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5. st. p.n.e. Leukip i Demokrit – atomisti (a-tome, nedjeljiv)
18. st. Ruđer Josip Bošković – čestice sa privlačnom i odbojnom silom
19. st. J. C. Maxwellova kinetička teorija plinova Johan Dalton – 1803. dokazuje atomsku građu materije Ernest Rutherford – pozitivna jezgra, negativan elektron; planetarni model atoma
20. st.
1900. Max Planck – atomi zrače energiju u diskretnim količinama – kvantima
1905. Albert Einstein – foto-električni efekt (fotoni – kvanti svjetlosti) i specijalna teorija relativnosti, 1913. opća teorija relativnosti
1913. Niels Bohr – Bohrov model atoma (vodikov atom), kvantni skokovi između orbita
1923. L. V. De Broglie – valno-čestična dvojnost (dualnost) mikročestica
1927. Werner Karl Heisenberg – relacija neodređenosti, (položaj – impuls, količina energije – vrijeme postojanja elektrona itd.)
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Dijelovi atoma (preko 200 vrsta):
hadroni (90%):barioni (proton, neutron, lambda...)mezoni (pion, kaon, ro...)leptoni (elektron, mion, neutrino...)
elementarne:fermioni, kvarkovi, leptoni...bozoni (fotoni, gluoni, gravitoni...)
- Simetrija (privlačenje-odbijanje, tvar-antitvar)- Jedinstvo: bootstrapt pristup: hadronse sastoji od hadrona i razmjenjuje energiju preko hadrona – svi u svakom i svaki je u svima
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Vladimir Devidé
Sićušni paukna beskrajnom putuide preko lista -
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“Leptirov učinak”
“Zbog čavla, izgubljena je potkova; Zbog potkove, izgubljen je konj; Zbog konja, izgubljen je jahač; Zbog jahača, izgubljena je bitka; Zbog bitke, izgubljeno je kraljevstvo!”
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Edward Lorenz: kompjuterski ispis vremenskih uvjeta, 1961.
Teorija kaosa se bavi proučavanjem pojava za koje je karakteristično da male promjene početnih uvjeta vodi na vrlo različita konačna stanja.
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Cantorova rešetka
Benoit Mandelbrot:raspodijela velikih i malih dohodaka,cijene pamuka,šumovi u telefonskim vezama...
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Samosličnost (selfsimilarity)
milimetar
decimetar
metar
centimetar
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Drveće - grananje
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sličnost grananja u krvožilnom sustavu
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Proporcionirano umanjivanje
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Paprat
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Persijski tepih
ritam,simetrija,razmjer,jedinstvo
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Helge von Koch, 1904.
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Pahulje
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Mjerenje obale Britanije:
Dužina obale se uvećavapovećanjem broja izmjerenihdetalja; aproksimacijarelativizira točnost.
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Doslovna samosličnost
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Granicečetiri jednakemogućnosti
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Benoit Mandelbrot: fraktali (lat. fraktus, frangere – razlomiti)
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Mandelbrotov skup
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Shanon
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Yellowstone,Wyoming
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Kaotične igre
160 točaka 10000 točaka50 točaka
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Obični i neobični atraktori
Lorenzov atraktor
atraktor: staza koja privlači druge bliske staze
Stabilni atraktorperiodičnog gibanja (klatno)
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Emanuel Vidović: Angelus
M. M., 8 godina
Ž. K., slikar, povjesničar umjetnostiD. R., slikarica
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Wacslaw Sierpinski: Trokut (“građenje rupama”)
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Gustave Eiffel: toranj za Svjetsku izložbu,1889.
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Wacslaw Sierpinski: Tepih
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Vražje stepenice(Devil’s stairs)
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Zenonova dihtomija:
B
1
1/2
1/4
1/32 ...
1/8
A
1/16