{"id":789,"date":"2015-01-03T15:00:25","date_gmt":"2015-01-03T07:00:25","guid":{"rendered":"http:\/\/www.jdcui.com\/?p=789"},"modified":"2026-02-14T21:23:59","modified_gmt":"2026-02-14T13:23:59","slug":"mandelbrot-set-julia-set%ef%bc%88%e5%88%86%e5%bd%a2%ef%bc%89","status":"publish","type":"post","link":"http:\/\/www.jdcui.com\/?p=789","title":{"rendered":"[\u6570\u5b66&#038;\u51e0\u4f55] Mandelbrot Set &#038; Julia Set"},"content":{"rendered":"<p>\u524d\u4e24\u5929\u5728\u7f51\u4e0a\u65e0\u610f\u770b\u5230\u4e86\u5f88\u591a\u5173\u4e8e\u5206\u5f62\u7684\u4e1c\u897f\u3002\u611f\u89c9\u5341\u5206\u6f02\u4eae\u3002\u5206\u5f62\u4f53\u73b0\u4e86\u4e00\u79cd\u6709\u5e8f\u548c\u65e0\u5e8f\u7684\u7edf\u4e00\u3002\u6709\u5174\u8da3\u7684\u53ef\u4ee5\u4e0a\u7f51\u641c\u4e9b\u8d44\u6599\u770b\u770b\uff0c\u8fd8\u6709\u5f88\u591a\u4e13\u95e8\u7684\u5206\u5f62\u8f6f\u4ef6\u3001\u7f51\u7ad9\u3001\u8bba\u575b\u3002<\/p>\n<p>\u6700\u51fa\u540d\u7684\u5206\u5f62\u6211\u60f3\u5c31\u662fMandelbrotSet\u548cJuliaSet\u4e86\u3002\u56e0\u4e3a\u5206\u5f62\u51e0\u4f55\u5b66\u7684\u521b\u59cb\u4eba\u5c31\u662fIBM\u7814\u7a76\u5ba4\u7684\u6570\u5b66\u5bb6B.B.Mandelbrot\u3002\u4e0b\u9762\u7b80\u5355\u4ecb\u7ecd\u4e00\u4e0bMandelbrotSet\u548cJuliaSet\u7684\u7b97\u6cd5\u3002\u5176\u5b9e\u7b97\u6cd5\u539f\u7406\u8fd8\u662f\u6bd4\u8f83\u7b80\u5355\u3002<\/p>\n<p>MandelbrotSet\u7531\u4e00\u4e2a\u4e8c\u6b21\u8fed\u4ee3\u65b9\u7a0b\uff1az<sub>n<\/sub>+1 = z<sub>n<sup>2<\/sup><\/sub> +c\uff0cz<sub>0<\/sub>=c\u6240\u5f97\u5230\u3002\u4e5f\u5c31\u662f\u5bf9\u6240\u6709\u7684\u590d\u5e73\u9762\u4e0a\u7684\u70b9c\u90fd\u8fdb\u884c\u8fed\u4ee3\uff0c\u4e0d\u53d1\u6563\u7684\u70b9\u90fd\u5c5e\u4e8eMandelbrot\u96c6\u7684\u8303\u56f4\u3002<\/p>\n<p>JuliaSet\u7531\u4e00\u4e2a\u4e8c\u6b21\u6620\u5c04\uff1az<sub>n<\/sub>+1 = z<sub>n<\/sub><sup>2<\/sup> +c \u4ea7\u751f\u3002c\u4e3a\u4e00\u5b9a\u503c\u3002\u4e5f\u5c31\u662f\u9009\u5b9a\u4e00\u4e2a\u5e38\u590d\u6570\uff0c\u7136\u540e\u5bf9\u6240\u6709\u7684\u590d\u5e73\u9762\u4e0a\u7684\u70b9z\u8fdb\u884c\u8fed\u4ee3\uff0c\u4e0d\u53d1\u6563\u7684\u70b9\u90fd\u5c5e\u4e8eJulia\u96c6\u7684\u8303\u56f4\u3002<\/p>\n<p>\u5176\u4e2dz\u548cc\u90fd\u662f\u590d\u6570\u3002\u8fed\u4ee3\u7684\u6b21\u6570\u8d8a\u591a\uff0c\u56fe\u5f62\u663e\u793a\u5c31\u8d8a\u7cbe\u7ec6\uff0c\u53ef\u4ee5\u65e0\u9650\u7ec6\u5206\uff0c\u540c\u65f6\u5206\u5f62\u8fd8\u6709\u81ea\u76f8\u4f3c\u6027\uff0c\u5c31\u662f\u65e0\u9650\u653e\u5927\u4e00\u4e2a\u7ec6\u5c0f\u7684\u90e8\u5206\uff0c\u770b\u8d77\u6765\u548c\u539f\u6765\u7684\u90e8\u5206\u4e00\u6837\u3002<\/p>\n<p>\u7531\u4e8e\u5206\u5f62\u7684\u65e0\u9650\u6027\uff0c\u5bf9\u56fe\u5f62\u7684\u663e\u793a\u548c\u7b97\u6cd5\u90fd\u662f\u6781\u5927\u7684\u6311\u6218\u3002\u4e00\u822c\u7f16\u7a0b\u7684\u4e66\u90fd\u4f1a\u7528\u8fd9\u4e2a\u4f8b\u5b50\u6765\u4ecb\u7ecd\u591a\u6838\u8ba1\u7b97\u3001\u5e76\u884c\u8ba1\u7b97\u3002\u54c8\u54c8\u3002\u624b\u75d2\u4e86\uff0c\u8fd8\u662f\u7f16\u4e2a\u7a0b\u5e8f\u6765\u770b\u4e00\u4e0b\u6548\u679c\u5427\u3002\u622a\u56fe\u5982\u4e0b\uff1a<\/p>\n<p>1\u3001\u5148\u662f<strong>Mandelbrot