프랙털

<!DOCTYPE html> <html lang="ko" data-agent="Mozilla/4.0 (compatible; MSIE 7.0; Windows NT 6.0; SLCC1; .NET CLR 2.0.50727; .NET CLR 3.0.04506; .NET CLR 3.5.21022; .NET CLR 1.0.3705; .NET CLR 1.1.4322)"> <head> <link rel="canonical" href="https://terms.naver.com/"> <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> <meta http-equiv="Content-Script-Type" content="text/javascript"> <meta http-equiv="Content-Style-Type" content="text/css"> <meta http-equiv="X-UA-Compatible" content="requiresActiveX=true;IE=edge"> <meta property="og:type" content="article"> <meta property="og:url" content="https://terms.naver.com/entry.naver?cid=47308&docId=2039091&categoryId=47308"> <meta property="og:title" content="프랙털"> <meta property="og:image" content="https://dbscthumb-phinf.pstatic.net/2831_000_1/20140102170020094_PG5LVWCUG.jpg/s_gn2_44_i1.jpg?type=w450_fst_n"> <meta property="og:description" content="프랙털은 컴퓨터 그래픽 이론에서 출발하여 현대 물리와 수학에서 빼놓을 수 없는 부분이 되었습니다. 프랙털 이론은 1975년 망델브로라는 수학자에 의해서 시작되었습니다. 프랙털이란 작은 구조가 전체 구조와 닮은 형태로 끝없이 되풀이되는 구조를 말합니다. 자신의 작은 부분에 자신과 닮은 모습이 나타나고 그 안의 작은 부분에도 자신과 닮은 모습이 무한히 반복되어 나타나는 현상입니다. 프랙털 구조는 자연에서 쉽게 찾을 수 있습니다. 고사리와 같은 양치류 식물, 공작의 깃털무늬, 구름과 산, 복잡하게 생긴 해안선의 모양, 은하의 신비스런 모습 등이 모두 프랙털 구조입니다. [가나일보 2007년 □월 △일] 울퉁불퉁한 해안선, 구름, 우주의 모습 등 자연 현상에는 무질서하게 보이는 것들이 많아요.그러나 이런 무질서한 모양도 잘 살펴보면 일정한 기하학적 구조로 되어 있어요.즉, 부분과 전체가 똑같은 모양을 하고 있지요. 이런 구조를 '프랙털'이라고 불러요. 기사에 난 나무..."> <meta property="og:article:author" content="네이버 지식백과" /> <meta property="og:article:author:url" content="https://m.terms.naver.com" /> <meta name="viewport" content="width=1110" />  <title>프랙털</title> <meta name="Description" CONTENT="어린이/학생백과, 동물/식물, 건강, 역사, 자연과학, 인문과학, 미술작품, 비주얼사전 등 전문가들이 정리한 지식을 제공하는 종합백과서비스" /> <link rel="stylesheet" type="text/css" href="https://ssl.pstatic.net/static/terms/terms/css/terms_tlist.css?250218060016"> <link rel="stylesheet" type="text/css" href="https://ssl.pstatic.net/static/terms/terms/css/terms_230427.css?250218060016"> <link rel="stylesheet" type="text/css" href="https://ssl.pstatic.net/static/terms/terms/css/subject_tmp_200508.css?250218060016"> <link rel="shortcut icon" href="/favicon.ico?250218060016" type="image/x-icon"> <link rel="stylesheet" type="text/css" 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class="blind">신규사전</span></strong> <ul class="notice_list"> <li class="notice_item"><a href="/list.naver?categoryId=72509" onclick="nclk(this, 'rec.source', '', '', 1);">기니비사우 개황</a></li> </ul> </div> </div> </div> </div> <hr> <div id="container"> <div id="content"> <div class="cont_util_wrap"> <div class="cont_util_area"> <ul class="util_list"> <li><a href="javascript:;" role="button" class="btn_add __TLIST_PUT" data-servicecode="TERMS" data-contentsid="2039091" onclick="nclk(this, 'toa.klstadd', '', '', 1);">지식리스트</a></li> <li><a href="javascript:;" onclick="nclk(this, 'toa.topmod', '', '', 1);window.open('/claim.naver?docId=' + 2039091 + '&serviceName=terms', '', 'width=970, height=820, location=no, status=no, toolbar=0, menubar=no, resizable=no, scrollbars=yes'); return false;">수정문의</a></li> <li><a href="javascript:;" role="button" class="btn_share naver-splugin" data-style="unity-v2" data-url="https://terms.naver.com/entry.naver?cid=47308&docId=2039091&categoryId=47308" data-title="프랙털" data-me-display="off" data-blog-source-form="2" data-cafe-source-form="2" title="보내기" onclick="nclk(this, 'toa.share', '', '', 1);">공유</a></li> <li><a href="/print.naver?docId=2039091&categoryId=47308" class="btn_print" role="button" target="_blank" onclick="nclk(this, 'toa.toppri', '', '', 1); window.open(this.href, '', 'width=788, height=600, toolbar=0, menubar=no, resizable=no, scrollbars=yes'); return false;">인쇄</a></li> </ul> <div class="font_area" id="btn_fs"> <a href="javascript:;" role="button" class="btn font" aria-expanded="false" aria-haspopup="listbox" id="font_set">글꼴</a> <div class="ly_font_list" id="fontset_area" role="listbox"> <a href="javascript:;" data-class="font1" role="option">나눔고딕</a> <a href="javascript:;" data-class="font2" role="option">맑은고딕</a> <a href="javascript:;" data-class="font3" role="option">돋움체</a> </div> <a href="javascript:;" role="button" class="btn sm __fontBtn">가<span class="blind">- 글꼴 작게</span></a> <a href="javascript:;" role="button" class="btn big __fontBtn">가<span class="blind">+ 글꼴 크게</span></a> </div> </div> </div> <div class="section_wrap "> <div class="headword_title"> <p class="cite"> <a href="list.naver?categoryId=42429&so=st4.asc" onclick="clickcr(this, 'toa.source', '', '', event);">재미있는 수학 이야기</a> </p> <h2 class="headword">프랙털</h2> <p class="desc">현대 수학의 산책</p> <p class="word"> </p> </div> <div id="size_ct" class="size_ct_v2"> <div class="att_type"> <div class="inner_att_type"> <div class="wr_tmp_profile"> <div class="tmp_profile"> <table class="tmp_profile_tb"> <colgroup> <col class="tmp_col"> <col width="*"> </colgroup> <tbody> <tr> <th scope="row"><span class="title">교과과정</span></th> <td> 5학년(나) 3. 도형의 합동 </td> </tr> </tbody> </table> </div> </div> </div> </div> <div class="na_block_quote"> <p>프랙털은 컴퓨터 그래픽 이론에서 출발하여 현대 물리와 수학에서 빼놓을 수 없는 부분이 되었습니다. 