Kuita chokwadi cheChisiko

Genesisi 1: 1 - "Pakutanga Mwari akasika matenga nepasi"

Nyaya 1 - Kodhi yeKusika - Masvomhu

Chikamu chekutanga - Mandelbrot equation - Kujeka mupfungwa dzaMwari

ziviso

Nyaya yeMathematics inowanzounza imwe yemhinduro mbiri.

1. 1. Hapana dambudziko, chero zvaro harisi rakawandisa uye
   2. Handidi maths dzeichi chikonzero xxxxxx.

Nekudaro, chero mhinduro yaionekwa izwi rekuti 'Mathematics' rakanyorwa mauri, zorora haufanire kuverenga chero maths kuti uzokwanisa kunzwisisa uhwu uchapupu hwakanaka hwekuvapo kwaMwari.

Chinyorwa ichi chichaedza kuburitsa zvikonzero zvekuvimba kuti zvechokwadi kuna Mwari, iye akasika zvinhu zvese, kupesana nesu isu tiri pano nemukana wekupofumadza sedzidziso yeEvolution.

Saka ndapota ramba uchiongorora neni iyi bvunzo, nekuti zvinoshamisa zvechokwadi!

masvomhu

Kana taona yakanaka kana inokwezva pendi yakadai sa Mona Lisa, tinogona kuikoshesa, uye nekutya musiki wayo kunyangwe isu hatife takashuva kupenda nenzira yakadaro. Zvakafanana neMasvomhu, tinogona kunge tisinga nzwisise iyo, asi isu tinogona vachiri kukoshesa runako rwayo, nekuti zvirokwazvo yakanaka!

Chii chinonzi Mathematics?

• • Masvomhu ndiko kudzidza kwehukama huripo pakati pehuwandu.

Chii chinhamba?

• • Ivo vanonyatsotsanangurwa se pfungwa nezvakawanda.

Chii chiri nhamba ipapo?

• • Akanyorwa manhamba haasi nhamba, ndiwo maitiro atinoratidza isu pfungwa yehuwandu mune yakanyorwa uye inoonekwa fomu.
  • Iwo anongova mamiririri enhamba.

Uyezve, chinhu chakakosha chekuisa mupfungwa ndechekuti mitemo yese yemasvomhu iri Conceptual.

• • Pfungwa chimwe chinhu chakafungwa mupfungwa.

Basis

Tese tinoziva pfungwa ye "Set". Iwe unogona kunge uine seti yemakadhi ekutamba, kana seti yemaseke chess kana seti yemagirazi ewaini.

Naizvozvo, tinogona kunzwisisa kuti tsananguro:

SET: = kuunganidzwa kwezvinhu zvine zvakajairika zvakatsanangurwa chivakwa.

Kuenzanisira, imwe neimwe kadhi yekutamba chimwe chinhu cheseti yakazara yemakadhi, uye saizvozvo munhu wega chess chidimbu chinhu chese chess yakaiswa. Pamusoro pezvo girazi rewaini ndeimwe yemitsetse yegirazi yeimwe chimiro ine zvivakwa zvakagadzirwa kuti zvibudise zvakanakisa kubva kune waini, sekunhuhwirira, uye kutaridzika.

Saizvozvo, mune maths, seti yenhamba ndeyekuunganidzwa kwehuwandu neine imwe nzvimbo kana zvivakwa zvinotsanangura iyo yakaisa asi inogona kunge isiri mune imwe kuunganidzwa.

Semuenzaniso, tora nhamba dzinotevera: 0, -2, 1, 2, -1, 3, -3, -½, ½.

Pane idzo nhamba dzinotevera ndezvedu

• • Yakasarudzika Seta: {-2, -1, -3, -½}
  • Yakanaka Set: {1, 2, 3, ½}
  • Zvidimbu Zvinoiswa: {-½, ½}
  • Iyo Nhamba Yese Yakanaka: {1, 2, 3}

Zvichingodaro.

Imwe yakadaro seyeMandelbrot yakaiswa:

Uku ndiko kuseta kwenhamba dzese (c) iyo formula Z_n² + c = Z_n+1 uye Z_n inoramba iri diki.

Kugadzira manhamba chikamu cheMandelbrot set

Semuenzaniso, kutarisa kana nhamba 1 iri chikamu cheMandelbrot yakaiswa:

Kana c = 1 wobva watanga naZ_n = 0.

Kutsiva idzi nhamba mune iyi fomati yatinowana:

(Z) 0² + (c) 1 = 1. Naizvozvo Z_n = 0 uye 1.

