fractals

fractals hauv lub neej

Lub fractal yog ib yam khoom geometric uas tuaj yeem muab faib ua ntu, txhua qhov zoo ib yam li cov khoom qub. Fractals muaj qhov nthuav dav tsis kawg thiab feem ntau nws tus kheej zoo sib xws thiab ntsuas. Feem ntau, fractals lawv tuaj yeem tsim los ntawm cov qauv rov ua dua, rov ua dua lossis rov ua dua.

Hauv tsab xov xwm no peb yuav qhia koj txhua yam koj xav paub txog fractals, lawv cov yam ntxwv thiab qhov tseem ceeb.

Cov khoom ntawm fractals

fractal geometry

Cov khoom tseem ceeb uas qhia txog fractals yog nws tus kheej zoo sib xws, infinite complexity thiab dimensionality.

tus kheej zoo sib xws

Kev sib piv ntawm tus kheej yog thaum ib feem ntawm daim duab lossis cov qauv tuaj yeem pom raws li tus qauv ntawm tag nrho, ntawm qhov me me.

infinite complexity

Nws hais txog qhov tseeb tias cov txheej txheem tsim cov duab yog recursive. Qhov no txhais tau hais tias thaum tus txheej txheem raug ua tiav, cov txheej txheem ua ntej nws tus kheej tau pom tias yog ib qho txheej txheem hauv nws cov txheej txheem.

Nws yog ib nqi sau cia hais tias nyob rau hauv cov ntaub ntawv ntawm lub iterative tsim ntawm ib tug lej txhais fractal, qhov kev pab cuam yuav tsum tau ua infinite, uas ua rau ib tug infinitely complex qauv.

Qhov ntev

Tsis zoo li Euclidean geometry, qhov ntev ntawm fractal tsis tas yuav muaj qhov tseem ceeb. Nyob rau hauv no ceg ntawm kev ua lej, cov ntsiab lus muaj pes tsawg qhov ntev, kab muaj ib qhov ntev, qhov chaw muaj ob qhov ntev, thiab cov ntim muaj peb qhov ntev. Nyob rau hauv cov ntaub ntawv ntawm fractal dimension, qhov no yog ib tug fractional kom muaj nuj nqis uas sawv cev zoo npaum li cas ib tug qauv occupies qhov chaw uas muaj nws.

piv txwv ntawm fractals

fractals

Thawj fractals kawm yog Cantor teeb, Koch snowflake, thiab daim duab peb sab Sierpinski. Fractals tuaj yeem tau txais geometrically lossis stochastically los ntawm cov txheej txheem recursive thiab tuaj yeem ua raws li cov yam ntxwv ntawm ntau hom duab pom hauv qhov xwm txheej.

Fractals muaj nyob txhua qhov chaw. Muaj ntau ntau yam khoom ntuj uas suav hais tias yog ntuj fractals vim lawv tus cwj pwm lossis cov qauv, tab sis cov no yog cov hom fractal zoo kawg nkaus, paub qhov txawv ntawm cov lej hom fractals tsim los ntawm kev sib cuam tshuam recursive. Piv txwv ntawm cov no yog huab thiab ntoo.

Lub ntsiab nta

fractal lej

Lo lus "fractal" los ntawm Latin fractus, uas txhais tau hais tias "fragmented", "pob", los yog yooj yim "tawg" los yog "tawg", thiab yog zoo haum rau cov khoom nrog fractional qhov ntev. Lub sij hawm tau coined los ntawm Benoît Mandelbrot nyob rau hauv 1977 thiab tshwm nyob rau hauv nws phau ntawv Fractal Geometry ntawm Xwm. Kev kawm ntawm cov khoom fractal feem ntau hu ua fractal geometry.

Lub fractal yog ib qho kev ua lej uas tuaj yeem txaus siab rau nws tus kheej zoo sib xws ntawm txhua qhov teev, thiab nws qhov ntev tsis yog cov lej, lossis yog tias lawv yog, lawv yuav tsis yog cov lej zoo tib yam. Qhov tseeb tias nws zoo ib yam txhais tau hais tias cov khoom fractal tsis nyob ntawm tus neeg soj ntsuam nws tus kheej, uas yog, yog tias peb coj qee yam fractal, peb tuaj yeem tshawb xyuas tias thaum peb muab ob npaug rau zoom, cov duab kos yog tib yam li thawj. Yog tias peb zoom los ntawm ib qho ntawm 1000, peb txheeb xyuas cov khoom qub, yog li yog tias peb nce n, cov phiaj xwm zoo ib yam, yog li qhov zoo ib yam li tag nrho.

Ib qho khoom sau los yog khoom tau hais tias yog fractal thaum nws loj tuaj raws li qhov ntsuas ntawm qhov ntsuas txo qis. Muaj ntau yam khoom zoo tib yam uas suav tias yog ntuj vim lawv cov qauv lossis tus cwj pwm.Txawm tias peb tsis paub lawv. Huab, roob, ntug hiav txwv dej, ntoo, thiab dej ntws yog tag nrho cov ntuj fractals, txawm tias qhov kawg thiab yog li ntawd tsis zoo tagnrho, tsis zoo li lej fractals uas nyiam infinity thiab zoo tagnrho.

Fractals thiab science

Fractal art yog ze ze rau kev ua lej, tshwj xeeb tshaj yog geometry, vim, raws li nws lub npe qhia, nws siv lub tswv yim ntawm fractals. Fractals yog nyob ntawm qhov rov ua dua ntawm tus kheej-correlated geometric qauv, uas yog, feem yog sib npaug rau tag nrho.

Thaum tsim lub Sierpinski daim duab peb sab, los ntawm daim duab peb sab sib npaug, coj nws qhov nruab nrab, tsim ib daim duab peb sab sib npaug tshiab, thiab tshem tawm qhov chaw nruab nrab. Tom qab ntawd ua tib yam nrog txhua daim duab peb sab seem, thiab lwm yam, yog li nws yog suav tias yog fractal. Benoit Mandelbrot, uas nrhiav pom cov ntaub ntawv lej hu ua fractals, tau tuag los ntawm mob qog noj ntshav thaum muaj hnub nyoog 85 xyoos. Mandelbrot, ib tug pej xeem Fab Kis thiab Asmeskas, tau tsim fractals raws li ib txoj hauv kev ua lej kom nkag siab txog qhov tsis txaus ntseeg ntawm qhov xwm txheej.

Txhawm rau hais txog kev faib tawm los ntawm qhov dav mus rau qhov tshwj xeeb, peb tuaj yeem faib lawv ua ob pawg dav: kev txiav txim siab fractals (uas tuaj yeem ua algebraic lossis geometric) thiab tsis yog kev txiav txim siab fractals (tseem hu ua stochastic fractals).

Linear fractals yog cov uas tau tsim raws li cov nplai sib txawv, uas yog, lawv zoo ib yam ntawm txhua qhov teev. Tsis yog-linear fractals, ntawm qhov tod tes, tshwm sim los ntawm complex distortions, los yog raws li lub npe qhia, siv ib lo lus nyob rau hauv chaotic lej, nonlinear distortions.

Lub neej niaj hnub

Feem ntau cov lej ua lej thiab cov khoom ntuj yog nonlinear. Hauv kev ua lej, kev sib piv ntawm tus kheej, qee zaum hu ua tus kheej zoo sib xws, yog ib qho khoom ntawm ib yam khoom (hu ua tus kheej zoo ib yam khoom) uas tag nrho yog raws nraim lossis kwv yees li qhov zoo ib yam, piv txwv li thaum tag nrho muaj tib yam. ib los yog ntau tshaj nyob rau hauv cov duab ntawm nws qhov chaw.

Lub fractal yog tus cwj pwm los ntawm ib puag ncig uas zoo li infinity li ntxiv cov ntsiab lus me me thiab cov ntsiab lus me me nrog kev ua tiav iterations. Txawm li cas los xij, qhov nkhaus no tsis sib tshooj txhua lub sij hawm txwv ntawm lub voj voog uas hla qhov pib daim duab peb sab. Huab, roob, circulatory systems, coastlines, los yog snowflakes yog tag nrho cov natural fractals. Qhov kev sawv cev no yog kwv yees vim hais tias cov khoom ntawm cov khoom zoo tagnrho, xws li kev nthuav dav tsis kawg, yog qhov txwv.

Fractal geometry sim ua qauv thiab piav qhia ntau yam tshwm sim thiab kev sim kev tshawb fawb, thiab hauv ob peb xyoos nws tau dhau los ua. ib lub cuab yeej siv ntau yam siv los ntawm cov kws tshawb fawb, kws kho mob, kws ua yeeb yam, sociologists, economists, meteorologists, suab paj nruag, kws tshawb fawb hauv computer, Thiab lwm yam

Kuv vam tias nrog cov ntaub ntawv no koj tuaj yeem kawm paub ntau ntxiv txog fractals thiab lawv cov yam ntxwv.


Cov ntsiab lus ntawm tsab xov xwm ua raws li peb cov ntsiab cai ntawm kev tswj hwm kev ncaj nceesCov. Tshaj tawm ib qho yuam kev nyem no.

Yog thawj tus tuaj tawm tswv yim

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  1. Lub luag haujlwm rau cov ntaub ntawv: Miguel Ángel Gatón
  2. Lub hom phiaj ntawm cov ntaub ntawv: Tswj SPAM, kev tswj xyuas tawm tswv yim.
  3. Sau raws cai: Koj kev tso cai
  4. Kev sib txuas lus ntawm cov ntaub ntawv: Cov ntaub ntawv yuav tsis raug xa mus rau lwm tus neeg thib peb tsuas yog los ntawm kev txiav txim siab raug cai.
  5. Cov ntaub ntawv khaws cia: Cov Ntaub Ntawv khaws tseg los ntawm Occentus Networks (EU)
  6. Txoj Cai: Txhua lub sijhawm koj tuaj yeem txwv, rov qab thiab tshem tawm koj cov ntaub ntawv.