Ho okumu, 'epekema
He aha mea he fractal? Fractals ma ka Nature
Pinepine maikaʻi loa discoveries i ma ka 'epekema, e radically hoʻololi i ko kakou mau ola. No ka laʻana, ka hana mea hou i hana muaʻole laʻau koʻokoʻo ke hoola i ka hailona ana o kanaka, a me ka hana mea kaua hou i hiki aku ai i ka makeʻana. Just nehinei (ma ka pālākiō o ka mōʻaukala) ke kanaka "tamed" uila, a me keia la hiki ole ia makou ke manao ke ola ole ia ia. Eia naʻe, loaʻa nō discoveries mea, e like me ka mea, e olelo aku nei, e noho i loko o ka malu, a me ka hoʻowahāwahā i ka mea i ka mea, kekahi i kekahi kanawai ma luna o mākou ola. I kekahi o kēia mau discoveries ua i ka fractal. ua, aole i lohe o ia i ka mea loa kanaka, aʻaʻole e e hiki ke wehewehe i kona manaʻo. Ma keia 'atikala mākou, e ho'āʻo i ka hana me ka ninau o ka mea fractal, noonoo i ke ano o keia manawa, mai ka kuanaʻike o ka' epekema a me ka ano.
Papa Hanohano ma chaos
I mea e maopopo mea i fractal e hoʻomaka debriefing me ke kulana o ka makemakika, akā, ma mua e hele ana i loko o ka sciences, ua mea he uuku philosophize. Kēlā me kēia kanaka ka hoʻomaopop 'ana i maoli lanakila ma ka mea āna i perceives ke ao nei a puni mākou. Pinepine i loko o kā lākou kona manaopaa o keʻikeʻo ia UOAAaOON e hana i ka ke kūpili o ka hoʻoponoponoʻana. Pela, ke kālailai i ka keʻano o ka hanaʻana i ka hana a puni ka mea UOAAaOON e hoʻomaulia i mea hoʻopili a me ka hōʻike 'ana i kekahi lauana. Ka nui manaʻo o ko ke ao nei e hana i loko o ka hoʻoponopono i kēia mau pilikia. 'ōlelo koʻikoʻi akula olelo ana, mākouʻepekema e huli no ka lauana kahi mea, aohe kekahi, a me ka pono ole ia. Aka, a hiki ma ka chaos he mea ka pili ma waena o kekahi mau hanana. He kēia pilina a me ka hana fractal. E like me oukou i kumu hana, E noʻonoʻo i kekahi lahuikanaka i mokumokuia lala e moe ana a puni ma luna o ke alanui. Inā 'oe pono e nana i ka mea, ua ike ia i nā mea a pau kā lākou mau lālā, a twigs ia iho e like me ka laau. He kēia similarity i kekahi hapa kaawale o hookahi heʻahahui Hōʻike ka ai-i kapaia rula o recursive ka hoʻoponopono-similarity. Fractals ma Nature hiki ke loaʻa manawa a me ka hou, e hana like me na mea he nui'okanikaʻole a me ke aloha 'ano apau loa. Keia ao, a me ke kai pūpū a me ka hometa pūpū, a me ka leialii o nā lāʻau, a hiki i ke koko nenoaiu. Kēia papa hiki ke hoomau loa. A pau kēia mau Random kinona me ka nanea iienuaaaony i ka fractal algorithm. Eia ke hele mai i kekahi wahi, e noonoo i ka mea a ka fractal mai ke kulana o ka mea kiko'ī sciences.
A mau maloʻo kūʻiʻo
Ka hua'ōlelo "fractal" mai Roma translates like "anoe", "kaawale ana", "mamala", a like no me ka maʻiʻo o keia makahiki, i ka hua'ōlelo like me neia, aole e nei. IeAUPIIe, IAa IO ka mea, ua malamaia lakou nei, me ka pakiko-like kau, hapa o ka a pau, i 'oe a kona' ole ma ke anakahi iki kiʻekiʻe. Kēia manawa dala ma na seventies o ka iwakalua kenekulia, Benoit Mandelbrot, ka mea i ike i ka makua kāne o fractal anahonua. I kēia manawa i ka manawa i manaoia fractal Kimia e hoohalike ai i ke 'ole ia mea ma ka hoonee aku i ka unahiʻole, i like ia iho. Naʻe, ka makemakika kumu no ka hana ana o keia kumumanaʻo i ua waiho mua o ka hanau ana o ka Mandelbrot i, akā, ka mea hiki ole ke hoʻomohala a ka uila kamepiula 'ē aʻe.
