{"id":7800,"date":"2026-05-24T04:42:27","date_gmt":"2026-05-24T01:42:27","guid":{"rendered":"https:\/\/www.schooler.org.ua\/uk-uaberegova-linija-ne-ye-fraktalom-ru-ruberegovaja-linija-ne\/"},"modified":"2026-05-24T04:42:27","modified_gmt":"2026-05-24T01:42:27","slug":"uk-uaberegova-linija-ne-ye-fraktalom-ru-ruberegovaja-linija-ne","status":"publish","type":"post","link":"https:\/\/www.schooler.org.ua\/cs\/uk-uaberegova-linija-ne-ye-fraktalom-ru-ruberegovaja-linija-ne\/","title":{"rendered":"Pob\u0159e\u017e\u00ed nen\u00ed frakt\u00e1l"},"content":{"rendered":"

Psal se rok 1967. Benoit Mandelbrot se pod\u00edval na mapu Velk\u00e9 Brit\u00e1nie. Nedok\u00e1zal zm\u011b\u0159it jeho pob\u0159e\u017e\u00ed. Obvod se prodlu\u017eoval, \u010d\u00edm pe\u010dliv\u011bji se jej sna\u017eil zm\u011b\u0159it. O osm let pozd\u011bji vymyslel nov\u00e9 slovo: frakt\u00e1ln\u00ed<\/strong>. <\/p>\n

Forma skl\u00e1daj\u00edc\u00ed se z men\u0161\u00edch prvk\u016f, kter\u00e9 navazuj\u00ed na strukturu celku. P\u0159ibli\u017ete a vzor se zacykl\u00ed. Donekone\u010dna. P\u0159esn\u011b tak jsme zvykl\u00ed vid\u011bt strukturu Zem\u011b. Alespo\u0148 z hlediska geografie. Slavn\u00fd “pob\u0159e\u017en\u00ed paradox”<\/strong> \u0159\u00edk\u00e1: okraj Zem\u011b nelze zm\u011b\u0159it. Je to chaotick\u00e9. M\u00e1 nekone\u010dnou slo\u017eitost. <\/p>\n

Nebo snad ne? <\/p>\n

Nov\u00fd v\u00fdzkum tuto my\u0161lenku zcela p\u0159evrac\u00ed. V\u00edce ne\u017e 130 001 ostrov\u016f. Pops\u00e1no. M\u011b\u0159eno. Studie publikovan\u00e1 na arXiv.org a v \u010dasopise Geophysical Research Letters<\/em> tvrd\u00ed, \u017ee Zem\u011b nen\u00ed tak frakt\u00e1ln\u00ed, jak bychom si cht\u011bli myslet. Mluv\u00edme konkr\u00e9tn\u011b o pob\u0159e\u017e\u00ed. Dopl\u0148uj\u00ed seznam. Co se t\u00fd\u010de slo\u017eitosti, samoz\u0159ejm\u011b. Topografie povrchu? Mnohem chaoti\u010dt\u011bj\u0161\u00ed. Distribuce velikosti? V\u00fdrazn\u00e1 fraktalita. <\/p>\n

\n

“Paradox pob\u0159e\u017e\u00ed je n\u011bco, o \u010dem lid\u00e9 sly\u0161\u00ed nej\u010dast\u011bji, ale v tomto p\u0159\u00edpad\u011b jsou pob\u0159e\u017e\u00ed nejjednodu\u0161\u0161\u00ed \u010d\u00e1st\u00ed rovnice.” <\/p>\n<\/blockquote>\n

Mat\u011bj Oline. Matematik. University of Chicago. Vedouc\u00ed autor. Frakt\u00e1lovou dimenzi pova\u017euje za m\u011b\u0159\u00edtko \u201e\u0161k\u00e1lovatelnosti\u201c. Vysok\u00fd rozm\u011br? Hrboly vid\u00edte znovu a znovu, bez ohledu na to, jak bl\u00edzko se dostanete. N\u00edzk\u00e1 dimenze? Pokud jde o detaily, v\u00edt\u011bz\u00ed hladkost. V\u011bt\u0161ina ostrov\u016f je n\u011bkde uprost\u0159ed. <\/p>\n

