili ndi manambala olakwika kudzera pa zero mpaka manambala Oyenera. Kenako olamulira a Y akuyenda motsetsereka kuchokera -i, - throughi kudutsa zero (chopingasa cha olamulira awiriwo) ndikukwera mpaka ½i ndi i.

Chithunzi 1: Kuwonetsa manambala olosera: Manambala ena mu Mandelbrot seti ndi 0, -1, -2, ¼, pomwe 1, -3, ½ sali. Manambala ambiri m'ndandanda iyi akuphatikizapo i, -i, ½i, - ½I, koma 2i, -2i sali.

Awo ndi mathero a masamu onse ovuta.

Tsopano ndipamene zimakhala zosangalatsa kwambiri!

Zotsatira za formula iyi

Monga momwe mungaganizire kuwerengera kenako ndikukonzekera mfundo zonse zovomerezeka ndi dzanja zimatenga nthawi yayitali.

Komabe makompyuta angagwiritsidwe ntchito bwino kwambiri kuwerengera anthu masauzande 100, ngakhale mamiliyoni azitsulo kenako kukonzekera zotsatira za fomuloli pa graph.

Kuti muzindikire mosavuta ndi maso mfundo zovomerezeka zidalembedwa zakuda, mfundo zosavomerezeka zidalembedwa zofiira, ndipo malowo omwe ali pafupi kwambiri, koma osavomerezeka amalembedwe chikaso.

Ngati timayendetsa pulogalamu ya pakompyuta kuchita izi, timapeza zotsatirazi zomwe zikuwonetsedwa pansipa.

(Mutha kuyesa nokha ndi mapulogalamu osiyanasiyana pa intaneti monga awa:

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

)

Chithunzi 2: Zotsatira Zakujambula Mapu a Mandelbrot

Kupeza 1

Timayamba kuwerengera nthambi zachikaso pamipira yayikulu yakuda pa impso yayikulu yakuda ngati mawonekedwe.

Pamndandanda wakuda wakuda pamwamba pa malo akulu okumbidwa ndi impso tili ndi nthambi zitatu. Tikasamukira ku bwalo laling'ono kwambiri kumanzere, timapeza nthambi 3.

Ukulu wotsatira wakumanzere uli ndi 7, ndi zina zotero, 9, 11, 13, ndi zina, manambala onse osamvetseka mpaka kutsika kopanda tanthauzo.

Chithunzi 3: Nthambi

Kupeza 2

Tsopano, kupita kumanja kwa mawonekedwe a impso yakuda kuchokera pamwamba amadziwa momwe ungawerengere. Timalandira 4, 5, 6, 7, 8, 9, 10, ndi mtsogolo monga kuwerengera kwa nthambi kumtunda kwa mipira yayikulu yakuda.

Kupeza 3

Koma sitinamalizebe. Kupita kumanzere kuchokera kumtunda, bwalo lakuda kwambiri kuchokera pamwamba pakati pa 3 ndi 5 nthambi kukhala ndi nthambi 8, kuchuluka kwa nthambi kuchokera kuzungulira mbali zonse! Pakati pa 5 ndi 7 mzere wakuda wozungulira uli ndi 12, ndi zina zotero.

Zowonjezera zomwezo zimapezeka ndikupita kumanja. Chifukwa chake, mpira waukulu kwambiri pakati pa 3 ndi 4 uli ndi nthambi 7, ndipo pakati pa 4 ndi 5 ali ndi nthambi 9 ndi zina zotero.

Chithunzi 4: Nthambi zimathanso kuchita masamu!

Kupeza 4

Kuphatikiza apo, mawonekedwe awa akhoza kukulitsidwa mosalekeza, ndipo mawonekedwe omwewo abwereza.

Chithunzi 5: Matchulidwe amodzimodziwo anabwereza

Dontho lakuda lakumanzere chakumanzere kwa mzere wakuda ndikupita kumanzere, ngati kukulitsidwa ndi chithunzi chomwechi monga tikuonera apa. Ndi malingaliro odabwitsa.

Kupeza 5

Pakati pa mawonekedwe akulu a mtima ndi bwalo lakuda lakumanzere ndi malo omwe akuwoneka ngati chigwa cha Seahorse pazithunzi zokongola zomwe zidawoneka pamenepo.

Chithunzi 6: Chigwa cha Seahorses!

Kusintha ofiira kukhala mtundu wamtambo ndi wachikaso kuti kuyera kukhala kosavuta, tikayandikira pafupi, tikuwona mawonekedwe okongola ndi kubwereza kowonjezereka kwa mawonekedwe oyambira a impso yakuda yoyumba ndi mpira womata kumanzere.

Chithunzi 7: Seahorse pafupi

Tikuyandikira pa malo oyera omwe timawona:

Chithunzi 8: Tsatanetsatane wa whorish whorl pakati pa Seahorse

Ndipo powonjezeranso zowonjezera pamtunda pomwe tikupezapo zotsatirazi:

Chithunzi 9: Wonjezerani!

Kubwereranso pamenepo tikupeza mawonekedwe athu ena:

Chithunzi 10: Mawonekedwe ake kachiwiri

Ngati tikhalanso mwamtopola, timalandira izi:

Chithunzi 11: Kuwongolera Pakulamulira

Ndipo pakatikati pa kamvuluko timalandira izi:

Chithunzi 12: Kodi maso anga akulowanso maluwa?

Kubwereranso mbali imodzi mwa malupanga awiriwo timalandira zithunzi ziwiri zotsatirazi zomwe zikuphatikizanso chithunzi china cha impso ya Mandelbrot ndi mpira.

