{"id":32601,"date":"2022-02-21T20:55:31","date_gmt":"2022-02-21T12:55:31","guid":{"rendered":"https:\/\/swarma.org\/?p=32601"},"modified":"2022-02-21T20:55:31","modified_gmt":"2022-02-21T12:55:31","slug":"%e8%87%aa%e9%80%82%e5%ba%94%e5%88%86%e5%bd%a2%ef%bc%9a%e5%a4%a7%e8%a7%84%e6%a8%a1%e7%be%a4%e4%bd%93%e6%8e%a7%e5%88%b6%e7%9a%84%e7%a1%ae%e5%ae%9a%e6%80%a7%e6%b7%b7%e6%b2%8c%e7%ba%a6%e6%9d%9f","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=32601","title":{"rendered":"\u81ea\u9002\u5e94\u5206\u5f62\uff1a\u5927\u89c4\u6a21\u7fa4\u4f53\u63a7\u5236\u7684\u786e\u5b9a\u6027\u6df7\u6c8c\u7ea6\u675f"},"content":{"rendered":"
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Josef Schaff<\/span> <\/span>| \u4f5c\u8005<\/strong><\/span><\/p>\n

\u674e\u5029\u5029<\/span> <\/span>| \u8bd1\u8005<\/strong><\/span><\/strong><\/span><\/p>\n

\u5218\u57f9\u6e90<\/span> <\/span>| \u5ba1\u6821<\/strong><\/span><\/strong><\/span><\/strong><\/span><\/p>\n

\u9093\u4e00\u96ea<\/span> | \u7f16\u8f91<\/strong><\/span>
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1. \u95ee\u9898\uff1a<\/strong><\/strong><\/p>\n

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1.2\u4ece\u6df7\u6c8c\u5230\u8fed\u4ee3\u987a\u5e8f\uff1a\u5e94\u7528\u5206\u5f62\u548c\u8fed\u4ee3\u51fd\u6570\u7cfb\u7edf (\u8fed\u4ee3\u51fd\u6570\u7cfb\u7edf)<\/span><\/strong><\/span><\/h2>\n


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\u8bb8\u591a\u73b0\u5b9e\u4e16\u754c\u7684\u73b0\u8c61\u662f\u81ea\u76f8\u4f3c\u7684<\/span>\uff08\u5373\u6574\u4f53\u7684\u8f83\u5c0f\u90e8\u5206\u53ef\u4ee5\u8fed\u4ee3\u7f29\u653e\u4ee5\u8868\u793a\u6574\u4f53\uff09<\/span>\u3002\u4f8b\u5b50\u5305\u62ec\u6709\u7740\u5927\u5c0f\u679d\u6748\u7684\u6811\u3001\u82b1\u6930\u83dc\uff1b\u6709\u591a\u4e2a\u536b\u661f\u7684\u884c\u661f\uff0c\u6709\u591a\u4e2a\u884c\u661f\u7684\u592a\u9633\u7cfb\uff1b\u53ef\u4ee5\u5411\u4e0a\u7f29\u5c0f\u548c\u5411\u4e0b\u653e\u5927\u7684\u6d77\u5cb8\u7ebf\uff1b\u8fd8\u6709\u8bb8\u591a\u5176\u4ed6\u73b0\u8c61\u3002\u5927\u91cf\u73b0\u8c61\u53ef\u4ee5\u7528\u9012\u5f52\u751f\u6210\u51fd\u6570\u6216\u8fed\u4ee3\u51fd\u6570\u7cfb\u7edf\u6765\u8868\u793a\uff0c\u8fed\u4ee3\u51fd\u6570\u7cfb\u7edf<\/span>\uff08Iterated Function Systems\uff09<\/span>\u901a\u5e38\u80fd\u591f\u751f\u6210\u5206\u5f62[10\u201312]\u3002\u8fed\u4ee3\u51fd\u6570\u7cfb\u7edf\u901a\u8fc7\u6784\u5efa\u81ea\u8eab\u7684\u8bb8\u591a\u526f\u672c\u5e76\u53e0\u52a0\u8fd9\u4e9b\u526f\u672c\u6765\u751f\u6210\u5206\u5f62\u56fe\u6848\uff0c\u4ece\u800c\u751f\u6210\u5206\u5f62\u5f62\u72b6\u3002\u526f\u672c\u662f\u539f\u59cb\u5f62\u72b6\u7684\u4eff\u5c04\u53d8\u6362<\/span>\uff08affine transformations\uff09<\/span>\uff0c\u901a\u5e38\u662f\u6536\u7f29\u4eff\u5c04\u6216\u539f\u59cb\u5f62\u72b6\u7684\u7f29\u5c0f\u526f\u672c\u3002\u8fd9\u4e2a\u8fed\u4ee3\u51fd\u6570\u7cfb\u7edf\u662f\u4e00\u7ec4\u538b\u7f29\u4eff\u5c04\u5143\u7d20\u7684\u7ed3\u679c\uff0c\u901a\u8fc7\u4f7f\u7528Hutchinson\u7b97\u5b50\uff0c\u5b83\u6536\u655b\u5230\u4e00\u4e2a\u552f\u4e00\u7684\u5438\u5f15\u5b50[13]\u3002\u8fd9\u4e9b\u4eff\u5c04\u53d8\u6362\u7684\u8986\u76d6\u5728\u6570\u5b66\u4e0a\u662f\u8fd9\u4e9b\u51fd\u6570\u53d8\u6362\u5f62\u72b6\u7684\u5e76\u96c6\uff0c\u8fd9\u4e9b\u5f62\u72b6\u521b\u5efa\u4e86\u5206\u5f62\u62d3\u6251\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u8fd9\u4e9b\u751f\u6210\u51fd\u6570\u53ef\u4ee5\u8fed\u4ee3\u5230\u76f8\u5bf9\u4e8e\u73b0\u5b9e\u4e16\u754c\u89c2\u5bdf\u6240\u9700\u7684\u884c\u4e3a\u4fdd\u771f\u5ea6\u3002\u8fd9\u610f\u5473\u7740\uff0c\u5c3d\u7ba1\u771f\u6b63\u7684\u5206\u5f62\u53ef\u80fd\u662f\u65e0\u9650\u7684\uff0c\u4f46\u6211\u4eec\u53ef\u4ee5\u5c06\u8fed\u4ee3\u51fd\u6570\u7cfb\u7edf\u7684\u8ba1\u7b97\u63d0\u9ad8\u5230\u51e0\u4e4e\u4efb\u4f55\u4efb\u610f\u6c34\u5e73\uff0c\u5e76\u4e14\u4ecd\u7136\u53ef\u4ee5\u770b\u5230\u7531\u6b64\u4ea7\u751f\u7684\u6d8c\u73b0\u6591\u56fe<\/span>\uff08emergent pattern\uff0c\u8bd1\u4e3a\u6d8c\u73b0\u6591\u56fe\u6216\u6d8c\u73b0\u6a21\u5f0f\uff0c\u7c7b\u4f3c\u4e8e\u5168\u606f\u56fe\uff0c\u5168\u606f\u56fe\u7684\u6bcf\u4e2a\u5c0f\u5143\u7d20\u4ecd\u7136\u5305\u542b\u8db3\u591f\u7684\u5173\u952e\u5c5e\u6027\u6765\u91cd\u5efa\u5b8c\u6574\u7684\u56fe\u50cf\uff09<\/span>\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u9759\u6001\u8fd8\u662f\u52a8\u6001\uff1f<\/span><\/strong><\/h4>\n