프랙털 이론은 1975년 망델브로라는 수학자에 의해서 시작되었습니다. 프랙털이란 작은 구조가 전체 구조와 닮은 형태로 끝없이 되풀이되는 구조를 말합니다. 자신의 작은 부분에 자신과 닮은 모습이 나타나고 그 안의 작은 부분에도 자신과 닮은 모습이 무한히 반복되어 나타나는 현상입니다. 프랙털 구조는 자연에서 쉽게 찾을 수 있습니다. 고사리와 같은 양치류 식물, 공작의 깃털무늬, 구름과 산, 복잡하게 생긴 해안선의 모양, 은하의 신비스런 모습 등이 모두 프랙털 구조입니다.</p> <em class="blockquote_source_bottom">[가나일보 2007년 □월 △일]</em> </div> <div class=" thmb" style="width:276px"> <a href="/imageDetail.naver?docId=2039091&imageUrl=https%3A%2F%2Fdbscthumb-phinf.pstatic.net%2F2831_000_1%2F20140102170020094_PG5LVWCUG.jpg%2Fs_gn2_44_i1.jpg%3Ftype%3Dm4500_4500_fst_n%26wm%3DY" target="_blank" onclick="clickcr(this, 'bdy.imgal', '', '', event);"><img src="https://dbscthumb-phinf.pstatic.net/2831_000_1/20140102170020094_PG5LVWCUG.jpg/s_gn2_44_i1.jpg?type=w276_fst_n&wm=Y" width="276" height="269" origin_src="https://dbscthumb-phinf.pstatic.net/2831_000_1/20140102170020094_PG5LVWCUG.jpg/s_gn2_44_i1.jpg?type=m4500_4500_fst_n&wm=Y" origin_width="731" origin_height="714" source="재미있는 수학 이야기" hasTitle="N" data-font-image="false" alt="프랙털 본문 이미지 1" desc="" data-title="" data-seq="1"></a> </div> <p class="txt"> 울퉁불퉁한 해안선, 구름, 우주의 모습 등 자연 현상에는 무질서하게 보이는 것들이 많아요. 그러나 이런 무질서한 모양도 잘 살펴보면 일정한 기하학적 구조로 되어 있어요. 즉, 부분과 전체가 똑같은 모양을 하고 있지요. 이런 구조를 '프랙털'이라고 불러요. </p> <p class="txt"> 기사에 난 나무 그림에서 알 수 있듯이 나무의 어느 부분을 확대해도 전체 나무와 똑같은 모양이 나타나요. 이러한 성질을 '자기 유사성'이라 부르고, 이러한 현상이 무한히 반복되는 것을 '순환성'이라 해요. 자기 유사성과 순환성은 프랙털 이론의 핵심이에요. 프랙털은 '쪼개다'란 뜻을 가진 라틴어 '프랙투스'에서 따온 용어랍니다. </p> <p class="txt">수학에 관한 책에는 프랙털 이론을 이용해 만든 도형이 나와요. 시어핀스키 삼각형은 프랙털을 이용한 예입니다.</p> <p class="txt"> 이 삼각형은 변의 가운데 점을 연결하여 네 개의 작은 삼각형으로 나눈 뒤, 한 가운데 있는 작은 삼각형을 지운 도형이에요. 이렇게 무한히 계속해 나가면 넓이는 0이 된답니다. </p> <div class="thmb c"> <a href="/imageDetail.naver?docId=2039091&imageUrl=https%3A%2F%2Fdbscthumb-phinf.pstatic.net%2F2831_000_1%2F20140102170031321_NJLNJVLGL.jpg%2Fs_gn2_44_i2.jpg%3Ftype%3Dm4500_4500_fst_n%26wm%3DY" target="_blank" onclick="clickcr(this, 'bdy.imgal', '', '', event);"><img src="https://dbscthumb-phinf.pstatic.net/2831_000_1/20140102170031321_NJLNJVLGL.jpg/s_gn2_44_i2.jpg?type=w492_fst_n&wm=Y" width="492" height="184" origin_src="https://dbscthumb-phinf.pstatic.net/2831_000_1/20140102170031321_NJLNJVLGL.jpg/s_gn2_44_i2.jpg?type=m4500_4500_fst_n&wm=Y" origin_width="1143" origin_height="428" source="재미있는 수학 이야기" hasTitle="N" data-font-image="false" alt="프랙털 본문 이미지 2" desc="" data-title="" data-seq="2"></a> </div> <p class="txt"> 정삼각형에서 시작하여 프랙털 이론을 적용하여 만든 도형에는 코흐 곡선이란 것도 있어요. 먼저 정삼각형의 변을 모두 삼등분한 뒤, 가운데 조각을 한 변으로 하는 정삼각형을 그려요. 