Tabbatar da gaskiyar Halitta

Farawa 1: 1 - “A cikin farko Allah ya halicci sammai da ƙasa”

Jeri na 1 - Lambar Halitta - Lissafi

Kashi na 1 - elaƙwalwar Mandelbrot - Haske cikin tunanin Allah

Gabatarwa

Darasin ilimin lissafi yana kan kawo ɗayan martani biyu.

1. 1. Babu matsala, idan ba shi da wahala sosai kuma
   2. Ba na son ilimin lissafi saboda wannan dalilin.

Koyaya, duk irin amsawar kalmar 'lissafi' wanda aka samu a cikin ku, ku tabbatar ba kwa buƙatar ƙididdige lissafin lissafi don ku iya fahimtar wannan kyakkyawar shaidar don kasancewar Allah.

Wannan labarin zaiyi kokarin isar da dalilai na tabbacin cewa akwai Allah, wanda ya halicci komai, akasin yadda muke kasancewa anan ta hanyar da ba makawa kamar yadda yake a ka'idar juyin halitta.

Don haka don Allah ci gaba da wannan binciken tare da ni, domin da gaske abin ban mamaki ne!

lissafi

Idan muka ga wani kyakkyawan zane ko daukar hoto kamar Mona Lisa, za mu iya godiya da shi, mu kuma ji tsoron mahaliccinsa duk da cewa ba za mu taba neman yin fenti ta irin wannan ba. Haka yake tare da ilmin Lissafi, da kyar muke iya fahimtar shi, amma har yanzu zamu iya godiya da kyawun sa, domin da gaske kyakkyawa ce!

Menene ilimin lissafi?

• • Ilimin lissafi shine nazarin dangantakar dake tsakanin lambobi.

Menene lambobi?

• • An yi bayanin su mafi kyau a ra'ayi mai yawa.

Menene lambobi sannan?

• • Lambobin da aka rubuta ba lambobi bane, suna yadda muke bayyana manufar lambobi a rubuce da kuma gani.
  • Suna kawai lambobi ne na lambobi.

Additionallyari, mahimmin abin lura da ya kamata a lura shi ne cewa duk dokokin lissafi suke na ra'ayi.

• • Tunani wani abu ne da aka tantauna a zuciya.

Basis

Dukkaninmu mun saba da ra'ayi na “Saiti”. Wataƙila kuna da saitin katunan wasa, ko tarin abubuwa na chess ko kuma gilashin giya.

Sabili da haka, zamu iya fahimtar cewa ma'anar:

SET: = tarin abubuwa tare da mallakar dukiyar da aka sani.

Misali, kowane katin wasa wani bangare ne na duk katunan wasan, kuma kowane guda yanki na dara shine asalin duk tsarin wasan chess. Glassari ga gilashin giya shine ɗayan gilashin gilashi na wani irin tsari tare da kaddarorin da aka ƙera don fitar da mafi kyawun daga giyar, kamar ƙanshi, da bayyanar.

Hakanan, a cikin lissafi, jerin lambobi tarin lambobi ne tare da takamaiman dukiya ko kaddarorin da suka ayyana tsarin amma mai yiwuwa ba ya cikin wani tarin.

Misali, dauki lambobi masu zuwa: 0, -2, 1, 2, -1, 3, -3, -½, ½.

Daga cikin waɗannan lambobin masu zuwa

• • Saiti mara kyau: {-2, -1, -3, -½}
  • Saitin kwarai: {1, 2, 3, ½}
  • Saitin yanki: {-½, ½}
  • Duk tabbatacce Lambobi: {1, 2, 3}

Da sauransu.

Suchaya daga cikin irin wannan saiti shine tsarin Mandelbrot:

Wannan shine saitin duk lambobi (c) wacce dabara Z take_n² +C = Z_n+1 da Z_n ya kasance ƙarami.

Kafa lambobi wani ɓangare na saita Mandelbrot

A matsayin misali, don bincika idan lambar 1 ta ɓangare na saita Mandelbrot:

Idan c = 1 sai a fara da Z_n = 0.

Sauya waɗannan lambobin a wannan dabara mun samu:

(Z) 0² + (c) 1 = 1. Saboda haka Z_n = 0 da 1.

Abu na gaba da sakamakon 1, saitin Z = 1 mun samu:

(Z) 1²+ (c) 1 = 2.