<\/span><\/p>\n

\u4e0a\u9762\u7684\u65b9\u6cd5\u4f1a\u7ed9\u6211\u4eec\u4e00\u4e2a\u9759\u6001\u7684\u753b\u9762\uff0c\u4f46\u662f\u4e00\u822c\u7684\u52a8\u6001\u7cfb\u7edf\u5462\uff1f\u8fd9\u786e\u5b9e\u662f\u6211\u4eec\u4e16\u754c\u7684\u672c\u8d28\u2014\u2014\u52a8\u6001\u7684\u3002\u5982\u679c\u6211\u4eec\u8003\u8651\u53e6\u4e00\u79cd\u65b9\u6cd5\uff0c\u5373\u4f7f\u7528\u81ea\u9002\u5e94\u7684\u72ec\u7acb\u8fed\u4ee3\u51fd\u6570\u7cfb\u7edf\u6765\u751f\u6210\u552f\u4e00\u7684\u81ea\u7ec4\u7ec7\u6591\u56fe<\/span>\uff08pattern\uff09<\/span>\u5408\u96c6\uff0c\u5e76\u8ba9\u8fd9\u4e9b\u6591\u56fe\u96c6\u6f14\u5316\u4e3a\u6709\u5e8f\u7ed3\u6784\u7684\u8868\u793a\uff0c\u4f1a\u600e\u4e48\u6837\uff1f\u8fd9\u79cd\u52a8\u6001\u7684\u8fed\u4ee3\u51fd\u6570\u7cfb\u7edf\u5c06\u9002\u5e94\u3001\u53d8\u5f62\u548c\u626d\u66f2\u5206\u5f62\uff0c\u4ee5\u4fbf\u5728\u83b7\u5f97\u65b0\u7684\u8282\u70b9\u65f6\u5bb9\u7eb3\u5b83\u4eec<\/span>\uff08\u4f8b\u5982\uff0c\u5b9e\u4f53\u53ef\u4ee5\u52a0\u5165\u6216\u79bb\u5f00\u7fa4\u6216\u81ea\u7ec4\u7ec7\u7f51\u7edc\uff09<\/span>\u3002\u56e0\u4e3a\u5206\u5f62\u662f\u81ea\u76f8\u4f3c\u7684\uff0c\u6240\u4ee5\u5b83\u4eec\u7684\u57fa\u672c\u90e8\u5206\u53ef\u4ee5\u5404\u81ea\u4ee3\u8868\u73b0\u5b9e\u4e16\u754c\u7684\u4e00\u4e2a\u65b9\u9762\u3002\u8fd9\u79cd\u201c\u6a61\u80f6\u201d\u5206\u5f62<\/span>\uff08rubber fractal\uff09<\/span>\u53ef\u4ee5\u4f38\u5c55\u548c\u9002\u5e94\uff0c\u672c\u8d28\u4e0a\u662f\u7ed3\u5408\u6216\u6536\u7f29\u6210\u4e00\u7ec4\u7a33\u5b9a\u7684\u6591\u56fe\u3002\u901a\u8fc7\u7c7b\u6bd4\uff0c\u8fd9\u4e2a\u5206\u5f62\u4e0a\u7684\u9876\u70b9<\/span>\uff08vertices\uff09<\/span>\u5c06\u4e0e\u771f\u5b9e\u4e16\u754c\u7684\u53c2\u6570\u76f8\u5173\u8054\u3002\u8fd9\u4ea7\u751f\u4e86\u4e00\u79cd\u8303\u5f0f\uff0c\u5141\u8bb8\u673a\u5668\u8868\u73b0\u5f97\u66f4\u63a5\u8fd1\u81ea\u7136\u73b0\u8c61\u7684\u52a8\u529b\u5b66\u673a\u5236\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u52a8\u6001\u8fed\u4ee3\u51fd\u6570\u7cfb\u7edf\u2014\u2014\u662f\u4ec0\u4e48\uff1f<\/span><\/strong><\/h4>\n


