Hausdorff dimension yog dab tsi?

Cov txheej txheem:

Hausdorff dimension yog dab tsi?
Hausdorff dimension yog dab tsi?

Video: Hausdorff dimension yog dab tsi?

Video: Hausdorff dimension yog dab tsi?
Video: Fractals are typically not self-similar 2024, Lub peb hlis ntuj
Anonim

Hauv kev ua lej, Hausdorff qhov ntev yog qhov ntsuas ntawm qhov ntxhib, lossis qhov tshwj xeeb tshaj plaws, fractal dimension, uas tau pib ua ntej xyoo 1918 los ntawm tus lej lej Felix Hausdorff. Piv txwv li, Hausdorff qhov ntev ntawm ib qho taw tes yog xoom, ntawm kab ntu yog 1, ntawm ib lub square yog 2, thiab ntawm lub voos xwmfab yog 3.

Hausdorff dimension xam li cas?

The Hausdorff Dimension

Peb xav txog N=rD, nqa lub cav ntawm ob sab, thiab tau log(N)=D log (r). Yog tias peb daws tau D. D=log(N)/log(r) Lub ntsiab lus: tshuaj xyuas qhov no, D tsis tas yuav yog tus lej, raws li nws nyob hauv Euclidean geometry.

txhais li cas los ntawm topological dimension?

Topological qhov ntev txhais qhov sib txawv ntawm cov txheej txheem topological xws li Hauv thiab Im thaum n=m. Qhov tsis muaj qhov txhais tau hais tshwj xeeb tshaj yog vim qhov yooj yim piav qhia ntawm geometric dimension. … Tseem tshuav: qhov chaw metrizable yog qhov chaw topological uas yog homeomorphic rau qhov chaw metric.

Howdorff method yog dab tsi?

Hauv kev ua lej, Hausdorff nrug, lossis Hausdorff metric, tseem hu ua Pompeiu–Hausdorff nrug, ntsuas deb npaum li cas ob lub subsets ntawm qhov chaw metric yog los ntawm ib leeg. Nws hloov cov txheej uas tsis yog qhov khoob khoob khoob ntawm qhov chaw metric rau hauv qhov chaw metric hauv nws tus kheej txoj cai.

Lub ntsiab lus ntawm fractal dimension yog dab tsi?

Nyob rau hauv lej, tshwj xeeb tshaj yog nyob rau hauv fractal geometry, ib tug fractal dimension yog tus piv muab ib tug statistical index ntawm complexity piv yuav ua li cas nthuav dav nyob rau hauv ib tug qauv (qhib hais lus, ib tug fractal qauv) hloov nrog lub scale ntawm uas yog ntsuas. … Ib qho piv txwv tsis tseem ceeb yog qhov fractal qhov ntev ntawm Koch snowflake.

Pom zoo: