{"id":60,"date":"2006-01-22T17:27:00","date_gmt":"2006-01-22T17:27:00","guid":{"rendered":"http:\/\/walking.72pines.com\/2006\/01\/22\/%e7%9c%8b%e4%b9%a6\/"},"modified":"2006-01-22T17:27:00","modified_gmt":"2006-01-22T17:27:00","slug":"%e7%9c%8b%e4%b9%a6","status":"publish","type":"post","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/60","title":{"rendered":"\u770b\u4e66"},"content":{"rendered":"<div class=\"kcite-section\" kcite-section-id=\"60\">\n<p><a href=\"http:\/\/kids.esc13.net\/images\/girl-reading-book.gif\"><img decoding=\"async\" src=\"http:\/\/kids.esc13.net\/images\/girl-reading-book.gif\" border=\"0\" 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in: <a href=\"http:\/\/del.icio.us\/blog_n_blah\/music\" rel=\"tag\">music<\/a><\/p>\n<!-- kcite active, but no citations found -->\n<\/div> <!-- kcite-section 60 -->","protected":false},"excerpt":{"rendered":"<p>\u8fd9\u51e0\u5929\u5f00\u59cb\u770b\u8fd9\u672c\u4e66\uff1a\u97f3\u4e50\u6279\u8bc4\u5bfc\u8bba\/\u51af\u6548\u521a\u8457.-\u5408\u80a5\uff1a\u5b89\u5fbd\u6587\u827a\u51fa\u7248\u793e\uff0c2002.7\u3002\u8be5\u4e66\u7531\u4e50\u8bc4\u5927\u5e08\u5c45\u5176\u5b8f\u4f5c\u4e86\u5e8f\u3002\u5c45\u5176\u5b8f\u5728\u9898\u4e3a\u300a\u94fa\u8def\u77f3\u5b50\u4e5f\u53ef\u8d35\u300b\u7684\u5e8f\u4e2d\uff0c\u5148\u662f\u8c28\u614e\u5730\u8d5e\u8bb8\u4e86\u4f5c\u8005\u7684\u52aa\u529b\uff0c\u7136\u540e\u5373\u660e\u663e\u5730\u6307\u51fa\u4e86\u4f5c\u8005\u548c\u4f5c\u54c1\u7684\u5c40\u9650\u3002\u8fd9\u91cc\u5f15\u7528\u51e0\u53e5\uff1a 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\u5728\u827a\u672f\u8fd9\u4e2a\u5708\u5b50\u91cc\uff0c\u786e\u5b9e\u6709\u827a\u672f\u5bb6\uff0c\u4f46\u4e5f\u6709\u5546\u4eba\u3002\u5546\u4eba\u7684\u76ee\u6807\u5c31\u662f\u8425\u5229\u3002\u8bda\u7136\uff0c\u5546\u54c1\u5316\u7684\u827a\u672f\u4f5c\u54c1\u603b\u4e0d\u81f3\u4e8e\u827a\u672f\u4ef7\u503c\u4e3a\u96f6\uff0c\u4f46\u5374\u53c8\u7edd\u4e0d\u4f1a\u5546\u4e1a\u4ef7\u503c\u4e3a\u96f6\uff1b\u53cd\u8fc7\u6765\u8bb2\uff0c\u5546\u4e1a\u4ef7\u503c\u4e3a\u96f6\u7684\u827a\u672f\u54c1\uff0c\u827a\u672f\u4ef7\u503c\u5374\u4e0d\u4e00\u5b9a\u4f4e\u3002\u827a\u672f\u4ef7\u503c\u9ad8\u3001\u5546\u4e1a\u4ef7\u503