이런 방법을 이용하면 울퉁불퉁한 해안선의 모습을 그릴 수 있답니다. </p> <div class="thmb c"> <a href="/imageDetail.naver?docId=2039091&imageUrl=https%3A%2F%2Fdbscthumb-phinf.pstatic.net%2F2831_000_1%2F20140102170036431_VTFB1N2YN.jpg%2Fs_gn2_44_i3.jpg%3Ftype%3Dm4500_4500_fst_n%26wm%3DY" target="_blank" onclick="clickcr(this, 'bdy.imgal', '', '', event);"><img src="https://dbscthumb-phinf.pstatic.net/2831_000_1/20140102170036431_VTFB1N2YN.jpg/s_gn2_44_i3.jpg?type=w492_fst_n&wm=Y" width="492" height="769" origin_src="https://dbscthumb-phinf.pstatic.net/2831_000_1/20140102170036431_VTFB1N2YN.jpg/s_gn2_44_i3.jpg?type=m4500_4500_fst_n&wm=Y" origin_width="1510" origin_height="2362" source="재미있는 수학 이야기" hasTitle="N" data-font-image="false" alt="프랙털 본문 이미지 3" desc="" data-title="" data-seq="3"></a> </div> <div class="thmb c"> <a href="/imageDetail.naver?docId=2039091&imageUrl=https%3A%2F%2Fdbscthumb-phinf.pstatic.net%2F2831_000_1%2F20140102170038201_3D7Y9SSMM.jpg%2Fs_gn2_44_i4.jpg%3Ftype%3Dm4500_4500_fst_n%26wm%3DY" target="_blank" onclick="clickcr(this, 'bdy.imgal', '', '', event);"><img src="https://dbscthumb-phinf.pstatic.net/2831_000_1/20140102170038201_3D7Y9SSMM.jpg/s_gn2_44_i4.jpg?type=w492_fst_n&wm=Y" width="492" height="187" origin_src="https://dbscthumb-phinf.pstatic.net/2831_000_1/20140102170038201_3D7Y9SSMM.jpg/s_gn2_44_i4.jpg?type=m4500_4500_fst_n&wm=Y" origin_width="1274" origin_height="485" source="재미있는 수학 이야기" hasTitle="N" data-font-image="false" alt="프랙털 본문 이미지 4" desc="" data-title="" data-seq="4"></a> </div> <p class="txt">다음과 같이 정오각형의 대각선을 그려서 잘라 만든 시어핀스키 오각형도 있답니다.</p> <div class="thmb c"> <a href="/imageDetail.naver?docId=2039091&imageUrl=https%3A%2F%2Fdbscthumb-phinf.pstatic.net%2F2831_000_1%2F20140102170048360_J1AROKPSY.jpg%2Fs_gn2_44_i5.jpg%3Ftype%3Dm4500_4500_fst_n%26wm%3DY" target="_blank" onclick="clickcr(this, 'bdy.imgal', '', '', event);"><img src="https://dbscthumb-phinf.pstatic.net/2831_000_1/20140102170048360_J1AROKPSY.jpg/s_gn2_44_i5.jpg?type=w492_fst_n&wm=Y" width="492" height="184" origin_src="https://dbscthumb-phinf.pstatic.net/2831_000_1/20140102170048360_J1AROKPSY.jpg/s_gn2_44_i5.jpg?type=m4500_4500_fst_n&wm=Y" origin_width="1304" origin_height="488" source="재미있는 수학 이야기" hasTitle="N" data-font-image="false" alt="프랙털 본문 이미지 5" desc="" data-title="" data-seq="5"></a> </div> <div class="box_content"> <h4><em class="pcate"><span>논술이의 쪽지시험</span></em> 다음은 프랙털에 대한 설명이에요. 맞으면 ○, 틀리면 X로 표시하세요.</h4> <p class="txt"> 1. 정사각형의 네 변의 중간을 서로 이으면 닮은꼴의 정사각형이 만들어진다.( )<br> 2. 한 부분만 봐도 전체 모양을 알 수 있다.