History, a me Pehea mea a pau, hoomaka ae la
Ma ka huli ana o 19-20 kenekulia, ke study o ke ano o fractals ua o ka episodic ano. O ke kumu ho i ka mea i mathematicians makemake e noiʻi i mea e mea amenable i ke ao ma muli ia mau theories a me epekema. I ka 1872, ua kūkuluʻia ka German mathematician Weierstrass, wahi differentiable i laʻana o ke ana kuleana pili i. Naʻe, i kēia hale ua loa Hōʻuluʻulu a me ka pilikia i maopopo. A laila, hele akula au i Shved Helge av Koch, ka mea i loko o 1904 kūkulu i ana hālawa, aʻaʻohe tangent anywhere. O nani oluolu e huki, a, e like me ka mea huli mai, ka mea, ua wehewehe aku ma ka fractal waiwai. Kekahi o na Lolina o ka hālawa i kapaʻia ma hope o ka mea kākau - ". Koch snowflake" Eia, i ka manaʻo o ka hoʻoponopono-i 'ano like kumu e hoʻomōhala ana i wā e hiki mai mentor B. Mandelbrot Farani Pol Levi. I ka 1938, oia paʻi i ka 'atikala ia "Kekoa a me ka makahiki curves a me surfaces oia hoi o māhele i' ano like me ka a pau." Ma ka mea,ʻo ia i ho'ākāka 'ia i ka hou laha' - ka C-hālawa Levi. A pau ma luna o huahelu ka mea conditional i ka mea i ano like geometric fractals.
Hōʻeuʻeu, a algebraic fractals
Keia papa ke koho Mandelbrot E kau iho. Ka mua explorers ma keia ala lilo i ka Palani mathematicians Pierre Fatou a me Gaston Julia. I ka 1918, Julia paʻi i ka pepa, a i ka nānā 'ana ma luna o ke ao o ka luna' iterations o ka naauao i hana '. Eia ka mea, wehewehe i ka ohana o fractals, i mea pili loa aku i ka Mandelbrot huapalapala. I loko nō o ka mea i keia hana i kaulana mea kākau i waena o mathematicians mea poina koke i ana. Ka mea, ua wale ma hope o kekahi hapa keneturia hoomaikai i kamepiula 'ē aʻe hana Julia loaa ka lua o ke ola. Kamepiula 'ae' ia e hiki ai no kela mea keia mea i ka nani a me ka richness o ko ke ao nei mai o fractals, a hiki "ike" i ka makemakika, e hoike ana ia lakou ma ka mana. Mandelbrot i ka mea mua, e hoʻohana i ke kamepiula, e ho (hana lima,ʻaʻole e like me ka leo hiki paʻa), i 'ae' e kūkulu i ke kiʻi o kēia mau huahelu.
La kekahi kanaka me ka māhele wale
Mandelbrot hoomaka ae la i kona mau 'epekema' oihana ma ka IBM noiʻi waena. Këiaʻikepili hoolilo ma lōʻihi mamao, i ke ehuehu o nä känaka 'epekema a me ka mea o ka nui ka pōʻino, a ala ae la no ia o ka leo. Benoit i huli no ka aoao e hoʻoponopono i kēia pilikia. Ke huli nei ma ka huahelu hualoaʻa, ike aku la ia i na kumu, o leo nńnń nana i ka ia i loko o kaʻokoʻa manawa pālākiō.
Julia - Mandelbrot
Kekahi o nā kiʻi mua o ka huahelu ua he Kimia ano o ke kau, i i hanau i ke aloha i ka hana o Gaston Julia a me Mandelbrot i finalized. Gaston ho'āʻo nei e noonoo ai i na pehea Looks hoʻonoho kūkulu nānā 'ana i kekahi mea haʻilula i iterated manaʻo loop. I aku la ho'āʻo i hoomaopopo kanaka 'ōlelo, no laila, e'ōlelo aku, ma luna o kona mau lima. No ka maopopo laulā cia ka hoʻohana 'ana i ka haʻilula mākou imi hou waiwai. Mākou e hookomoia ka mea, i loko o ka haʻilula, a ua loaʻa i ka eia. Ka hopena mea he nui helu kaʻina. O ia ho i ia ka huapalapala ua koi 'ia e hana i kēia hana he nui helu o ka manawa: haneri, na tausani, miliona. Keia ua hana Benoit. He pēpē ihola i nā kaʻina, a laila 'o ia i nā hualoaʻa ma ka mea kiʻi palapala. A laila,ʻo ia pena i ka kūpono shape (kēlā me kēia kala hoʻopili like i kekahi mau helu o iterations). Kēia Kimia e hoohalike ai i ka inoa o "Mandelbrot fractal."
