{"id":503,"date":"2011-06-10T11:31:46","date_gmt":"2011-06-10T09:31:46","guid":{"rendered":"https:\/\/abonyita.inf.elte.hu\/?p=503"},"modified":"2011-06-10T11:31:46","modified_gmt":"2011-06-10T09:31:46","slug":"utazas-a-mandelbrot-halmazba","status":"publish","type":"post","link":"https:\/\/abonyita.inf.elte.hu\/?p=503","title":{"rendered":"Utaz\u00e1s a Mandelbrot-halmazba"},"content":{"rendered":"<p>A Frakt\u00e1lok vil\u00e1g\u00e1t sokan, sokf\u00e9le m\u00f3don szeml\u00e9ltett\u00e9k m\u00e1r, el\u00e9g ha megn\u00e9zz\u00fck a <a href=\"http:\/\/www.google.hu\/search?q=fractals&amp;um=1&amp;hl=hu&amp;client=firefox-a&amp;hs=cVw&amp;rls=org.mozilla:hu:official&amp;channel=s&amp;biw=1280&amp;bih=784&amp;tbm=isch&amp;source=lnt&amp;tbs=isz:l&amp;sa=X&amp;ei=X7_xTbr7BcaBsway2ayIBw&amp;ved=0CAoQpwUoAQ\">Google tal\u00e1lati oldal\u00e1t<\/a>.<\/p>\n<p>De mit is nevez\u00fcnk frakt\u00e1lnak?<\/p>\n<p>&#8222;A frakt\u00e1lok a matematikat\u00f6rt\u00e9net sor\u00e1n m\u00e1r az 1880-as \u00e9vekt\u0151l kezdve fellelhet\u0151ek, igaz, csak mint egyed\u00fcl\u00e1ll\u00f3, egym\u00e1st\u00f3l elszigetelt matematikai \u00e9rdekess\u00e9gek \u00e9s ellenp\u00e9ld\u00e1k. Jelent\u0151s\u00e9g\u00fckre Benoit B. Mandelbrot amerikai matematikus figyelt fel, \u0151 gy\u0171jt\u00f6tte ezeket a matematikai &#8222;kakukktoj\u00e1sokat&#8221; egy csoportba, \u00e9s \u0151 nevezte el \u0151ket 1975 k\u00f6r\u00fcl frakt\u00e1loknak. A frakt\u00e1l sz\u00f3 a latin fractus sz\u00f3b\u00f3l sz\u00e1rmazik, melynek jelent\u00e9se t\u00f6r\u00f6tt, t\u00f6redezett. Olyan alakzatokat, ponthalmazokat nevezett \u00edgy, melyek l\u00e9nyegesen szab\u00e1lytalanabbak, \u00f6sszetettebbek, t\u00f6redezettebbek a klasszikus geometri\u00e1ban el\u0151fordul\u00f3 alakzatokn\u00e1l.&#8221;\u00a0 Forr\u00e1s: <a href=\"http:\/\/teamlabor.inf.elte.hu\/logosecsetvonasok\/lecke7.html\">L\u00f3g\u00f3s Ecsetvon\u00e1sok tananyag<\/a>.<\/p>\n<p>Ha p\u00e9ld\u00e1ul megn\u00e9zz\u00fck az im\u00e9nt id\u00e9zett <a href=\"http:\/\/teamlabor.inf.elte.hu\/logosecsetvonasok\/lecke7.html\">tananyag 7.leck\u00e9j\u00e9t<\/a>, l\u00e1thatjuk, hogy a Log\u00f3 nyelv seg\u00edts\u00e9g\u00e9vel milyen egyszer\u0171en lehet l\u00e1tv\u00e1nyos frakt\u00e1lokat k\u00e9sz\u00edteni. Hasonl\u00f3 frakt\u00e1l rajzol\u00e1si\u00a0 feladatok rendre megtal\u00e1lhat\u00f3k a k\u00fcl\u00f6nb\u00f6z\u0151 munkaf\u00fczetekben, illetve versenyfeladatokban.<\/p>\n<p>A tegnapi HungaroLogo konferencia egyik el\u0151ad\u00f3ja, Pavel Boytchev egy m\u00e9g l\u00e1tv\u00e1nyosabb m\u00f3dj\u00e1t v\u00e1lasztotta a Frakt\u00e1lok szeml\u00e9ltet\u00e9s\u00e9nek.<\/p>\n<div id=\"attachment_521\" style=\"width: 440px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-521\" class=\"size-full wp-image-521\" title=\"fraktals\" src=\"https:\/\/abonyita.inf.elte.hu\/wp-content\/uploads\/2011\/06\/fraktals.png\" alt=\"P\u00f3kh\u00e1l\u00f3ra eml\u00e9keztet\u0151 frakt\u00e1l\" width=\"430\" height=\"304\" srcset=\"https:\/\/abonyita.inf.elte.hu\/wp-content\/uploads\/2011\/06\/fraktals.png 430w, https:\/\/abonyita.inf.elte.hu\/wp-content\/uploads\/2011\/06\/fraktals-300x212.png 300w\" sizes=\"auto, (max-width: 599px) calc(100vw - 50px), (max-width: 767px) calc(100vw - 70px), (max-width: 991px) 429px, (max-width: 1199px) 637px, 354px\" \/><p id=\"caption-attachment-521\" class=\"wp-caption-text\">Frakt\u00e1l vagy p\u00f3kh\u00e1l\u00f3?