c\u4e3a\u96f6\u7684\u552f\u4e00\u547d\u8fd0\u5c31\u662f\u6d88\u5931\u3002\u6240\u4ee5\uff0c\u81f3\u4eca\u4e3a\u6b62\u6ca1\u6709\u6d88\u5931\u7684\u827a\u672f\u4f5c\u54c1\uff0c\u6ca1\u6709\u4e00\u4ef6\u662f\u8fd9\u6837\u7684\u3002\u7ecf\u5e38\u542c\u5230\u72d7\u4ed4\u961f\u8d28\u95ee\u827a\u4eba\u7c7b\u4f3c\u201c\u60a8\u7684\u65b0\u5531\u7247\u4e00\u6539\u4ee5\u5f80\u7684\u6587\u827a\u98ce\u683c\uff0c\u662f\u5426\u5c5e\u4e8e\u5546\u4e1a\u8003\u8651\u201d\u7684\u95ee\u9898\uff0c\u4e00\u79cd\u5706\u6da6\u7684\u56de\u7b54\u53ef\u4ee5\u662f\u8fd9\u6837\u7684\uff1a\u201c\u6211\u7684\u521b\u4f5c\u6001\u5ea6\u9664\u4e86\u8bda\u5b9e\u8fd8\u662f\u8bda\u5b9e\uff0c\u4f5c\u54c1\u4e00\u5b9a\u4fdd\u8bc1\u8d28\u91cf\uff0c\u662f\u5426\u5546\u4e1a\u5316\u662f\u5426\u5815\u843d\uff0c\u6211\u60f3\u542c\u4f17\u5fc3\u91cc\u4f1a\u6e05\u695a\u3002\u201d\u662f\u7684\uff0c\u90a3\u4e9b\u4ece\u5185\u5fc3\u6df1\u5904\u538c\u6076\u5546\u4e1a\u8fd0\u4f5c\u7684\u3001\u5374\u53c8\u4e0d\u5f97\u4e0d\u9760\u7cbe\u660e\u7684\u7ecf\u7eaa\u4eba\u6323\u4e2a\u4e00\u65e5\u4e09\u9910\u827a\u4eba\u4eec\uff0c\u5fc3\u91cc\u552f\u4e00\u7684\u5b89\u6170\u5c31\u662f\uff0c\u7ec8\u5f52\u8fd8\u662f\u6709\u61c2\u6b23\u8d4f\u7684audience\u2014\u2014\u5373\u90a3\u4e9b\u80fd\u8d8a\u8fc7\u5546\u4e1a\u5e7f\u544a\u6240\u529b\u63a8\u7684\u5356\u70b9\uff0c\u654f\u9510\u5730\u611f\u53d7\u5230\u827a\u672f\u5bb6\u9690\u85cf\u5728\u4f5c\u54c1\u91cc\u7684\u771f\u6b63highlights\u7684\u90a3\u4e9b\u53d7\u4f17\u3002\u5927\u4f17\u9700\u8981\u901a\u8fc7\u5546\u4e1a\u6765\u4e86\u89e3\u827a\u4eba\u548c\u827a\u672f\u4f5c\u54c1\u7684\u5b58\u5728\uff0c\u4f46\u827a\u672f\u5bb6\u548c\u827a\u672f\u5bb6\u4e4b\u95f4\u7684\u7ebd\u5e26\u53ea\u9700\u827a\u672f\u672c\u8eab\u5373\u53ef\u3002\u4f8b\u5982\u674e\u6dfc\u8001\u5e08\u5982\u679c\u51fa\u8bd7\u96c6\uff0c\u51fa\u7248\u793e\u4f1a\u5927\u529b\u6e32\u67d3\u5176\u7406\u8bba\u7269\u7406\u5b66\u5bb6\u8fd9\u4e00\u80cc\u666f\u4f5c\u4e3a\u5356\u70b9\u3002\u4f46\u4ed6\u6bd5\u7adf\u51fa\u7684\u662f\u8bd7\u96c6\u3002\u8bd7\u4eba\u4eec\u4e70\u4ed6\u7684\u8bd7\u96c6\u770b\u7684\u662f\u4ed6\u7684\u8bd7\u3002\u67d0\u4e9b\u79d1\u5b66\u7814\u7a76\u4eba\u5458\u53d1\u5de5\u4f5c\u53d1\u8868\u5728Nature\u3001Science\u3001Cell\u4e0a\uff0c\u300a\u79d1\u5b66\u65f6\u62a5\u300b\u751a\u81f3\u7f51\u6613\u65b0\u95fb\u4f1a\u62a5\u9053\u8be5\u6d88\u606f\u3002\u4f46\u5316\u5b66\u5bb6\u4eec\u770b\u4ed6\u7684\u8bba\u6587\u770b\u7684\u662f\u5316\u5b66\u3001\u7269\u7406\u5b66\u5bb6\u770b\u4ed6\u7684\u8bba\u6587\u770b\u7684\u662f\u7269\u7406\u3002\u53ef\u662f\u597d\u591a\u7814\u7a76\u751f\u5c0f\u670b\u53cb\u770b\u7684\u662fNature\u3001Science\u3002\u5982\u679c\u4f5c\u8005\u662f\u8bfa\u5956\u5f97\u4e3b\uff0c\u90a3\u751a\u81f3\u4ed6\u4eec\u770b\u7684\u5c31\u662f\u8bfa\u5956\u5f97\u4e3b\u3002\u597d\u591a\u6240\u8c13\u201c\u5927\u725b\u201d\u5e76\u4e0d\u907f\u8bb3\u201c\u5ba3\u4f20\u201d\u3002\u6700\u8fd1\u5927\u5bb6\u4e89\u7740\u7eaa\u5ff5\u7684Mandelbrot\u81ea\u5df1\u5c31\u4e0d\u9057\u9014\u529b\u5730\u5ba3\u4f20\u5206\u5f62\u51e0\u4f55\u3002\u5ba2\u89c2\u4e0a\u8bb2\u662f\u4ed6\u81ea\u5df1\u5199\u7684\u4e66The Fractal Geometry of Nature\u628a\u5206\u5f62\u51e0\u4f55\u5e26\u8fdb\u4e86\u5e7f\u6cdb\u7684\u4e3b\u6d41\u5b66\u672f\u5708\u3002\u4e00\u4e2a\u6982\u5ff5\u8981\u706b\uff0c\u4e00\u822c\u9700\u8981\u5341\u5230\u4e8c\u5341\u5e74\u5de6\u53f3\u5dee\u4e0d\u591a\uff08\u4f8b\u5982\u5316\u5b66\u8bfa\u5956Heck\u53cd\u5e94\uff09\u3002\u8fd9\u672c\u4e66\u51fa\u6765\u4e4b\u540e\u5c31\u5dee\u4e0d\u591a\u8fd9\u4e48\u957f\u65f6\u95f4\uff0cMandelbrot\u5728Yale\u62ff\u5230tenure\uff0c\u90fd75\u5c81\u4e86\u3002\u8fd9\u662f\u4ed6\u63a5\u53d7\u6e90\u6e90\u4e0d\u65ad\u7684\u7531\u5206\u5f62\u51e0\u4f55\u5e26\u6765\u7684\u5404\u79cd\u8363\u8000\u7684\u5f00\u7aef\u3002de Gennes\u5199\u7684\u4e66\u66f4\u591a\u3002J. Flory\u4e5f\u5199\u4e66\u3002Heck\u6ca1\u5199\u4e66\uff0c\u4ed6\u5f88\u7531\u4e8e\u62ff\u4e0d\u5230\u7ecf\u8d39\u63d0\u65e9\u9000\u4f11\u53bb\u83f2\u5f8b\u5bbe\u517b\u8001\u53bb\u4e86\u3002\u5f53\u7136\uff0c\u8fd9\u53ea\u662f\u6781\u5404\u522b\u6848\u4f8b\u3002\u5f88\u96be\u7528\u5f88\u4e25\u8c28\u7684\u65b9\u6cd5\u6765\u8bc1\u660e\u5199\u4e66\u5c31\u600e\u6837\u4e0d\u5199\u4e66\u53c8\u600e\u6837\u3002\u4f46\u8fd8\u662f\u591a\u7f57\u55e6\u4e00\u53e5\uff1aH-index\u7b2c\u4e00\u540dG. Whitesides\u6700\u8fd1\u4e5f\u53bbTED\u7ed9talk\uff08\u819c\u62dc\u4e00\u4e0b\u4ed6\u7684\u6f14\u8bb2\u9b45\u529b\u5427\uff09\u3002\u800c\u6700\u65e9\u505a\u79bb\u5b50\u6db2\u4f53\uff08ionic liquids\uff09\u5de5\u4f5c\u7684K. Seddon\u9ed8\u9ed8\u5e72\u4e86\u4e8c\u5341\u5e74\u624d\u53d1\u7b2c\u4e00\u7bc7\u6587\u7ae0\uff08\u4e3a\u4ec0\u4e48\uff09\u3002\u987a\u4fbf\u63d0\u4e00\u4e0b\uff0c\u5173\u4e8e\u5206\u5f62\uff0c\u6211\u66fe\u7ecf\u4f5c\u4e3a\u81ea\u5df1\u535a\u58eb\u8bfe\u9898\u5f00\u9898\u7684\u8d44\u6599\u603b\u7ed3\u4ecb\u7ecd\u8fc7\uff0c\u73b0\u5728\u6211\u4e8b\u5b9e\u4e0a\u4f5c\u7684\u8bfe\u9898\u8ddf\u5206\u5f62\u5173\u7cfb\u5df2\u7ecf\u4e0d\u5927\u4e86\u3002\u5173\u4e8ede Genne\uff0c\u6211\u201c\u7eaa\u5ff5\u201d\u8fc7\u4e24\u6b21\u3002\u5173\u4e8eK. Seddon\uff0c\u6211\u5728\u8c08publish or perish\u95ee\u9898\u65f6\u987a\u5e26\u63d0\u5230\u8fc7\u3002\u5e42\u7387\u3001\u81ea\u76f8\u4f3c\u3001\u5206\u5f62\u848b\u654f\u5f3a\u535a\u58eb\u662f\u7814\u7a76\u65e0\u673a\u6750\u6599\u7684\uff0c\u8ddf\u9ad8\u5206\u5b50\u5dee\u5f88\u8fdc\u3002\u4f46\u662f\u5bf9\u4ed6\u7684\u535a\u5ba2\u91cc\u4ecb\u7ecd\u7684\u5206\u5f62\u73b0\u8c61\u5374\u5f88\u773c\u719f\u3002\u6587\u5b57\u53e3\u53e3\u58f0\u58f0\u5730\u8bf4\u81ea\u76f8\u4f3c\u3001\u5206\u5f62\uff0c\u4f46\u662f\u56fe\u53ea\u662f\u7ed9\u51fa\u4e86\u4e00\u4e2a\u5e42\u7387\u5173\u7cfb\u3002\u4f46\u662f\uff0c\u5bf9\u4e8e\u5927\u4f17\u800c\u8a00\uff0c\u5206\u5f62\u660e\u660e\u662f\u90a3\u4e2a\u201c\u5927\u5c41\u80a1\u201d\u56fe\u6848\uff08Mandelbrot set\uff09\u3002\u4f60\u8ddf\u4eba\u5bb6\u8bf4\u8fd9\u6750\u6599\u91cc\u6709\u5206\u5f62\uff0c\u90a3\u6750\u6599\u91cc\u53c8\u6709\u5206\u5f62\uff0c\u5149\u753b\u4e00\u6761\u76f4\u7ebf\u600e\u4e48\u884c\uff1f\u4eba\u5bb6\u542c\u4e86\u8fd9\u8bdd\u5fc3\u91cc\u4ee5\u4e3a\u4f60\u6750\u6599\u91cc\u6709\u597d\u591a\u5927\u5c41\u80a1\u5462\u3002\u6211\u5f00\u9898\u65f6\u6d89\u53ca\u5230\u7684\u5206\u5f62\u5b58\u5728\u4e8e\u6e17\u6e1d\u95ee\u9898\uff0c\u8bf4\u51dd\u80f6\u5316\u70b9\u5904\u6574\u4e2a\u51dd\u80f6\u4f53\u7cfb\u662f\u4e00\u4e2a\u904d\u5e03\u7684\u81ea\u76f8\u4f3c\u7f51\u7edc\u3002\u4e8e\u662f\u66fe\u7ecf\u6709\u4eba\u95ee\u6211\uff0c\u53bb\u505a\u7535\u955c\u80fd\u4e0d\u80fd\u770b\u5230\u7c7b\u4f3c\u53f6\u8109\u7684\u90a3\u79cd\u81ea\u76f8\u4f3c\u56fe\u6848\uff1f\u8fd9\u5c31\u662f\u827a\u672