Inotevera kutora mhedzisiro ye1, kuisa Z = 1 yatinowana:

(Z) 1²+ (c) 1 = 2.

Inotevera kutora mhedzisiro ye2, kuisa Z = 2 yatinowana:

2²+1 = 5

Inotevera kutora mhedzisiro ye5, kuisa Z = 5 yatinowana:

5²+1 = 26

Inotevera kutora mhedzisiro ye26, kuisa Z = 26 yatinowana:

26²+1 = 677

Naizvozvo Z_n= 0, 1, 2, 5, 26, 677,…

Isu tinogona saka kuona kuti kukosha kwe c = 1 ndiko kwete chikamu cheMandelbrot chakaiswa sezvo nhamba yacho isingagare idiki, muchikurumidza zvikuru yave 677.

Saka, ndizvo c = -1 chikamu cheMandelbrot chakaiswa?

Mhinduro pfupi ndeyekuti hongu, sekutevera nhanho dzakafanana zvoteverwa pamusoro tinowana kuteedzana kwehuwandu.

Kutanga zvakare neZ_n = 0. Kutsiva idzi nhamba mufomura iyi yatinowana:

(Z) 0² (c) -1 = -1. Naizvozvo Z_n = -1.

Inotevera kutora mhedzisiro ye -1, kuisa Z = -1 isu tinowana:

-1² -1 = 0.

Inotevera kutora mhedzisiro ye0, kuisa Z = 0 yatinowana:

 0²-1 = -1

Inotevera kutora mhedzisiro ye -1, kuisa Z = -1 isu tinowana:

-1² -1 = 0.

Inotevera kutora mhedzisiro ye0, kuisa Z = 0 yatinowana:

 0²-1 = -1

Mhedzisiro yacho ndeyekuti Z_n= 0, -1, 0, -1, 0, -1, 0, -1,….

Naizvozvo tinogona kuzviona c = -1 is chikamu cheMandelbrot chakaiswa sezvo chinogara chidiki.

Kune imwezve pfungwa tinoda kukurukura semashure tisati tagona kuona runako.

Iyo Mandelbrot set inewo 'inofungidzira' nhamba.

• • Chikwere che 'kufungidzira nhamba' inhamba isina kunaka.
  • Sezvazviri mu i²= -1 pandiri inhamba yekufungidzira.

Kuti vafungidzire ivo vachifunga nezve yakatwasuka x axis yegirafu ine iyo Negative manhamba kuburikidza zero kusvika Positive manhamba. Ipapo iyo Y axis ichienda yakatwasuka kubva -i, - throughi kuburikidza zero (nzvimbo yekuchinjika yemaviri axis) uye kumusoro kumusoro kuna andi neni i.

Dhayagiramu 1: Kuratidza kwekufungidzira manhambaMamwe manhamba muMandelbrot akaisirwa 0, -1, -2, ¼, nepo 1, -3, ½ asiri. Mamwe manhamba mune iyi seti anosanganisira i, -i, ½i, - ½I, asi 2i, -2i haasi.

Ndiwo mugumo wemasvomhu akaoma kunzwisisa.

Ikozvino ndipo apo panonyanya kunakidza!

Migumisiro yeiyo fomula

Sezvaunogona kufungidzira kuverenga uye kuronga zvese zvinoenderana uye zvisingaitike nemaoko zvaizotora nguva yakareba chaizvo.

Nekudaro makomputa anogona kushandiswa zvakanaka kwazvo kuverenga zana remakumi ezviuru, kunyangwe mamirioni ezvibodzwa uye ozoronga mhedzisiro yedzidziso iyi zvakajeka pagirafu.

Kuti uzive zviri nyore neziso iro rakabvumikiswa akanyorwa mune dema, iwo mapoinzi asina kukodzera akaiswa mutsvuku, uye mapepa ari padyo kwazvo, asi asingaiti chaizvo akaiswa mune yero.

Kana isu tikamhanya chirongwa checomputer kuita icho, tinowana mhedzisiro inotevera inoratidzwa pazasi.

(Unogona kuzviyedza iwe nemapurogiramu akasiyana siyana epamhepo senge anotevera:

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

)

Dhiagari 2: Mhedzisiro yeMepu iyo Mandelbrot equation

Kuwanikwa 1

Isu tinotanga kuverenga matavi ehombodo pane makuru matema emabhora pane hombe dema dema senge chimiro.

Pamusoro diki diki denderedzwa pamusoro penzvimbo hombe dema yetsvo yakaumbwa isu tine matavi matatu Kana tikatamira kune diki diki rinotevera denderedzwa kuruboshwe, tinowana matavi mashanu.