L. kamana: i kou wahi i hanaia ma ke ano maoli
Ka pähola 'ana o fractals loaʻa koke e pili ana. E like me ka mea, ua nui pili loa ua hoʻopili i ka visualization o ka pakiko-like nā kiʻi, ka mea mua nana i aponoia i nā kumu a me nā algorithms no? Ieoaeunoai kēia mau hana kinona i lilo Artists. Ka mua o kēia,ʻo ia ka wā e hiki mai i hoʻokumu o Pixar o Nuioka ma Lauren kamana. Hana ana ma ka hōʻike o ka prototype mokulele, pii mai la oia me ka manao e hana i ke kāʻei kua kiʻi o nā kuahiwi. I kēia lā, e like me ka hana hiki lawelaweʻaneʻane kela kamepiula hoʻohana, a ma na seventies o ka hope ke kenekulia, kamepiula 'ē aʻe i ole i hiki ke lawe mai ia keʻano o ka hanaʻana, e like me ke kiʻi me ka luna hoʻoponopono a me nā palapala noi kiʻi ekolu-dimensional i ka manawa no ia i keia manawa. A me Lauren loaʻa Mandelbrot puke "Fractals:, palapala, a me ka mea hiki wale ke Ana" It Benoit i lawe mai ai na mea he nui examples e hoike ana i ka loaʻa i fractal ma ke ano maoli (fyva),ʻo ia i ho'ākāka 'ia i ko lakou likeʻole ano apau loa, a lilo i ka mea, e oluolu ia i ho'ākāka' makemakika, ka 'aoʻao. Kēia analogy mathematician alakai i kekahi manaʻo hoʻopiʻi hoʻomohala i kona pähola 'o ka pili i ka hoʻoponopono ma muli o ka barrage o ka noʻonoʻo loi, mai kona mau nā hoapili. Ka mea, ua kūkākūkāʻia i ka fractal - e Aloha e ka nani kiʻi, aʻaʻohe waiwai, i mea he ma-huina hoonui o ka hana o ka uila kamepiula 'ē aʻe. Kamana manao, e ho'āʻo mai i kēia hana ma ka hoʻomaʻamaʻa. Me ka pono a nānā aku i ka puke, hoomaka ae la i ka wā e hiki mai animator imi i ke ala e? Ii ka fractal anahonua kiʻi kamepiula ma. Ua iʻekolu lā iā ia, e hoʻihoʻi mai nōʻoia iʻo kiʻi o ka mauna panorama ma kāu kamepiula. I kēia lā, ua rula ua hoʻomano i hoʻohana. E like me ka mea huli mai, i ka hanaia'na o fractals, aole e lawe i ka manawa a me ka hana.
pāʻoihana kamana
I ka rula hoʻohanaʻia Loren, ua noonoo ole. Ua mea e Wāwahi i ka nui geometric kinona i loko o ka poe liilii, hehee wale, a me ka poe - no ka like uuku, a no laila, ma luna o. Kamana hoʻohana 'ana i ka nui triangle, māhelehele au iā lāua i loko o 4 liʻiliʻi, a no laila, ma luna, i loa e like me kana i i kiʻi i kaʻoia iʻo kuahiwi panorama. Penei, ka mea, o ka mea mua artist nana i haawi i ka fractal algorithm kiʻi kamepiula i loko no ka kūkulu i makemake kiʻi. I kēia lā, ua rula ua hoʻohana 'ia e simulate i kekahiʻano oʻoia iʻo maoli' ano apau loa.
Ka mua 3D-visualization o ka fractal algorithm
I loko o kekahi mau makahiki, Lauren Ua hoopili kona hoao ana i ka nui-me ka unahiʻole pāhana - ka Animated wikiō Vol Libre, e hōʻike 'ia ma Siggraph 1980. Kēia wikiō i walawala ai na mea he nui, a me kona mea nāna i hana i kono e hana i Lucasfilm. Here animator hiki ke hoʻomaopopo i ka piha,ʻo ia i hana i ka ekolu-dimensional panorama (he holoʻokoʻa Honua) no ka hiʻona ho film "Star Trek". Kela a me keia kēia polokalamu ( "Fractals") a he noi no 'ekolu-dimensional kiʻi (Terragen, Vue, Bryce) e pili ana hoʻohana a pau i ka hookahi algorithm no ka hōʻulu o textures a me surfaces.
Tom Beddard
I ka hala, kukuna ke kālaikūlohea, a me ka manawa kikohoʻe-hana a me ka artist, Beddard i hana i ka helu o ka loa intriguing geometric ano, i ka poe i kaheaia fractals Faberge. Mawaho, nana e like'āhihi hua Lūkini jeweler ka mea,ʻo ka mea, i ka mea maikaʻi loa pohihihi kumu. Beddard hoʻohana i nōhie iaoia no e pili ana i ko lakou kikohoʻe visualization Ke Ana Hoʻohālike. Ua kūpono huahana e luku mai ana ma ko lakou nani. Aka, he nui hōʻole e hoohalike i ka huina hoonui mea handmade me ka polokalamu kamepiula, akā, ka mea e e ike i ka mea kūpono shape extraordinarily maikai. Zest mea ia e kūkulu i kēia fractal ke mea hoʻohana 'ana i ka lako polokalamu WebGL hale waihona puke. Ua apono 'oe e makaikai i okoa fractal hale i maoli manawa.
Fractals ma ka Nature
Mau kanaka e lohe, akā, i kēia mau kii kupaianaha ka nanaia mai na wahi a pau. Nature hana mai pakiko-like na kii, akā, mākou e mai kaʻina hana. Iki nana ma ke kiʻiona aniani ma luna o mākouʻili a me kekahi apana o ka lāʻau, a me ka makou e ike fractals. A lawe, no ka laʻana, Pineapple paha hoi he peacock ka huelo - ka mea, e haku o like huahelu. Aʻano o ka broccoli Romanescu ano laulā, e loli ai i ko lakou mau helehelena, no ka mea, oiaio hiki ke kapa i ka mana o ke ano.
Ke mele mō'ī,
Ua huli mai i fractals - mea ole wale geometric ano, ka mea hiki e, a kani. No laila, mele Dzhonatan Kolton kākau mele me ka fractal algorithms. He hoʻopaʻapaʻa ia ia i keʻoli hoʻopili like i ka kūlohelohe aloha. Haku mele a pau kana mau hana a paʻiʻia ma lalo o ka laikini CreativeCommons Attribution-Noncommercial, a ua hoakaka no ka noa hoi o ka makana, ka hoʻopiliʻana, EYI o na hana ma ka 'ē aʻe.
anakahi fractal
Kēiaʻano hana i Ua loa unexpected palapala noi. Ma kona kumu, e hana i kahi mea paahana no ka Ikepili o ka lahuikanaka e loaa hou mai market, a me ka hopena, ka mea, hoomaka ae la e e pili ana ma ka "Forex" makeke. Ano, i ka malamalama-fractal mea ma luna o nā mea a pau kuai paepae ai, a ua hoʻohana 'ia i loko o ke kālepaʻano hana, a ua kapaia ka Hopu kumukuai. Au hoʻomohala i kēia hana o Bill Williams. E like me ua'ōleloʻia i kona hana mea hou i hana muaʻole o ka mea kākau, keia algorithm mea he huihui 'ana o kekahi mau "ihoiho", i Hōʻike' ke kikowaena i kā mākou paha, ma ka mea ku ole, he palena iki lōʻihi wahi.
ma ka hopena
A nana aku la makou i ka ke fractal. Ua huli mai ia i loko o ka chaos e hoopuni iho la makou, ma ka mea, he mea maikaʻi 'ano apau loa. Nature o ka maikaʻi kanaka kuhikuhi puʻuʻone, hana, ai kukulu a me ka lunaʻenehana maikaʻi. Ua Ua hooponopono loa kekahi hoʻonohonoho, a ina ua hiki ole loaʻa i ke kumu, ka mea, 'aʻole i manaʻo i ia mea ole. Malia paha e pono e nana aku i loko o kaʻokoʻa pālākiō. Mākou hiki, he olelo i na fractals hale kūʻai i ka puu o ka mea i mākou i koe i ka hōʻike.
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