f\u4e0e\u5546\u4e1a\u7684\u95ee\u9898\u3002\u5927\u4f17\u975e\u8981\u901a\u8fc7\u94fa\u5929\u76d6\u5730\u7684\u5927\u5c41\u80a1\u624d\u8ba4\u8bc6\u5206\u5f62\u662f\u5565\uff0c\u4f46\u771f\u6b63\u7684\u7814\u7a76\u5b9e\u8df5\u4e2d\u5374\u662f\u5728\u627e\u76f4\u7ebf\u3002\u6750\u6599\u5b66\u91cc\u7684\u524d\u6cbf\u6709\u5f88\u5927\u4e00\u5757\u662f\u7814\u7a76\u65e0\u5e8f\u95ee\u9898\uff0c\u65b9\u6cd5\u65e0\u975e\u662f\u4ece\u65e0\u5e8f\u4e2d\u627e\u6709\u5e8f\u3002\u5206\u5f62\u5c31\u662f\u65e0\u5e8f\u4e2d\u80fd\u627e\u5230\u4e00\u79cd\u6709\u5e8f\u3002\u4f46\u4ece\u65e0\u5e8f\u4e2d\u627e\u5230\u7684\u7edd\u4e0d\u4f1a\u662f\u51e0\u4f55\u5206\u5f62\uff0c\u53ea\u4f1a\u662f\u968f\u673a\u5206\u5f62\u2014\u2014\u4e5f\u5c31\u662f\u8bf4\uff0c\u5b83\u7684\u81ea\u76f8\u4f3c\u6027\u4e0d\u662f\u51e0\u4f55\u610f\u4e49\u4e0a\u7684\uff0c\u800c\u662f\u7edf\u8ba1\u610f\u4e49\u4e0a\u7684\u3002\u9664\u4e86\u628a\u5206\u5e03\u51fd\u6570\u5bf9\u5206\u5e03\u6240\u5728\u7a7a\u95f4\u5c3a\u5ea6\u4f5c\u56fe\u80fd\u770b\u5230\u5e42\u7387\u5173\u7cfb\u4e4b\u5916\uff0c\u4f60\u518d\u4e5f\u770b\u4e0d\u5230\u201c\u66f4\u52a0\u5206\u5f62\u201d\u7684\u4e1c\u897f\u4e86\uff0c\u4f8b\u5982\u90a3\u4e2aMandelbrot\u5927\u5c41\u80a1\u3002\u848b\u654f\u5f3a\u535a\u58eb\u7684\u535a\u5ba2\u91cc\u5217\u4e3e\u4e86\u8bb8\u591a\u65e0\u673a\u6750\u6599\u7814\u7a76\u4e2d\u7684\u5206\u5f62\u73b0\u8c61\u3002\u6750\u6599\u5b66\u7814\u7a76\u91cc\u6700\u901a\u5e38\u7684\u60c5\u51b5\u662f\u5728\u9759\u6001\u6563\u5c04\u5b9e\u9a8c\uff08\u5149\u3001\u4e2d\u5b50\uff09\u4e2d\u6563\u5c04\u5149\u5f3a\u7684\u89d2\u5ea6\u4f9d\u8d56\u6027\u5728\u4e00\u5b9a\u89d2\u5ea6\u8303\u56f4\u5185\u9075\u5faa\u67d0\u79cd\u5e42\u5f8b\u5173\u7cfb\uff1aS(q)~q-D\uff0c\u5176\u4e2dD\u662f\u5206\u5f62\u7ef4\u6570\uff0cq\u662f\u6ce2\u77e2\u3002\u6309\u6211\u7684\u4e13\u4e1a\u80cc\u666f\u6211\u4e5f\u5c31\u53ea\u6709\u8d44\u683c\u8bf4\u8bf4\u9ad8\u5206\u5b50\u7684\u4f8b\u5b50\u3002\u4e00\u4e2a\u6559\u79d1\u4e66\u7ea7\u522b\u7684\u4f8b\u5b50\u5c31\u662f\u94fe\u6784\u8c61\u7edf\u8ba1\u3002\u4ece\u81ea\u76f8\u4f3c\u7684\u6982\u5ff5\u51fa\u53d1\uff0c\u4e00\u67613\u7ef4\u7406\u60f3\u9ad8\u65af\u94fe\u7684\u81ea\u76f8\u4f3c\u6027\u662f\u6307\u5176\u5747\