Inotevera yakakura kuruboshwe ine 7, uye zvichingodaro, 9, 11, 13, zvichingodaro, nhamba dzese dzisinganzwisisike kusvika mukusavimbika.

Dhaigiramu 3: matavi

Kuwanikwa 2

Zvino, kuenda kurudyi rwechitema itsvo chimiro kubva kumusoro inoziva kuverenga. Tinowana 4, 5, 6, 7, 8, 9, 10, uye zvichidzika sekuverenga kwematavi ari pamusoro pemabhola makuru matema.

Kuwanikwa 3

Asi hatisati tapedza. Kuenda kuruboshwe kubva kumusoro, denderedzwa dema rakakura kubva kumusoro pakati pematatu uye mashanu ebazi denderedzwa rine matavi masere, iwo uwandu hwematavi kubva kumatenderedzwa ese ari maviri mbali! Pakati pe3 ne5 mudiki diki denderedzwa rine gumi nemaviri, zvichingodaro.

Izvozvi zvakafanana zvinowanikwa zvichienda kurudyi. Saka, bhora rakakura pakati pe3 ne4 riine matavi manomwe, uye pakati pe7 ne4 rine matavi 5 zvichingodaro.

Dhiganhi 4: Matavi anogona kuitawo maths futi!

Kuwanikwa 4

Uyezve, aya mafomu anogona kuve nekuenderera achikudzwa, uye iwo maumbirwo akafanana achadzokorora.

Dhiagari 5: Matanho akafanana akadzokororwa zvisingaperi

Diki diki diki kurudyi kuruboshwe rwetsetse nhema kuenda kuruboshwe, kana yakakwidziridzwa ndiyo yakafanana mufananidzo sezvatinoona pano. Chokwadi ipfungwa dzinonetsa.

Kuwanikwa 5

Pakati peiyo yakakura yemoyo chimiro uye yakasungirirwa denderedzwa denderedzwa kuruboshwe inzvimbo inotaridzika seSeahorse mupata kune iwo akanaka maficha akaonekwa ipapo.

Dhiagiri 6: Mupata weSeahorses!

Kuchinja tsvuku kuti kuve bhuruu uye yero kuti ive chena kusiyana nyore, kana isu tava kuswededza padhuze, tinoona mamwe maitiro akanaka uye kudzokorora kwakawanda kwenzira yekutanga yeiyo itsvo yakasviba-yakavezwa nebhora rakasungirirwa kuruboshwe.

Dhiagiri 7: Seahorse in closeup

Kupinda mukati chena inopenya nzvimbo isu tinoona:

Dhiagari 8: Ruzivo rweWhite whorl pakati peSeahorse

Uye kuswededza zvakatowanda mune imwe nzvimbo panzvimbo tinowana zvinotevera:

Dhiagari 9: Wedzera Zoom mukati!

Kuuya mune imwezve zvakare tinowana imwe yemhando dzemhando dzekutanga:

Dhiganho 10: Hayo chimiro zvekare

Kana tikatenderera pane imwe yemafashama, tinowana zvinotevera:

Dhigramu 11: Kuita Banga Mukudzora

Uye pakati pe whirl tinowana zvinotevera:

Dhigiramu 12: Iwo maziso angu ari kupinda mumakoronyera futi?

Kuswededza kumberi pane imwe yemabhuru emhepo tinowana iyo miviri inotevera mifananidzo iyo inosanganisira imwezve inotanga Mandelbrot itsvo chimiro uye bhora.

Dhiagiramu 13: Panguva yawaifunga kuti waona yekupedzisira yeiyo nhema chimiro.

Dhiagiramu 14: Ehe, iri kudzoserwazve, yakakomberedzwa neimwe yakanaka nzira

Kuwanikwa 6

Kudzokera kumufananidzo wedu wekutanga weMandelbrot set uye kutendeukira kune 'mupata' kurudyi-kurudyi rwechimiro chikuru chemoyo uye kuswededza mukati tinoona maumbwe akaita senzou, isu watichatumidza zita rekuti Eleembo mupata.

Dhaigiramu 15: Rwizi rweNdlovu

Patinoswededza mukati, tinowana imwe setsetse dzakanaka asi dzakasiyana dzichidzokorora zvimiro zvinotevera:

Dhaigiramu 16: Tevera Herd. Hup mbiri, vatatu, vana, Elephant.

Isu taigona kuenderera mberi.

Kuwanikwa 7

Saka, chii chinokonzera runako mune izvi Fractals kubva kuMandelbrot equation?

