Fractal geometry - ib tug amazing txuj ci tseem ceeb

Lub tswvyim ntawm "fractal geometry" thiab "fractal" sawv nyob rau hauv lub lig 70s., Thiab lub thib ob ib nrab ntawm lub 80s, lawv tau ua ib feem ntawm cov lus ntawm programmers, mathematicians thiab txawm nyiaj txiag traders. Lub sij hawm "fractal" yog muab los ntawm latin "fractus" thiab txhais "tawg tsam muaj." Cov lus nyob rau hauv 1975, ib tug American thiab ib tug Fabkis txoj paub txog Benoit Mandelbrot teev tseg lus tab sis nws tus kheej-zoo xws li cov qauv, uas nws ces tau ua. Nyob rau hauv 1977 nws luam tawm nws phau ntawv, uas twb nkaus mob siab rau qhov no cim thiab zoo nkauj phenomenon ntawm fractal geometry ntawm qhov.

Sam Benoit Mandelbrot yog ib tug mathematician, tab sis lub sij hawm "fractal" tsis xa mus rau cov zauv tswv yim. Raws li ib tug txoj cai, nws yog meant ib geometric zoo muaj ib los yog ntau tshaj ntawm cov nram qab no cov khoom:

1) nrog ib qho kev nce rau hauv nws kuaj complex qauv;

2) ib tug ntau dua los yog tsawg raws li, qhov no daim duab yog zoo li nws tus kheej;

3) nws yuav raug ua lub tsev siv recursive txoj kev;

4) nws yog yus muaj los ntawm fractional Hausdorff (fractal) dimension siab tshaj topology.

Fractal geometry - qhov no yog ib tug tiag tiag kiv puag ncig nyob rau hauv cov zauv piav qhia ntawm qhov. Koj muaj peev xwm siv nws los piav qhia txog lub ntiaj teb no ntau npaum li cas meej npaum li nws ib txwm ua lej los yog physics. Noj, piv txwv li, Brownian tsab ntawv tsa suab. Seemingly random zog hais ntawm hmoov av tshem tawm nyob rau hauv cov dej, muaj tiav chaos. Cuaj kaum, txawm no yog fractal geometry. Promiscuous Brownian tsab ntawv tsa suab muaj ib zaus cov yam ntxwv uas yuav siv tau los twv seb tej xwm txheej nrog ib tug loj tus naj npawb ntawm tej ntaub ntawv. Qhov no yuav tsis tab sis ua surprise. Txawm li cas los, nws yog Brownian tsab ntawv tsa suab pab nyob rau hauv lawv lub sij hawm Mandelbrot twv nqi hloov mus hloov los nyob rau hauv tus nqi ntawm wool.

Fractal geometry tau lug siv nyob rau hauv lub computer kos duab. Cia li xav txog tej yam uas koj yuav tau ua ib qhov kev pab cuam uas yuav tso saib ib tug peb-dimensional qauv ntawm lub coastline, lub roob los yog lub ntug ntawm lub hav zoov. Yuav ua li cas cov qauv qhia txog tag nrho cov ua tau? Yuav ua li cas siv zog? Thiab ntawm no tuaj rau cov kev pab fractals. Saib cov me me ceg - qhov no me me ntsis ib tug loj tsob ntoo. Ib tug me me huab yog ib yam ntawm cov loj huab, thiab cov molecule - ib tug me me analogue ntawm lub galaxy. Yog li ntawd, siv tsis tshua mob heev qauv, uas yog, cov neeg uas xa mus rau lawv tus kheej, nws yog ua tau rau simulate heev tiag duab.

Fractal geometry pom nws daim ntawv thov nyob rau hauv architecture, fine arts (Impressionism fractal). Sensational nyob rau hauv nws lub sij hawm painting ntawm Jackson Pollock yog ib tug prime piv txwv. Nrog kev pab los ntawm fractals zaj duab xis kev lag luam tau ua ib tug tiag tiag txhob - ua ntej dag nta tau yeej tsis ntsia li tiag. Economists siv lawv twv seb rau chav kawm ntawm kev nyab xeeb hloov mus hloov los. Ntiaj teb fractals khw muag khoom noj ntau ntau ceeb, vim hais tias nws yog ib hom lus nyob ntawm qhov, thiab leej twg paub uas foundations nws yuav thawb cov tib neeg tom ntej no 5-10 xyoo?