Chithunzi 13: Pomwe munangoganiza kuti mwawona chomaliza cha mawonekedwe akuda aja!

Chithunzi 14: Inde, yabwerera, yazunguliridwa ndi mawonekedwe ena okongola

Kupeza 6

Kubwereranso ku chithunzi chathu choyamba cha Mandelbrot tidayang'ana ndikutembenukira ku 'chigwa' kudzanja lamanja la mawonekedwe akulu mtima ndikuyandikira tikumawona mawonekedwe ngati a Njovu, omwe tidzawatcha chigwa cha Elephant.

Chithunzi 15: Chigwa cha Njovu

Tikamayandikira, timapeza mawonekedwe ena okongola koma osiyanasiyana obwereza motere:

Chithunzi 16: Tsatirani Mchidwi. Anthu awiri, atatu, anayi, azungulira.

Titha kumangopitilirabe.

Kupeza 7

Chifukwa chake, nchiyani chimapangitsa kukongola mu Fractals izi kuchokera ku equation ya Mandelbrot?

Inde, kompyuta ikhoza kugwiritsa ntchito njira yopangidwa ndi anthu, koma mawonekedwe omwe mitundu imawonetsa ndi chifukwa cha mtundu wa masamu womwe unakhalapo kuyambira kale. Sizingasinthe, kapena kusintha.

Kukongola kwake kumakhudza masamu, monganso momwe zovuta.

Kupeza 8

Muyenera kuti mwazindikira kuti mawu amodzi akupitilirabe. Mawu oti "Lingaliro".

• Lingaliro silabisika mu chilengedwe.
• Lingaliro limangokhala mu malingaliro athu.

Kupeza 9

Izi zimadzutsa mafunso otsatirawa m'maganizo a anthu oganiza.

Kodi malamulo a masamu amachokera kuti?

• • Pokhala lingaliro, zimatha kungobwera kuchokera ku malingaliro ena, omwe ayenera kukhala anzeru zapamwamba kuposa zathu kuti azikhala ovomerezeka m'chilengedwe chonse.

Kodi malamulo a masamu anakhalako? Ngati ndi choncho, akanatha bwanji?

• • Zinthu zonyansa sizingasinthe popeza sizachilengedwe.

Kodi anthu adapanga kapena kupanga malamulo awa a Maths?

• • Ayi, Malamulo a masamu adalipo pamaso pa anthu.

Kodi zimachokera kumwamba?

• • Ayi, china chake chadongosolo sichingachokere mwachisawawa. Thambo lilibe malingaliro.

Mapeto ake omwe timafika ndikuti amayenera kuchokera ku lingaliro la kukhala wamkulu kwambiri kuposa munthu. Chokhacho chomwe chitha kukhalapo chifukwa chake ndiyenera kukhala mlengi wa chilengedwe chonse, motero kuchokera kwa Mulungu.

Malamulo a masamu ndi:

• • malingaliro
  • konsekonse,
  • wolowerera,
  • mabungwe ochepera.

Amatha kubwera kuchokera kwa Mulungu chifukwa:

• • Malingaliro a Mulungu ndiwotsimikizika (Yesaya 55: 9)
  • Mulungu adalenga chilengedwe chonse (Genesis 1: 1)
  • Mulungu sasintha (Yesaya 43: 10b)
  • Mulungu amadziwa zolengedwa zonse zakumwamba, palibe chosowa (Yesaya 40:26)

Mawuwo

1. 1. M'maphunzirowa pang'onopang'ono pa ma fractals ndi Mandelbrot equation tawona kukongola komanso makonzedwe achilengedwe mu Masamu ndi kapangidwe ka chilengedwe.
   2. Izi zikutiuza pang'ono m'malingaliro a Mulungu, omwe ali ndi dongosolo, kukongola ndi mitundu yosiyanasiyana ndipo ndi umboni kwa anthu anzeru kuposa anthu.
   3. Zimawonetseranso chikondi chake popeza adatipatsa luntha kuti tizitha kuzindikira (lingaliro lina!) Kuyamika zinthu izi.

Chifukwa chake tiwonetsere lingaliro lakelo la kuyamika pazomwe adamulenga komanso monga iye mlengi.

Zikomo:

Tithokoze kwambiri chifukwa cha Kukhudzidwa komwe kwatumizidwa ndi kanema wa YouTube "The Code Code of Creation" kuchokera pa Sourceins Series ya Cornerstone Television Network.

Kugwiritsa Ntchito Bwino: Zina mwa zithunzi zomwe zimagwiritsidwa ntchito kukhala ndi ufulu wokhala nazo, kugwiritsidwa ntchito kwake komwe kumakhala sikuvomerezedwa ndi eni ufulu. Tikupanga zinthu ngati izi kuti tithe kupititsa patsogolo kumvetsetsa kwa nkhani za sayansi ndi zipembedzo, etc. Tikukhulupirira kuti izi ndizoyenera kugwiritsa ntchito pazinthu zokhala ndi ufulu monga zomwe zaperekedwa mgawo la 107 la US Copyright Law. Malinga ndi mutu 17 USC Gawo 107, zomwe zili patsamba lino zimapezeka popanda phindu kwa iwo omwe ali ndi chidwi chofuna kulandira ndikuwona zomwezi pazakufufuza kwawo komanso zolinga zawo. Ngati mukufuna kugwiritsa ntchito zinthu zomwe zili ndi copyright zomwe sizingagwiritsidwe ntchito moyenera, muyenera kupeza kaye chilolezo kuchokera kwa eni ake.

Tadua

Zolemba za Tadua.