Hongu, komputa inogona kunge yakaisa chirongwa chemavara-akagadzirwa nevanhu, asi mapatani ayo mavara anojekesa ndiwo mhedzisiro yemasvomhu formula yakagara iripo. Haigoni kushanduka, kana kuchinja.

Runako runopinda mukati memasvomhu, sezvazvakaita nekunetseka.

Kuwanikwa 8

Iwe unogona kunge wakawona izwi rimwe chete rinoramba ririkuoneka. Iro izwi rinoti "Pfungwa".

• Pfungwa haibvumike mune zvakasikwa.
• Pfungwa inongovapo mupfungwa dzedu.

Kuwanikwa 9

Izvi zvinomutsa mibvunzo inotevera mupfungwa dzevanhu vanofunga.

Mitemo yemasvomhu inobvepi?

• • Kuve pfungwa, vanogona chete kubva kune imwe pfungwa, iyo inofanirwa kuve yehungwaru yakakwirira kupfuura neyedu kuti ive inoshanda mune zvakasikwa zvese.

Mitemo yemasvomhu yakavapo here? Kana zvakadaro, vaizozvigona sei?

• • Zvinhu zvinobuda hazvigone kubuda sezvo zvisiri zvemuviri.

Vanhu vakatanga here kana kugadzira iyi mitemo yeMaths?

• • Kwete, iyo Mitemo yemasvomhu yaivapo pamberi pevanhu.

Vanobva kune zvakasikwa here?

• • Kwete, chimwe chinhu chekuraira hachina kubva kubva pamukana mukana. Zvepadenga hazvina pfungwa.

Mhedzisiro bedzi yatinogona kusvika ndeyekuti vaifanira kubva mundangariro yekuve ari kuresa kupfuura munhu. Kungova chete kwavanogona kubva nenzira inonzwisisika kubva kune saka kunofanira kuve kuve musiki wezvese, kubva kuna Mwari.

Mitemo yemasvomhu ndeiyi:

• • pfungwa,
  • zvakasikwa,
  • anopinda,
  • kunze-kushoma masangano.

Ivo vaigona chete kubva kuna Mwari nekuti:

• • Pfungwa dzaMwari ndedzechokwadi (Isaya 55: 9)
  • Mwari akasika zvakasikwa (Mavambo 1: 1)
  • Mwari haachinje (Isaya 43: 10b)
  • Mwari anoziva zvisikwa zvese zvekudenga, hapana chinoshaya (Isaya 40:26)

mhedziso

1. 1. Muongororo pfupi iyi yemaprobiti uye Mandelbrot equation takaona runako uye kurongeka kwakadzika mukati kweMasvomhu uye magadzirirwo akaitwa zvakasikwa.
   2. Izvi zvinotipa kupenya mundangariro dzaMwari, iyo ine zvakajeka kurongeka, kunaka uye kusingaperi akasiyana uye chiratidzo chepfungwa dzakapusa kudarika vanhu.
   3. Zvinoratidzawo rudo rwake nekuti akatipa huchenjeri kuti tikwanise kuwana uye (imwe pfungwa!) Kukoshesa zvinhu izvi.

Naizvozvo isu ngatiratidzei iwo zano rekuonga pane izvo zvaakasika uye kwaari seMusika.

Zvitendero:

Ndichitenda zvikuru neChiwedzero chakapihwa neYouTube vhidhiyo "Iyo Chakavanzika Code Yezvekusikwa" kubva kuOptins Series naCornerstone Television Network.

Kushandisa Kwakafanira: Mimwe yemifananidzo yakashandiswa inogona kunge iri copyright, kushandiswa kwayo uko kwanga kusiri kupihwa mvumo nemuridzi we copyright. Tiri kugadzira zvinhu zvakadaro kuwanikwa mukuedza kwedu kusimudzira kunzwisisa kwesainzi nenyaya dzechitendero, nezvimwewo .. Tinotenda kuti izvi zvinopa mukana wakakwana wekushandisa chero akachengetedza zvinhu sezvakapihwa muchikamu chegumi nenomwe cheMutemo weMutemo weUnited States. Zvinoenderana neChinyorwa 107 USC Chikamu chegumi neshanu, zvinyorwa zviri pane ino saiti zvinowanikwa zviripo pasina pundutso kune avo vanoratidza kufarira kugamuchira nekuona izvo zvinyorwa zvekutsvaga kwavo uye zvinangwa zvekudzidzisa. Kana uchishuvira kushandisa zvigadzirwa zvine copyright zvinopfuura kushandiswa kwakanaka, iwe unofanirwa kuwana mvumo kubva kumuridzi we copyright.

Tadua

Zvinyorwa naTadua.