Abu na gaba da sakamakon 2, saitin Z = 2 mun samu:

2²+1 = 5

Abu na gaba da sakamakon 5, saitin Z = 5 mun samu:

5²+1 = 26

Abu na gaba da sakamakon 26, saitin Z = 26 mun samu:

26²+1 = 677

Saboda haka Z_n= 0, 1, 2, 5, 26, 677,…

Don haka zamu iya ganin cewa darajar c = 1 ita ce ba wani ɓangare na Mandelbrot saita kamar yadda lambar ba ta zama ƙarami ba, a zahiri da sauri ya zama 677.

Don haka, shi ne c = -1 wani ɓangare na tsarin Mandelbrot?

Amsar takaice ita ce, kamar bin matakai guda biyun da muka biyo a sama muna samun jerin lambobi kamar haka.

Fara sake tare da Z_n = 0. Sauya wadannan lambobin a cikin wannan dabara mun samu:

(Z) 0² (c) -1 = -1. Saboda haka Z_n = -1.

Abu na gaba da sakamakon -1, saitin Z = -1 mun samu:

-1² -1 = 0.

Abu na gaba da sakamakon 0, saitin Z = 0 mun samu:

 0²-1 = -1

Abu na gaba da sakamakon -1, saitin Z = -1 mun samu:

-1² -1 = 0.

Abu na gaba da sakamakon 0, saitin Z = 0 mun samu:

 0²-1 = -1

Sakamakon shine Z_n= 0, -1, 0, -1, 0, -1, 0, -1,….

Saboda haka muna iya ganin hakan c = -1 is wani ɓangare na Mandelbrot saita kamar koyaushe yana kasancewa ƙarami.

Akwai daya more ra'ayi muna bukatar mu tattauna a matsayin baya kafin mu iya ganin kyakkyawa.

Hakanan saitin Mandelbrot ya ƙunshi lambobin 'hasashe'.

• • Fa'idar 'lambar hasashe' lamba ce mara kyau.
  • Irin su a i²= -1 inda ni lambar hasashe ne.

Don hango su suyi tunanin z x a kwance na hoto wanda ke da lambobi mara kyau ta hanyar sifili zuwa tabbatattun lambobi. Bayan haka Y axis yana tafiya a tsaye daga -i, - throughi zuwa sifili (gicciyen ginshiƙan biyu) kuma zuwa sama zuwa andi da i.

Hoto 1: Nuna wasu kirkirarrun lambobi Wasu lambobi a tsarin Mandelbrot sune 0, -1, -2, ¼, yayin da 1, -3, ½ ba. Numbersarin lambobi a cikin wannan saitin sun haɗa da i, -i, ½i, - ½I, amma 2i, -2i ba haka bane.

Wannan shine ƙarshen duk lissafin rikitarwa.

Yanzu wannan shine inda yake samun ban sha'awa sosai!

Sakamakon wannan dabara

Kamar yadda zaku iya tunanin yin lissafi sannan kuma shirya duk ingantattun halaye masu amfani da hannu zai dauki lokaci mai tsawo.

Koyaya za'a iya amfani da kwamfutoci don yin amfani da kyau don ƙididdige 100 na dubun, har ma miliyoyin dabi'u sannan kuma su tsara sakamakon wannan dabara ta gani akan allon zane.

Don ganowa cikin ido alamun maki masu alama cikin baƙi, alamun mara kyau suna alama cikin ja, kuma maki da suke kusa, amma ba ingantaccen inganci ana alamar su a rawaya.

Idan muka gudanar da shirin kwamfuta don yin hakan, muna samun sakamako mai zuwa wanda aka nuna a kasa.

(Kuna iya gwadawa don kanku tare da shirye-shirye na kan layi daban-daban kamar waɗannan:

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

)

Shafi na 2: Sakamakon Zaman Kwatanta daidaituwa na Mandelbrot

Gano 1

Mun fara kirgaro rassan rawaya akan manyan kwallayen baƙar fata akan babban ƙwayar fata kamar ƙira.

A saman kananan baki da'ira a saman babban baki koda mai siffa yankin muna da rassa 3. Idan muka matsa zuwa da'irar karami na gaba akan hagu, zamu sami rassa 5.