Set<\/strong>\uff08\u8fed\u4ee3\u6b21\u657050\uff09\uff1a<\/p>\n<p>\uff081\uff09\u6765\u4e2a\u9ed1\u767d\u8c03\u8272\u65b9\u6848\uff08\u9ed1\u8272\u7684\u5c31\u662fMandelbrot\u96c6\u7684\u8303\u56f4\uff09<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-802 size-full\" title=\"Mandelbrot Set\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2015\/01\/Mandelbrot1.jpeg\" alt=\"Mandelbrot1\" width=\"846\" height=\"637\" \/><\/p>\n<p>\uff082\uff09\u9ed1\u767d\u7684\u8c03\u8272\u65b9\u6848\u592a\u5355\u8c03\u4e86\uff0c\u6765\u770b\u770b\u5f69\u8272\u7684\u6548\u679c\u5982\u4f55<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-792\" title=\"Mandelbrot Set\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2015\/01\/Mandelbrot2.jpeg\" alt=\"Mandelbrot2\" width=\"857\" height=\"644\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-793 size-full\" title=\"Mandelbrot Set\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2015\/01\/Mandelbrot4.jpeg\" alt=\"Mandelbrot4\" width=\"846\" height=\"637\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-794 size-full\" title=\"Mandelbrot Set\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2015\/01\/Mandelbrot5.jpeg\" alt=\"Mandelbrot5\" width=\"846\" height=\"637\" \/><\/p>\n<div><span style=\"font-size: small;\">2\u3001<b>JuliaSet<\/b>\u662f\u4ec0\u4e48\u6837\u7684\u5462\uff0c\u6211\u4eec\u63a5\u4e0b\u6765\u770b\u770b\uff0c\u8fd9\u6b21\u9009\u62e9\u8fed\u4ee3\u6b21\u4e3a500\u6b21\uff0c\u4ece\u4e0b\u9762\u7684\u56fe\u4e5f\u53ef\u4ee5\u770b\u5230\uff0c\u663e\u793a\u7684\u5185\u5bb9\u66f4\u52a0\u7ec6\u81f4\u548c\u6f02\u4eae\u3002<\/span>\u7531\u4e8eJulia\u96c6\u548c\u9009\u62e9\u7684\u590d\u5e38\u6570C\u6709\u5173\uff0c\u4e0b\u9762\u9009\u62e9\u4e86\u51e0\u4e2a\u5178\u578b\u7684\u4f8b\u5b50\u6765\u770b\u770b\u6548\u679c\u3002<img decoding=\"async\" src=\"http:\/\/b.bst.126.net\/common\/portrait\/face\/preview\/face30.gif\" alt=\"Mandelbrot Set Julia Set - Alejandro - AlejandroS Blog\" \/>\u3002<\/div>\n<p><span style=\"font-size: small;\"> \uff081\uff09c=-0.8+0.17i<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-796 size-full\" title=\"Julia Set\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2015\/01\/Julia2.jpg\" alt=\"Julia2\" width=\"868\" height=\"657\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-795 size-full\" title=\"Julia Set\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2015\/01\/Julia1.jpg\" alt=\"\" width=\"868\" height=\"657\" \/><\/p>\n<p>\uff082\uff09c=-0.7-0.38i<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-798 size-full\" title=\"Julia Set\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2015\/01\/Julia4.jpg\" alt=\"Julia4\" width=\"868\" height=\"657\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-797 size-full\" title=\"Julia Set\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2015\/01\/Julia3.jpg\" alt=\"Julia3\" width=\"868\" height=\"657\" \/><\/p>\n<p>(3) \u00a0c=0.3<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-799 