( )<br> 3. 프랙털 이론을 발표한 사람은 아인슈타인이다.( )<br> 4. 프랙털은 '쪼개다'란 뜻의 그리스어에서 유래했다.( )<br><br>정답 : ↓ 아랫부분을 마우스로 긁어보세요.<br><span class="hidden">1번 ○, 2번 ○, 3번 X, 4번 X</span> </p> </div> </div> <div class="section_group"> <div class="section_area" id="relatedContentsArea" data-docId="2039091" data-expCategoryId="47308"> </div> </div> <div class="section_group cite_group"> <div class="section_area"> <h3 class="title">출처</h3> <div class="cite_area_wrap "> <h3 class="blind">제공처 정보</h3> <div class="thumb_area"> <div class="thumb"> <a href="/list.naver?categoryId=42429" onclick="nclk(this, 'soc.simg', '', '', 1);"> <img src="https://bookthumb-phinf.pstatic.net/cover/029/084/02908495.jpg?type=m96" height="94" alt="재미있는 수학 이야기 이미지"><span class="mask"></span> </a> </div> </div> <div class="cite_area"> <div class="cite_info"> <strong class="title"> <a href="/list.naver?categoryId=42429" onclick="nclk(this, 'soc.source', '', '', 1);">재미있는 수학 이야기</a> </strong> <span class="sub_info">2007. 4. 27.</span> <a href="http://book.naver.com/bookdb/book_detail.nhn?bid=2908495" class="link" target="_blank" onclick="nclk(this, 'soc.bmore', '', '', 1);">책보러가기<i class="ico_arrow"></i></a> </div> </div> <div class="writer_area"> <ul class="writer_list"> <li> <div class="cite_area"> <p class="writer_info"> <strong>글</strong> <span class="writer"> <a href="/list.naver?searchId=au140" onclick="nclk(this, 'soc.expertname', '', '', 1);">권현직</a> </span> </p> <p class="desc"> 서울대학교 수학과를 졸업하고, KAIST 수학과에서 석사와 박사 학위를 받았습니다. KAIST와 한밭대학교 영재교육원에서 수학 교재 개발, 한국과학영재학교에서 전자 교재 개발에 참여했습니다. 현재 대덕창의과학교육원의 소장으로 있습니다. 저서로는 〈자와 컴퍼스로 배우는 수학〉, 〈영재아를 위한 무한의 신비〉, 〈읽기만 해도 답이 보이는 수학〉, 〈논리로 생각하고 추리로 풀어보는 수학 이야기〉, 〈인터넷 전자 교재 - 미분방정식〉이 있습니다. </p> </div> </li> <li> <div class="cite_area"> <p class="writer_info"> <strong>그림</strong> <span class="writer"> <a href="/list.naver?searchId=au173" onclick="nclk(this, 'soc.expertname', '', '', 1);">김영랑</a> </span> </p> <p class="desc"> 프리랜서 일러스트레이터로, 일러스트와 만화를 접목한 재미있는 그림을 그리고 있습니다. 작품으로는 〈외계 침공〉, 〈바둑아 놀자〉, 〈이솝우화〉, 〈지킬 박사와 하이드〉, 〈톰아저씨 오두막〉, 〈신문이 보이고 뉴스가 들리는 재미있는 환경 이야기〉 등이 있습니다. </p> </div> </li> <li> <div class="cite_area"> <p class="writer_info"> <strong> 제공처 </strong> <span class="writer"> <a href="/list.naver?searchId=pv293" onclick="nclk(this, 'soc.expertname', '', '', 1);">가나출판사</a> </span> <span class="sub_info"> <a href="http://post.naver.com/my.nhn?memberNo=24413396" class="url_link" target="_blank" onclick="nclk(this, 'soc.experurl', '', '', 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