<\/p><\/div>\n<p>A fenti k\u00e9p egy olyan vide\u00f3b\u00f3l sz\u00e1rmazik, amelyben a szerz\u0151 a Mandelbrot-halmaz alkot\u00f3elemei \u00e1ltal inspir\u00e1lt fotorealisztikus k\u00e9peket is elhelyezett, amelyek m\u00e9g l\u00e1tv\u00e1nyosabb\u00e1 teszik a bemutat\u00f3t. De err\u0151l mindenki maga is meggy\u0151z\u0151dhet, ha megn\u00e9zi az al\u00e1bbi -mind\u00f6ssze 5 perces &#8211; vide\u00f3t.<\/p>\n<p>httpvh:\/\/www.youtube.com\/watch?v=93akxnQ1xxw<\/p>\n<p>\u00c9rdekess\u00e9g, hogy a vide\u00f3 egy olyan 3D-s Log\u00f3 k\u00f6rnyezetben (<a href=\"http:\/\/www.elica.net\/\">ELICA Log\u00f3<\/a>) k\u00e9sz\u00fclt, amely Pavel Boytchev saj\u00e1t fejleszt\u00e9se.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A Frakt\u00e1lok vil\u00e1g\u00e1t sokan, sokf\u00e9le m\u00f3don szeml\u00e9ltett\u00e9k m\u00e1r, el\u00e9g ha megn\u00e9zz\u00fck a Google tal\u00e1lati oldal\u00e1t. De mit is nevez\u00fcnk frakt\u00e1lnak? &#8222;A frakt\u00e1lok a matematikat\u00f6rt\u00e9net sor\u00e1n m\u00e1r az 1880-as \u00e9vekt\u0151l kezdve fellelhet\u0151ek, igaz, csak mint egyed\u00fcl\u00e1ll\u00f3, egym\u00e1st\u00f3l elszigetelt matematikai \u00e9rdekess\u00e9gek \u00e9s ellenp\u00e9ld\u00e1k. Jelent\u0151s\u00e9g\u00fckre Benoit B. Mandelbrot amerikai matematikus figyelt fel, \u0151 gy\u0171jt\u00f6tte ezeket a matematikai &#8222;kakukktoj\u00e1sokat&#8221; &#8230;<\/p>\n<a href=\"https:\/\/abonyita.inf.elte.hu\/?p=503\" class=\"read-more-link\">Tov\u00e1bb olvasom  <span class=\"screen-reader-text\">\"Utaz\u00e1s a Mandelbrot-halmazba\"<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[29],"tags":[47,46],"class_list":["post-503","post","type-post","status-publish","format-standard","hentry","category-erdekessegek","tag-fraktal","tag-logo","penguin-post","penguin-post-not-sticky"],"_links":{"self":[{"href":"https:\/\/abonyita.inf.elte.hu\/index.php?rest_route=\/wp\/v2\/posts\/503","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/abonyita.inf.elte.hu\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/abonyita.inf.elte.hu\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/abonyita.inf.elte.hu\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/abonyita.inf.elte.hu\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=503"}],"version-history":[{"count":27,"href":"https:\/\/abonyita.inf.elte.hu\/index.php?rest_route=\/wp\/v2\/posts\/503\/revisions"}],"predecessor-version":[{"id":531,"href":"https:\/\/abonyita.inf.elte.hu\/index.php?rest_route=\/wp\/v2\/posts\/503\/revisions\/531"}],"wp:attachment":[{"href":"https:\/\/abonyita.inf.elte.hu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=503"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/abonyita.inf.elte.hu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=503"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/abonyita.inf.elte.hu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=503"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}