Ale p\u0159edchoz\u00ed model byl \u0161patn\u00fd. Tradi\u010dn\u00ed v\u011bda o Zemi aplikuje jedin\u00e9 frakt\u00e1ln\u00ed pravidlo na ka\u017ed\u00fd tvar ter\u00e9nu. Velikost souvis\u00ed s tvarem, tvar s v\u00fd\u0161kou. Na tom nez\u00e1le\u017e\u00ed. Oline data \u0159\u00edkaj\u00ed ne. Neexistuje \u017e\u00e1dn\u00e1 korespondence. N\u011bkter\u00e9 oblasti se hod\u00ed k detail\u016fm l\u00e9pe ne\u017e jin\u00e9. <\/p>\n

Pob\u0159e\u017e\u00ed bylo p\u0159ekvapiv\u011b klidn\u00e9. <\/p>\n

P\u0159em\u00fd\u0161lejte o tom. Usazeniny se hromad\u00ed. Eroze vyma\u017ee obrysy. Okraj zem\u011b je vyhlazen vodou, \u010dasem a fyzik\u00e1ln\u00edmi z\u00e1kony. Vrchol hory? Drsn\u011bj\u0161\u00ed. Star\u0161\u00ed. M\u00e9n\u011b ovlivn\u011bna touto vyhlazovac\u00ed silou. Oline naz\u00fdv\u00e1 star\u0161\u00ed modely \u201ehra\u010dky\u201c. Jsou samoz\u0159ejm\u011b u\u017eite\u010dn\u00e9 pro u\u010den\u00ed. Ale to nejsou p\u0159esn\u00e9 mapy. <\/p>\n

Andreas Baas nebyl do studie zapojen. Geomorfolog z King’s College London. Zkontroloval pr\u00e1ci. Metodu ozna\u010dil za p\u0159\u00edsnou. Ale z\u016fst\u00e1v\u00e1 opatrn\u00fd. Hladk\u00e9 pob\u0159e\u017e\u00ed? \u00da\u017easn\u00e9. Zejm\u00e9na ve srovn\u00e1n\u00ed s p\u0159edchoz\u00edmi odhady. <\/p>\n

Z\u00e1le\u017e\u00ed na tom? Mo\u017en\u00e1. Mo\u017en\u00e1 to pom\u016f\u017ee uzav\u0159\u00edt mezeru mezi t\u00edm, jak modelujeme povrchy a jak m\u011b\u0159\u00edme hrany. Baas chce modely sjednotit. Pod\u00edvejte se, zda snesou kritiku. Zkontrolujte, zda matematika odpov\u00edd\u00e1 ne\u010distot\u011b. <\/p>\n

Nen\u00ed to tak, \u017ee by b\u0159eh byl jednoduch\u00fd. Faktem je, \u017ee na\u0161e domn\u011bnky byly jednodu\u0161\u0161\u00ed ne\u017e realita. Vybudovali jsme vesm\u00edr frakt\u00e1lov\u00fdch smy\u010dek, proto\u017ee n\u00e1m to p\u0159i\u0161lo spr\u00e1vn\u00e9. Proto\u017ee matematika byla kr\u00e1sn\u00e1. Zem\u011b se nestar\u00e1 o na\u0161i estetiku. Ni\u010d\u00ed, co se j\u00ed zl\u00edb\u00ed. <\/p>\n

Tak co te\u010f? P\u0159ekreslujeme mapy? S nejv\u011bt\u0161\u00ed pravd\u011bpodobnost\u00ed ano.<\/p>\n","protected":false},"excerpt":{"rendered":"

Psal se rok 1967. Benoit Mandelbrot se pod\u00edval na mapu Velk\u00e9 Brit\u00e1nie. Nedok\u00e1zal zm\u011b\u0159it jeho pob\u0159e\u017e\u00ed. Obvod se prodlu\u017eoval, \u010d\u00edm pe\u010dliv\u011bji se jej sna\u017eil zm\u011b\u0159it. O osm let pozd\u011bji vymyslel nov\u00e9 slovo: frakt\u00e1ln\u00ed. Forma skl\u00e1daj\u00edc\u00ed se z men\u0161\u00edch prvk\u016f, kter\u00e9 navazuj\u00ed na strukturu celku. P\u0159ibli\u017ete a vzor se zacykl\u00ed. Donekone\u010dna. P\u0159esn\u011b tak jsme zvykl\u00ed vid\u011bt […]<\/p>\n","protected":false},"author":1,"featured_media":7799,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"tdm_status":"","tdm_grid_status":""},"categories":[1],"tags":[],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/posts\/7800"}],"collection":[{"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/comments?post=7800"}],"version-history":[{"count":0,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/posts\/7800\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/media\/7799"}],"wp:attachment":[{"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/media?parent=7800"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/categories?post=7800"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/tags?post=7800"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}