Mafi girma na gaba zuwa hagu yana da 7, da sauransu, 9, 11, 13, da dai sauransu, duk lambobi masu ƙima da rashin daidaituwa ne.

Shafi 3: Rassa

Gano 2

Yanzu, zuwa hannun dama na ƙirar koda daga sama ya san yadda ake ƙidaya. Mun sami 4, 5, 6, 7, 8, 9, 10, kuma gaba kamar ƙididdigar rassa a saman manyan ƙwallon baƙar fata.

Gano 3

Amma ba mu gama ba tukuna. Tafiya zuwa hagu daga sama, mafi girma da'irar baki daga sama tsakanin da'irori 3 da 5 suna da rassa 8, jimlar rassan daga da'irori ko dai gefe! Kuma tsakanin 5 da 7 ƙaramin ɗakin duhu yana da 12, da sauransu.

Ana samun tara kuɗaɗen daidai da ke hannun dama. Don haka, ball mafi girma tsakanin 3 zuwa 4 yana da rassa 7, kuma tsakanin 4 zuwa 5 yana da rassa 9 da sauransu.

Shafi na 4: Rassan suna iya yin lissafi kuma!

Gano 4

Bugu da kari, wadannan sifofin ana iya cigaba dasu gaba daya, kuma sifofin guda daya zasu maimaita.

Tsarin hoto 5: Hakanan ake maimaita irinta

Dotan ƙaramin baƙar fata na gefen hagu na layin baƙi yana komawa hagu, idan an ɗaukaka shi hoto iri ɗaya ne kamar yadda muke gani a nan. Yana da gaske hankali boggling.

Gano 5

Tsakanin girman girman zuciya da wani da'irar baki da aka makala a gefen hagu wani yanki ne mai kama da kwari kogin Baha don kyawawan siffofi da ake gani a wurin.

Hoto na 6: kwarin kogin Nilu!

Canza launin ja don shuɗi da rawaya don fari don sauƙaƙa mai sauƙi, lokacin da muka zuƙo kusa, zamu ga mafi kyawun tsarin ƙira da ƙarin maimaita yanayin tsarin ƙirar fata mai launin fata tare da ƙwallan da aka haɗe a hagu.

Hoto na 7: Wasan Teku a cikin ɗaukar hoto

Zuƙowa cikin farin haske da muke gani:

Hoto na 8: Cikakken bayani na Whitish wanda ke a tsakiyar Seahorse

Kuma kara gaba a cikin maimaikon cibiyar mun samu masu zuwa:

Hoto na 9: Karin inari a ciki!

Omoƙari a cikin ƙarin ƙari muna samun wani ɗayan sifofinmu na asali:

Hoto na 10: Siffar ta sake

Idan muka zuƙowa ɗayan raƙuman ruwa, mun sami waɗannan masu zuwa:

Tsarin hoto 11: Yin Karkace Cikin Kulawa

Kuma a tsakiyar tsakiyar whirl mun sami waɗannan:

Zane zane na 12: Shin idanuna suna shiga birgima kuma?

Zuƙowa gaba a ɗayan ɗayan ruɗu biyu muna samun waɗannan hotuna biyu masu zuwa wanda ya haɗa da wani nau'in fara wasan Mandelbrot koda da ƙwallo.

HOTO NA 13: Lokacin da kuka yi tunanin kun ga ƙarshen wannan baƙin baƙar fata!

Hoto 14: Haka ne, ya dawo kuma, an kewaye shi da wani kyakkyawan tsari

Gano 6

Komawa ga hotonmu na farko na saita Mandelbrot da juya zuwa 'kwari' a gefen dama na dama na babban sifar zuciya da zuƙowa cikin ganin wasu siffofin giwaye, waɗanda zamu sa wa suna kwarin Elephant.

Hoto na 15: Kwarin giwa

Yayinda muke karasowa, zamu sami wani salo daban daban mai kyau amma daban daban kamar haka:

Hoto na 16: Bi Manya. Guda biyu, uku, hudu, tafiya Elephant.

Za mu iya ci gaba kuma ci gaba.

Gano 7

Don haka, menene ke haifar da kyakkyawa a cikin waɗannan Fractals daga daidaitawar Mandelbrot?