size-full\" title=\"Julia Set\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2015\/01\/Julia5.jpg\" alt=\"Julia5\" width=\"868\" height=\"657\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-801 size-full\" title=\"Julia Set\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2015\/01\/Julia7.jpg\" alt=\"Julia7\" width=\"868\" height=\"657\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-800 size-full\" title=\"Julia Set\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2015\/01\/Julia6.jpg\" alt=\"Julia6\" width=\"868\" height=\"657\" \/><\/p>\n<p><span style=\"font-size: small;\">\u54c8\u54c8\uff0c\u771f\u7684\u5f88\u6f02\u4eae\uff0c\u914d\u8272\u5f88\u91cd\u8981\uff0c\u914d\u8272\u6ca1\u914d\u597d\uff0c\u5728\u7f51\u4e0a\u968f\u4fbf\u627e\u4e86\u51e0\u4e2a\u914d\u8272\u65b9\u6848\u3002\u7b97\u6cd5\u4e5f\u6ca1\u6709\u4ed4\u7ec6\u53bb\u8003\u8651\u3002\u5f88\u591a\u4e66\u6709\u4e13\u95e8\u7684\u5206\u5f62\u7b97\u6cd5\u4ecb\u7ecd\u3002<\/span><\/p>\n<p><span style=\"font-size: small;\"> \u5c0f\u7ed3\uff1a\u6570\u5b66\u771f\u7684\u5f88\u7f8e\uff0c\u5f88\u597d\u73a9\u3002<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u524d\u4e24\u5929\u5728\u7f51\u4e0a\u65e0\u610f\u770b\u5230\u4e86\u5f88\u591a\u5173\u4e8e\u5206\u5f62\u7684\u4e1c\u897f\u3002\u611f\u89c9\u5341\u5206\u6f02\u4eae\u3002\u5206\u5f62\u4f53\u73b0\u4e86\u4e00\u79cd\u6709\u5e8f\u548c\u65e0\u5e8f\u7684\u7edf\u4e00\u3002\u6709\u5174\u8da3\u7684\u53ef\u4ee5\u4e0a\u7f51\u641c\u4e9b\u8d44\u6599\u770b\u770b\uff0c\u8fd8\u6709\u5f88\u591a\u4e13\u95e8\u7684\u5206\u5f62\u8f6f\u4ef6\u3001\u7f51\u7ad9\u3001\u8bba\u575b\u3002 \u6700\u51fa\u540d\u7684\u5206\u5f62\u6211\u60f3\u5c31\u662fMandelbrotSet\u548cJuliaSet\u4e86\u3002\u56e0\u4e3a\u5206\u5f62\u51e0\u4f55\u5b66\u7684\u521b\u59cb\u4eba\u5c31\u662fIBM\u7814\u7a76\u5ba4\u7684\u6570\u5b66\u5bb6B.B.Mandelbrot\u3002\u4e0b\u9762\u7b80\u5355\u4ecb\u7ecd\u4e00\u4e0bMandelbrotSet\u548cJuliaSet\u7684\u7b97\u6cd5\u3002\u5176\u5b9e\u7b97\u6cd5\u539f\u7406\u8fd8\u662f\u6bd4\u8f83\u7b80\u5355\u3002 MandelbrotSet\u7531\u4e00\u4e2a\u4e8c\u6b21\u8fed\u4ee3\u65b9\u7a0b\uff1azn+1 = zn2 +c\uff0cz0=c\u6240\u5f97\u5230\u3002\u4e5f\u5c31\u662f\u5bf9\u6240\u6709\u7684\u590d\u5e73\u9762\u4e0a\u7684\u70b9c\u90fd\u8fdb\u884c\u8fed\u4ee3\uff0c\u4e0d\u53d1\u6563\u7684\u70b9\u90fd\u5c5e\u4e8eMandelbrot\u96c6\u7684\u8303\u56f4\u3002 JuliaSet\u7531\u4e00\u4e2a\u4e8c\u6b21\u6620\u5c04\uff1azn+1 = zn2 +c \u4ea7\u751f\u3002c\u4e3a\u4e00\u5b9a\u503c\u3002\u4e5f\u5c31\u662f\u9009\u5b9a\u4e00\u4e2a\u5e38\u590d\u6570\uff0c\u7136\u540e\u5bf9\u6240\u6709\u7684\u590d\u5e73\u9762\u4e0a\u7684\u70b9z\u8fdb\u884c\u8fed\u4ee3\uff0c\u4e0d\u53d1\u6563\u7684\u70b9\u90fd\u5c5e\u4e8eJulia\u96c6\u7684\u8303\u56f4\u3002 \u5176\u4e2dz\u548cc\u90fd\u662f\u590d\u6570\u3002\u8fed\u4ee3\u7684\u6b21\u6570\u8d8a\u591a\uff0c\u56fe\u5f62\u663e\u793a\u5c31\u8d8a\u7cbe\u7ec6\uff0c\u53ef\u4ee5\u65e0\u9650\u7ec6\u5206\uff0c\u540c\u65f6\u5206\u5f62\u8fd8\u6709\u81ea\u76f8\u4f3c\u6027\uff0c\u5c31\u662f\u65e0\u9650\u653e\u5927\u4e00\u4e2a\u7ec6\u5c0f\u7684\u90e8\u5206\uff0c\u770b\u8d77\u6765\u548c\u539f\u6765\u7684\u90e8\u5206\u4e00\u6837\u3002 \u7531\u4e8e\u5206\u5f62\u7684\u65e0\u9650\u6027\uff0c\u5bf9\u56fe\u5f62\u7684\u663e\u793a\u548c\u7b97\u6cd5\u90fd\u662f\u6781\u5927\u7684\u6311\u6218\u3002\u4e00\u822c\u7f16\u7a0b\u7684\u4e66\u90fd\u4f1a\u7528\u8fd9\u4e2a\u4f8b\u5b50\u6765\u4ecb\u7ecd\u591a\u6838\u8ba1\u7b97\u3001\u5e76\u884c\u8ba1\u7b97\u3002\u54c8\u54c8\u3002\u624b\u75d2\u4e86\uff0c\u8fd8\u662f\u7f16\u4e2a\u7a0b\u5e8f\u6765\u770b\u4e00\u4e0b\u6548\u679c\u5427\u3002\u622a\u56fe\u5982\u4e0b\uff1a 1\u3001\u5148\u662fMandelbrot Set\uff08\u8fed\u4ee3\u6b21\u657050\uff09\uff1a \uff081\uff09\u6765\u4e2a\u9ed1\u767d\u8c03\u8272\u65b9\u6848\uff08\u9ed1\u8272\u7684\u5c31\u662fMandelbrot\u96c6\u7684\u8303\u56f4\uff09 \uff082\uff09\u9ed1\u767d\u7684\u8c03\u8272\u65b9\u6848\u592a\u5355\u8c03\u4e86\uff0c\u6765\u770b\u770b\u5f69\u8272\u7684\u6548\u679c\u5982\u4f55 2\u3001JuliaSet\u662f\u4ec0\u4e48\u6837\u7684\u5462\uff0c\u6211\u4eec\u63a5\u4e0b\u6765\u770b\u770b\uff0c\u8fd9\u6b21\u9009\u62e9\u8fed\u4ee3\u6b21\u4e3a500\u6b21\uff0c\u4ece\u4e0b\u9762\u7684\u56fe\u4e5f\u53ef\u4ee5\u770b\u5230\uff0c\u663e\u793a\u7684\u5185\u5bb9\u66f4\u52a0\u7ec6\u81f4\u548c\u6f02\u4eae\u3002\u7531\u4e8eJulia\u96c6\u548c\u9009\u62e9\u7684\u590d\u5e38\u6570C\u6709\u5173\uff0c\u4e0b\u9762\u9009\u62e9\u4e86\u51e0\u4e2a\u5178\u578b\u7684\u4f8b\u5b50\u6765\u770b\u770b\u6548\u679c\u3002\u3002 \uff081\uff09c=-0.8+0.17i \uff082\uff09c=-0.7-0.38i (3) \u00a0c=0.3 \u54c8\u54c8\uff0c\u771f\u7684\u5f88\u6f02\u4eae\uff0c\u914d\u8272\u5f88\u91cd\u8981\uff0c\u914d\u8272\u6ca1\u914d\u597d\uff0c\u5728\u7f51\u4e0a\u968f\u4fbf\u627e\u4e86\u51e0\u4e2a\u914d\u8272\u65b9\u6848\u3002\u7b97\u6cd5\u4e5f\u6ca1\u6709\u4ed4\u7ec6\u53bb\u8003\u8651\u3002\u5f88\u591a\u4e66\u6709\u4e13\u95e8\u7684\u5206\u5f62\u7b97\u6cd5\u4ecb\u7ecd\u3002 \u5c0f\u7ed3\uff1a\u6570\u5b66\u771f\u7684\u5f88\u7f8e\uff0c\u5f88\u597d\u73a9\u3002<\/p>\n","protected":false},"author":1,"featured_media":22014,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4,36],"tags":[136,134,133,1364,132,135],"class_list":["post-789","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-math-geometry","category-notes","tag-fractals","tag-julia","tag-mandelbrot","tag-1364","tag-132","tag-135"],"aioseo_notices":[],"views":3177,"_links":{"self":[{"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/posts\/789","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=789"}],"version-history":[{"count":0,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/posts\/789\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/media\/22014"}],"wp:attachment":[{"href":"http:\/\/www.jdcui.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=789"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=789"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=789"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}