u65b9\u56de\u8f6c\u534a\u5f84<Rg2>~n2\u3002\u8981\u201c\u770b\u201d\u5230\u8fd9\u4e2a\u81ea\u76f8\u4f3c\u73b0\u8c61\uff0c\u5c31\u8981\u505a\u9759\u6001\u6563\u5c04\u5b9e\u9a8c\u3002\u4e00\u5b9a\u6ce2\u957f\u7684\u5149\u6700\u6613\u88ab\u4e00\u5b9a\u5c3a\u5bf8\u7684\u539f\u5b50\u6216\u7535\u5b50\u5bc6\u5ea6\u6563\u5c04\uff08\u539f\u5b50\u8fd8\u662f\u7535\u5b50\u8981\u770b\u4f60\u7684\u5149\u6e90\u662f\u4e2d\u5b50\u8fd8\u662fX\u5c04\u7ebf\uff09\u3002\u6563\u5c04\u51fd\u6570S(q)\u662f\u5728q-1\u5c3a\u5ea6\u5c0f\u4e8eRg\u7684\u524d\u63d0\u4e0b\uff0c\u53ef\u4ee5\u201c\u770b\u201d\u5230\u94fe\u6bb5\u5bc6\u5ea6\u7684\u7a7a\u95f4\u5206\u5e03\uff0c\u6570\u5b66\u4e0a\u7528\u5bc6\u5ea6\u81ea\u76f8\u5173\u51fd\u6570\u0393\u8868\u793a\u3002\u0393\u7684Fourier\u53d8\u6362\u5c31\u662f\u5149\u6563\u5c04\u51fd\u6570S(q)\u3002\u5982\u679c\u6709<Rg2>~n2\uff0c\u5149\u6563\u5c04\u5b9e\u9a8c\u4e2d\u5c31\u80fd\u201c\u770b\u5230\u201dS(q)~q-2\uff0c\u5373\u5206\u5f62\u7ef4\u6570D=2\u3002\u8fd9\u662f\u7406\u60f3\u94fe\u3002Flory\u8003\u8651\u4f53\u79ef\u6392\u9664\u6548\u5e94\u7b97\u51faD=6\/5\u3002\u4ee5\u4e0a\u8fd9\u4e9b\u6750\u6599\u5b66\u7684\u4f8b\u5b50\u4f30\u8ba1\u7ed9\u75f4\u8ff7\u4e8e\u5927\u5c41\u80a1\u7684\u5927\u4f17\u8bfb\u8005\u6cfc\u4e86\u51b7\u6c34\u3002\u4e0d\u662f\u5206\u5f62\u4e48\uff1f\u600e\u4e48\u4e0d\u89c1\u5927\u5c41\u80a1\u5462\uff1f\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u6570\u5b66\u89c6\u9891\u7cfb\u5217Dimensions\u7684\u7b2c\u516d\u96c6\u8db3\u4ee5\u6ee1\u8db3\u6b64\u7c7b\u89c2\u4f17\uff08\u8981\u7ffb\u5899\uff09\uff1a\u6211\u662f\u4ece\u8fd9\u4e2a\u89c6\u9891\u91cc\u7b2c\u4e00\u6b21\u77e5\u9053\u539f\u6765Mandelbrot\u96c6\u5408\u662f\u63cf\u8ff0Julia\u96c6\u5408\u51fa\u73b0\u5206\u5f62\u7684\u533a\u57df\u800c\u5df2\u3002Julia\u96c6\u5408\u5206\u5f62\u662fT(z)=z2+c\u64cd\u4f5c\u65e0\u9650\u8fed\u4ee3\u7684\u7ed3\u679c\u3002\u53ea\u6709\u590d\u5e38\u6570c\u5728\u4e00\u5b9a\u53d6\u503c\u8303\u56f4\u5185\uff0c\u8fed\u4ee3\u7684\u7ed3\u679c\u624d\u662f\u4e00\u4e2a\u80fd\u770b\u5230\u4e00\u7247\u9762\u79ef\u7684\u5206\u5f62\uff08\u8fde\u901a\uff09\u2014\u2014\u5154\u5b50\uff01\u3002\u5728\u6b64\u8303\u56f4\u5916\uff0cJulia