Haka ne, kwamfutar na iya amfani da tsarin launi na mutum-mutum, amma alamu waɗanda launuka ke nunawa sune sakamakon tsarin lissafi wanda koyaushe ya kasance. Ba zai iya canzawa, ko canzawa.

Kyakkyawan abu ne sananne a cikin lissafi, kamar yadda ake rikitarwa.

Gano 8

Wataƙila ka lura da kalma ɗaya tak takan ci gaba da bayyana. Maganar ita ce "Ra'ayi".

• Tunani shine ba abu bane a zahiri.
• Tunani kawai yana cikin tunaninmu.

Gano 9

Wannan yana haifar da waɗannan tambayoyin a cikin tunanin masu tunani.

Daga ina dokokin ilimin lissafi suka zo?

• • Kasancewa mai ma'ana, zasu iya zuwa ne daga wata tunani, wanda dole ne ya kasance ya kasance mafi girman hankali fiye da namu don ya kasance yana aiki a duk sararin duniya.

Shin dokokin ilimin lissafi sun samo asali ne? Idan haka ne, ta yaya za su iya?

• • Abubuwa masu kauracewa abubuwa ba zasu iya canzawa ba kamar yadda suke ba na zahiri bane.

Shin mutane sun kirkiro ko ƙirƙirar waɗannan dokokin lissafi?

• • A'a, dokokin lissafi sun wanzu a gaban mutane.

Shin sun zo ne daga sararin samaniya?

• • A'a, wani abu ne ba zai iya zo daga bazuwar dama ba. Sararin samaniya bashi da tunani.

Abinda kawai za mu iya samu shi ne cewa dole ne su fito daga tunanin kasancewarsa ya fi mutum girma. Iyakar abin da za su iya fitowa daga hankali saboda haka dole ne ya kasance mai kirkirar duniya, daga nan ne daga Allah.

Dokokin lissafi sune:

• • manufa,
  • na kowa,
  • masu mamayewa,
  • banda abubuwan da ba a sani ba.

Zasu iya zama daga Allah kaɗai:

• • Tunanin Allah tunani ne (Ishaya 55: 9)
  • Allah ya halicci duniya (Farawa 1: 1)
  • Allah ba ya canzawa (Ishaya 43: 10b)
  • Allah yasan duk halittar sama, babu abinda aka rasa (Ishaya 40:26)

karshe

1. 1. A cikin wannan taƙaitaccen jarrabawa na fractals da daidaituwa na Mandelbrot mun ga kyakkyawa da tsari a cikin ilimin lissafi da ƙirar sararin samaniya.
   2. Wannan yana bamu haske game da tunanin Allah, wanda a fili ya ƙunshi tsari, kyakkyawa da bambanci mara iyaka kuma shaida ce ga mutum mai hankali fiye da mutum.
   3. Hakanan yana nuna ƙaunarsa a cikin cewa ya bamu hikima don mu iya ganowa kuma (wani ra'ayi!) Muna godiya da waɗannan abubuwan.

Don haka bari mu nuna wancan tunanin don nuna godiya ga abin da ya halitta kuma domin shi mahalicci.

Amincewa:

Tare da godiya da godiya ga wahayin da aka bayar ta hanyar bidiyo ta YouTube "Asirin Halittar Halitta" daga Asali Series daga Cornerstone Television Network.

Amfani da Gaskiya: Wasu daga hotunan da aka yi amfani da su na iya zama kayan haƙƙin mallaka, amfanin wanda ba'a bayar da izini koyaushe daga haƙƙin mallaka ba. Muna samar da irin wannan kayan a cikin ƙoƙarinmu don haɓaka fahimtar abubuwan da suka shafi kimiyya da addini, da dai sauransu. Mun yi imanin wannan ya ƙunshi yin amfani da kowane irin haƙƙin mallaka na kayan da aka mallaka kamar yadda aka bayar a sashe na 107 na Dokar Hakkin Mallaki ta Amurka. Dangane da taken 17 Sashe na USC US 107, kayan da ke wannan shafin an samar dasu ba tare da riba ga wadanda suka nuna sha'awar karba da kallon kayan don binciken kansu da dalilai na ilimi. Idan kana son amfani da kayan haƙƙin mallak wanda ya wuce amfanin gaskiya, dole ne ka sami izini daga wurin haƙƙin mallaka.

Tadua

Labarai daga Tadua.