\u4eca\u5929\u7684\u4e3b\u89d2\u53eb\u505a\u535a\u52aa\u74e6\u00b7\u66fc\u5fb7\u5c14\u5e03\u7f57\u7279<\/strong>\uff08Beno\u00eet B. Mandelbrot\uff09<\/p>\n\n\n\n \u4e0e\u4e4b\u524d\u540a\u6253\u6211\u4eec\u82b8\u82b8\u4f17\u751f\u7684\u5929\u624d\u4eec\u4e00\u6837<\/p>\n\n\n\n \u4ed6\u53c8\u662f\u4e00\u4e2a\u641e\u6570\u5b66\u7684<\/p>\n\n\n\n \u66fc\u5fb7\u5c14\u5e03\u7f57\u7279\u7684\u8eab\u4efd\u6bd4\u8f83\u590d\u6742<\/p>\n\n\n\n \u9996\u5148\u4ed6\u662f\u4e00\u4e2a\u51fa\u751f\u5728\u6ce2\u5170\u7684\u6cd5\u56fd\u88d4\u7f8e\u56fd\u4eba<\/p>\n\n\n\n \u5bb6\u91cc\u6709\u4e00\u7fa4\u641e\u5b66\u672f\u7684\u4eb2\u621a\uff0c\u4e0d\u8fc7\u4eb2\u7238\u7238\u662f\u505a\u751f\u610f\u7684<\/p>\n\n\n\n \u6240\u4ee5\u5bb6\u5b66\u6e0a\u6e90\u91cd\u8981<\/p>\n\n\n\n \u7238\u7238\u6709\u94b1\u4e5f\u5f88\u91cd\u8981\u554a\uff01<\/p>\n\n\n\n \u4e0d\u8fc7\u66fc\u5fb7\u5c14\u5e03\u7f57\u7279\u7684\u540d\u5b57\u5728\u56fd\u5185\u7ffb\u8bd1\u7684\u975e\u5e38\u4e71<\/p>\n\n\n\n \u6709\u65f6\u5019\u53eb\u66fc\u5fb7\u535a<\/p>\n\n\n\n \u6709\u65f6\u5019\u8fd8\u53eb\u8292\u5fb7\u5e03\u7f57<\/p>\n\n\n\n \u611f\u89c9\u8fd9\u4e2a\u7ffb\u8bd1\u5e94\u8be5\u662f\u4e2a\u957f\u6c99\u4eba<\/p>\n\n\n\n \u7531\u4e8e\u540d\u5b57\u592a\u957f<\/p>\n\n\n\n \u540e\u6587\u6211\u4eec\u5c31\u53eb\u4ed6\u66fc\u5927\u7237\u597d\u4e86<\/p>\n\n\n\n \u66fc\u5927\u7237\u7684\u5927\u5b66\u662f\u5728\u6cd5\u56fd\u5ff5\u7684<\/p>\n\n\n\n \u4ed6\u7684\u8001\u5e08\u662f\u4fdd\u7f57\u00b7\u5217\u7ef4\uff08Paul Levy\uff09<\/p>\n\n\n\n \u6211\u4eec\u603b\u662f\u5047\u8bbe\u91d1\u878d\u4ef7\u683c\u662f\u7b26\u5408\u6b63\u6001\u4e5f\u5c31\u662f\u9ad8\u65af\u5206\u5e03\u7684<\/p>\n\n\n\n \u4f46\u662f\u5b9e\u9645\u4e0a\u4ef7\u683c\u7684\u53d8\u5316\u5e45\u5ea6\u90fd\u6bd4\u9ad8\u65af\u5206\u5e03\u8981\u5927<\/p>\n\n\n\n \u8fd9\u4f1a\u5bfc\u81f4\u6211\u4eec\u4f4e\u4f30\u98ce\u9669<\/p>\n\n\n\n \u800c\u5217\u7ef4\u5f53\u65f6\u63d0\u51fa\u4e86\u4e00\u4e2a\u5217\u7ef4\u7a33\u5b9a\u975e\u9ad8\u65af\u5206\u5e03<\/strong><\/p>\n\n\n\n \u540e\u6765\u66fc\u5927\u7237\u7528\u8fd9\u4e2a\u53bb\u68c0\u9a8c\u4e86\u68c9\u82b1\u5e02\u573a\u7684\u6536\u76ca\u7387\u5206\u5e03<\/p>\n\n\n\n \u7ed3\u679c\u4e00\u4e0b\u53d1\u73b0\u62df\u5408\u6548\u679c\u771f\u597d<\/p>\n\n\n\n \u8001\u5e08\u662f\u4e2a\u5929\u624d<\/p>\n\n\n\n \u81ea\u5df1\u6ca1\u8ddf\u9519\u4eba<\/p>\n\n\n\n \u800c\u8fd9\u4e5f\u5c31\u662f\u540e\u6765\u6211\u4eec\u5e38\u89c1\u7684\u5c16\u5cf0\u80a5\u5c3e\u5206\u5e03<\/p>\n\n\n\n \u56fe\u7247\u6765\u81ea\uff1aWikipedia<\/p>\n\n\n\n \u4e4b\u524d\u6211\u4eec\u8bf4\u4e86\u4e00\u5927\u5806\u559c\u6b22\u8de8\u754c\u7684\u6570\u5b66\u5bb6<\/p>\n\n\n\n \u4f46\u662f\u8c01\u8de8\u7684\u90fd\u6ca1\u6709\u66fc\u5927\u7237\u591a<\/p>\n\n\n\n \u9664\u4e86\u6570\u5b66\u4e4b\u5916<\/p>\n\n\n\n \u8bed\u8a00\u5b66\u3001\u4fe1\u606f\u5b66\u3001\u751f\u7406\u5b66\u548c\u91d1\u878d\u5b66<\/p>\n\n\n\n \u4ed6\u90fd\u53bb\u63ba\u548c\u4e86\u4e00\u4e0b<\/p>\n\n\n\n \u4f46\u662f\u53e4\u8bed\u8bf4\u7684\u597d\uff0c\u672f\u4e1a\u6709\u4e13\u653b<\/p>\n\n\n\n \u4ed6\u8fd9\u4e48\u5f04\u5c31\u628a\u81ea\u5df1\u641e\u5f97\u5f88\u4e0d\u53d7\u6b22\u8fce<\/p>\n\n\n\n \u6240\u4ee5\u524d\u534a\u751f\u4ed6\u597d\u50cf\u4e5f\u6ca1\u4ec0\u4e48\u7279\u522b\u597d\u7684\u6210\u679c<\/p>\n\n\n\n \u4e0d\u8fc7\u8c01\u4e5f\u6ca1\u60f3\u5230\u4ed6\u662f\u5728\u6512\u4e00\u6ce2\u5927\u7684<\/p>\n\n\n\n 1975\u5e74\u4ed6\u521b\u9020\u4e86\u5206\u5f62<\/strong>\uff08fractal\uff09\u8fd9\u4e2a\u8bcd<\/p>\n\n\n\n \u8fd9\u4e2a\u6982\u5ff5\u7279\u522b\u6709\u610f\u601d<\/p>\n\n\n\n \u5c31\u662f\u6211\u4eec\u628a\u4e00\u4e2a\u4e0d\u89c4\u5219\u56fe\u5f62\u62c6\u89e3\u6210\u51e0\u4e2a\u90e8\u5206\u540e<\/p>\n\n\n\n \u53d1\u73b0\u8fd9\u51e0\u4e2a\u90e8\u5206\u548c\u6574\u4f53\u56fe\u5f62\u662f\u76f8\u4f3c\u7684<\/p>\n\n\n\n \u6700\u5e38\u89c1\u7684\u5c31\u662f\u82b1\u6930\u83dc\uff08\u524d\u65b9\u5bc6\u6050\uff09<\/p>\n\n\n\n \u800c\u4f20\u7edf\u4e0a\u51e0\u4f55\u5b66\u90fd\u662f\u7814\u7a76\u90a3\u4e9b\u89c4\u5219\u7684\u56fe\u5f62<\/p>\n\n\n\n \u6bd5\u7adf\u6700\u7b80\u6d01\u7684\u6700\u7f8e\u662f\u6570\u5b66\u5bb6\u7684\u5171\u540c\u8ba4\u77e5<\/p>\n\n\n\n \u4f46\u662f\u66fc\u5927\u7237\u7684\u8fd9\u4e2a\u53d1\u73b0\u7ed9\u5927\u5bb6\u5f00\u8f9f\u4e86\u4e00\u6761\u65b0\u7684\u9053\u8def<\/p>\n\n\n\n \u5c31\u662f\u590d\u6742\u4e4b\u7f8e<\/p>\n\n\n\n \u6bd5\u7adf\u5728\u7834\u788e\u4e2d\u5bfb\u627e\u89c4\u5f8b\u6216\u8005\u5b9a\u4e49\u662f\u4e00\u4ef6\u975e\u5e38\u670b\u514b\u7684\u4e8b\u60c5<\/p>\n\n\n\n \u6240\u4ee5\u540e\u9762\u5206\u5f62\u5b66\u53d8\u6210\u4e86\u827a\u672f\u754c\u7684\u4e00\u573a\u72c2\u6b22<\/p>\n\n\n\n \u66fc\u5927\u7237\u51e0\u4e4e\u4e00\u5df1\u4e4b\u529b\u5960\u5b9a\u4e86\u5206\u5f62\u5b66\u79d1\u7684\u57fa\u7840<\/p>\n\n\n\n \u6240\u4ee5\u540e\u4e16\u90fd\u79f0\u4ed6\u4e3a\u5206\u5f62\u4e4b\u7236<\/p>\n\n\n\n \u5149\u542c\u540d\u5b57\u4f3c\u4e4e\u8ddf\u4f0f\u5730\u9b54\u7684\u9b42\u5668\u6709\u70b9\u5173\u7cfb<\/p>\n\n\n\n \u4e4b\u524d\u63d0\u5230\u66fc\u5927\u7237\u7528\u81ea\u5df1\u8001\u5e08\u7684\u5206\u5e03\u53bb\u7814\u7a76\u4e86\u68c9\u82b1\u5e02\u573a<\/p>\n\n\n\n \u5176\u5b9e\u4ed6\u81ea\u5df1\u4e5f\u6709\u5f88\u591a\u5173\u4e8e\u91d1\u878d\u5b66\u5c3e\u90e8\u98ce\u9669\u7684\u7814\u7a76<\/p>\n\n\n\n \u5728\u4ed6\u770b\u6765<\/p>\n\n\n\n \u98ce\u9669\u672c\u8eab\u4e0d\u50cf\u7ecf\u5178\u7406\u8bba\u91cc\u63cf\u8ff0\u7684\u90a3\u6837<\/p>\n\n\n\n \u7b26\u5408\u6f02\u4eae\u7684\u968f\u673a\u6027\u5206\u5e03<\/p>\n\n\n\n \u4ed6\u5c06\u8fd9\u6837\u7684\u968f\u673a\u6027\u79f0\u4e4b\u4e3a\u6e29\u548c\u7684\u968f\u673a\u6027\uff08Mild Randomness\uff09<\/p>\n\n\n\n \u76f8\u53cd\u5e02\u573a\u5e94\u5f53\u662f\u4e00\u79cd\u72c2\u91ce\u7684\u968f\u673a\u6027\uff08Wild Randomness\uff09<\/p>\n\n\n\n \u8fd9\u79cd\u968f\u673a\u6027\u5e38\u5e38\u4f1a\u51fa\u73b0\u6ce2\u52a8\u7387\u7684\u7a81\u7136\u53d8\u5316<\/p>\n\n\n\n \u540e\u6765\u6211\u4eec\u79f0\u8fd9\u6837\u7684\u73b0\u8c61\u4e3a\u9ed1\u5929\u9e45<\/p>\n\n\n\n \u800c\u66fc\u5927\u7237\u5219\u79f0\u4e4b\u4e3a\u201c\u8bfa\u4e9a\u6548\u5e94<\/strong>\u201d<\/p>\n\n\n\n \u6bd4\u55bb\u6e90\u81ea\u5723\u7ecf\u91cc\u7684\u8bfa\u4e9a\u65b9\u821f<\/p>\n\n\n\n \u56e0\u4e3a\u5e02\u573a\u7684\u5de8\u5927\u6ce2\u52a8\u5176\u5b9e\u5c31\u548c\u8bfa\u4e9a\u65b9\u821f\u91cc\u7684\u6d2a\u6c34\u4e00\u6837<\/p>\n\n\n\n \u5e2d\u5377\u4e00\u5207<\/p>\n\n\n\n \u6ca1\u4eba\u80fd\u591f\u72ec\u5584\u5176\u8eab<\/p>\n\n\n\n \u800c\u66fc\u5927\u7237\u7684\u53e6\u4e00\u4e2a\u91d1\u878d\u5b66\u8d21\u732e<\/p>\n\n\n\n \u5219\u662f\u91d1\u878d\u5e02\u573a\u7684\u957f\u671f\u76f8\u5173\u6027<\/p>\n\n\n\n \u4f5c\u4e3a\u4e00\u4e2a\u559c\u6b22\u5728\u5404\u4e2a\u5b66\u79d1\u95f4\u6e38\u8d70\u7684\u767e\u79d1\u5168\u4e66<\/p>\n\n\n\n \u4ed6\u53c8\u60f3\u5230\u4e00\u4e2a\u5723\u7ecf\u6545\u4e8b\u6bd4\u55bb\u6765\u5f62\u5bb9\u8fd9\u79cd\u76f8\u5173\u6027<\/p>\n\n\n\n \u6cd5\u8001\u5f53\u5e74\u505a\u4e86\u4e2a\u68a6<\/p>\n\n\n\n \u68a6\u89c1\u5c3c\u7f57\u6cb3\u91cc\u5347\u8d77\u4e86\u4e03\u5934\u80d6\u6bcd\u725b<\/p>\n\n\n\n \u4e0d\u4e00\u4f1a\u513f\u6cb3\u91cc\u53c8\u51fa\u73b0\u4e86\u4e03\u5934\u7626\u6bcd\u725b<\/p>\n\n\n\n \u6bcd\u725b\u4eec\u90fd\u4e0d\u7406\u4ed6<\/p>\n\n\n\n \u4f46\u662f\u7626\u6bcd\u725b\u5374\u628a\u80d6\u6bcd\u725b\u90fd\u5403\u4e86<\/p>\n\n\n\n \u6cd5\u8001\u68a6\u9192\u540e\u89c9\u5f97\u5f88\u5947\u602a\uff0c\u5c31\u627e\u4eba\u89e3\u68a6<\/p>\n\n\n\n \u7ed3\u679c\u5723\u7ea6\u745f\u592b\u8bf4<\/p>\n\n\n\n \u8fd9\u610f\u5473\u7740\u57c3\u53ca\u4f1a\u5728\u4e03\u5e74\u7684\u4e30\u6536\u540e\u6709\u4e03\u5e74\u7684\u9965\u8352<\/p>\n\n\n\n \u8bf4\u5b9e\u8bdd\u8fd9\u4e2a\u89e3\u68a6\u6c34\u5e73\u6bd4\u6211\u4eec\u5c0f\u533a\u95e8\u53e3\u7684\u738b\u778e\u5b50\u8fd8\u6487<\/p>\n\n\n\n \u4e0d\u8fc7\u66fc\u5927\u7237\u8ba4\u4e3a<\/p>\n\n\n\n \u6570\u636e\u7684\u957f\u671f\u76f8\u5173\u6027<\/p>\n\n\n\n \u5176\u5b9e\u5c31\u662f\u5386\u53f2\u4f1a\u5f71\u54cd\u73b0\u5728\u7684\u968f\u673a\u6027<\/p>\n\n\n\n \u4e5f\u5c31\u662f\u8bf4\u91d1\u878d\u5e02\u573a\u672c\u8eab\u5e76\u975e\u5982\u7406\u8bba\u5047\u8bbe\u7684\u90a3\u6837\u662f\u72ec\u7acb\u7684<\/p>\n\n\n\n \u76f8\u53cd\u73b0\u5728\u4e00\u5b9a\u662f\u8fc7\u53bb\u7684\u7ed3\u679c<\/p>\n\n\n\n \u4ed6\u5c06\u8fd9\u4e2a\u79f0\u4e4b\u4e3a\u201c\u7ea6\u745f\u592b\u6548\u5e94<\/strong>\u201d<\/p>\n\n\n\n \u5e76\u7528\u8fd9\u4e2a\u548c\u201c\u8bfa\u4e9a\u6548\u5e94\u201d\u4f5c\u4e3a\u4ed6\u89e3\u91ca\u91d1\u878d\u5e02\u573a\u7684\u4e24\u4e2a\u91cd\u8981\u5de5\u5177<\/p>\n\n\n\n \u800c\u5927\u7237\u6700\u5927\u7684\u6210\u5c31\u2014\u2014\u5206\u5f62\u5b66<\/p>\n\n\n\n \u4e5f\u88ab\u7528\u5728\u91d1\u878d\u9886\u57df\u7684\u7814\u7a76\u4e4b\u4e2d<\/p>\n\n\n\n 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