set\u5c31\u53d8\u6210\u65e0\u9650\u7cbe\u7ec6\u7684\u56fe\u6848\uff08\u975e\u8fde\u901a\uff09\u2014\u2014\u5565\u90fd\u770b\u4e0d\u89c1\u4e86\u3002\u8fd9\u4e2a\u8303\u56f4\u5728\u590d\u5e73\u9762\u4e0a\u7684\u56fe\u5f62\u5c31\u662fMandelbrot\u5206\u5f62\uff0c\u5b83\u754c\u5b9a\u4e86\u8fde\u901a\u548c\u975e\u8fde\u901a\u7684Julia set\u3002\u97f3\u4e50\u4e0e\u5316\u5b66\u56de\u5e94\u5b8c\u5bf9Mandelbrot\u7684\u7eaa\u5ff5\u4e4b\u540e\uff0c\u518d\u56de\u5e94\u674e\u6dfc\u7814\u7a76\u5458\u7684\u201c\u827a\u672f\u5174\u8da3\u201d\u8bdd\u9898\u3002\u674e\u6dfc\u7814\u7a76\u5458\u5bf9\u7269\u7406\u5b66\u5bb6\u6216\u6570\u5b66\u5bb6\u4e2d\u7684\u8bd7\u4eba\u6bd4\u8f83\u719f\u6089\uff0c\u6211\u662f\u53e4\u5178\u97f3\u4e50\u7231\u597d\u8005\uff0c\u56e0\u6b64\u6211\u80fd\u4e3e\u51fa\u4e00\u4e9b\u5316\u5b66\u5bb6\u4e2d\u7684\u97f3\u4e50\u5bb6\uff0cor vise versa\u3002\u4f8b\u5982\uff0cAlexander Borodin\u662f\u4fc4\u7f57\u65af\u4f5c\u66f2\u5bb6\uff0c\u6240\u8c13\u201c\u4e94\u4eba\u56e2\u201d\u4e4b\u4e00\u3002\u4ed6\u521b\u4f5c\u7684\u6700\u4f18\u7f8e\u7684\u65cb\u5f8b\u5e94\u8be5\u662f\u5f26\u4e50\u56db\u91cd\u594f\u7684\u7b2c\u4e8c\u4e50\u7ae0\u201c\u591c\u66f2\u201d\u3002\u4ee5\u4ed6\u547d\u540d\u7684\u53cd\u5e94\uff1a E. Elgar\uff0c\u82f1\u56fd\u4f5c\u66f2\u5bb6\u3002\u7535\u5f71\u300a\u5979\u6bd4\u70df\u82b1\u5bc2\u5bde\u300b\u91cc\u7684\u5973\u4e3b\u89d2\uff0c\u5927\u63d0\u7434\u624bdu Pre\u7684\u6210\u540d\u4f5c\u5c31\u662fElgar\u7684\u5927\u63d0\u7434\u534f\u594f\u66f2\u3002\u800c\u6211\u8ba4\u4e3aElgar\u6700\u4f18\u7f8e\u7684\u65cb\u5f8b\u5e94\u8be5\u662f\u5c0f\u63d0\u7434\u534f\u594f\u66f2\u7684\u6162\u4e50\u7ae0\u3002\u4ed6\u53d1\u660e\u4e86\u4e00\u4e2a\u5236\u5907\u786b\u5316\u6c22\u7684\u88c5\u7f6e\u5e76\u6210\u529f\u7533\u8bf7\u4e86\u4e13\u5229\u3002\u8fd9\u4e24\u4e2a\u4eba\u4e5f\u8bb8\u5728\u97f3\u4e50\u754c\u6bd4\u5728\u5316\u5b66\u754c\u6709\u540d\u3002\u90a3\u597d\uff0cJohannes Br\u00f8nsted\u8fd9\u4e2a\u540d\u5b57\uff0c\u6240\u6709\u5316\u5b66\u7cfb\u7684\u5b66\u751f\u90fd\u5e94\u8be5\u8ba4\u8bc6\u2014\u2014\u9178\u78b1\u7684\u8d28\u5b50\u7406\u8bba\u3002\u4ed6\u662f\u4e1a\u4f59\u7537\u4e2d\u97f3\u6b4c\u5531\u5bb6\u548c\u753b\u5bb6\u3002 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