<\/span><\/p>\n

\u4e0b\u9762\u63cf\u8ff0\u7684\u52a8\u6001\u8fed\u4ee3\u51fd\u6570\u7cfb\u7edf\u53ea\u662f\u53ef\u80fd\u65e0\u9650\u591a\u7684\u65b0\u7684\u6216\u672a\u77e5\u7684\u6570\u5b66\u51fd\u6570\u4e4b\u4e00\uff0c\u8fd9\u4e9b\u51fd\u6570\u4e0d\u662f\u4ece\u5f62\u5f0f\u8bc1\u660e\u548c\u73b0\u6709\u7684\u6570\u5b66\u51fd\u6570\u4e2d\u5bfc\u51fa\u7684\uff0c\u800c\u662f\u4f7f\u7528\u5b9e\u9a8c\u6570\u5b66\u8fdb\u884c\u7814\u7a76\u7684\u4ea7\u7269\u3002\u5728\u6b64\u80cc\u666f\u4e0b\uff0c\u5b83\u662f\u4f5c\u8005\u4eceBarnsley\u7684\u201c\u6df7\u6c8c\u6e38\u620f\u201d[11\uff0c14]\u7684\u4e00\u4e2a\u65b9\u9762\u63a8\u5bfc\u51fa\u6765\u7684\uff0c\u662f\u4e00\u79cd\u7b80\u5355\u7684\u7ebf\u6027\u7b97\u6cd5\uff0c\u53ea\u9700\u8981\u6700\u5c0f\u7684\u8ba1\u7b97\u80fd\u529b\u5c31\u80fd\u751f\u6210\u53ef\u91cd\u590d\u548c\u53ef\u9884\u6d4b\u7684\u590d\u6742\u7cfb\u7edf\u3002\u8fd9\u79cd\u7279\u5b9a\u7684\u7b97\u6cd5\uff0c\u4f5c\u8005\u547d\u540d\u4e3a\u975e\u9884\u5b9a\u53c2\u6570\u968f\u673a<\/strong><\/span>\uff08Non-predetermined Parametric Random\uff0cNPPR\uff09<\/span>\u8fed\u4ee3\u51fd\u6570\u7cfb\u7edf[15]\uff1a\u521b\u5efa\u4e00\u4e2a\u81ea\u9002\u5e94\u5206\u5f62\uff0c\u5176\u5f62\u72b6\u7531\u8bb8\u591a\u81ea\u76f8\u4f3c\u6216\u91cd\u590d\u6591\u56fe\u4e2d\u7684\u70b9\u5f62<\/span>\u6210\uff0c\u6700\u5c0f\u5c3a\u5ea6\u4e0a\u7c7b\u4f3c\u4e8e\u6811\u7684\u672b\u7aef\u679d\u6748\uff0c\u5728\u6700\u5927\u5c3a\u5ea6\u4e0a\u5219\u7c7b\u4f3c\u4e8e\u6811\u5e72\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u8fd9\u4e2a\u52a8\u6001\u8fed\u4ee3\u51fd\u6570\u7cfb\u7edf\u662f\u4ece\u62d3\u6251\u4e0a\u8868\u793a\u8282\u70b9\u6216\u7b80\u5355\u4e3b\u4f53\u4f4d\u7f6e\u7684\u70b9\u521b\u5efa\u7684\u3002\u8fd9\u4e9b\u8282\u70b9\u7684\u4f4d\u7f6e\u88ab\u6620\u5c04\u5230\u8fed\u4ee3\u51fd\u6570\u7cfb\u7edf\u65b9\u7a0b\uff0c\u8be5\u65b9\u7a0b\u4f9d\u8d56\u4e8e\u51e0\u4e2a\u53c2\u6570\uff0c\u7279\u522b\u662f\u6210\u4e3a\u5438\u5f15\u5b50\u7684\u521d\u59cb\u70b9\u6216\u9876\u70b9\u7684\u5c0f\u5b50\u96c6<\/span>\uff08\u4f8b\u5982\uff0c\u79fb\u52a8\u5b9e\u4f53\u7684\u76ee\u6807\u6216\u822a\u8def\u70b9\uff09<\/span>\u548c\u6807\u5ea6\u7f29\u653e\u56e0\u5b50<\/span>\uff08contractive scaling factor\uff09<\/span>\u3002\u5f53\u7f29\u653e\u56e0\u5b50\u63a5\u8fd1+1\u6216-1\u65f6\uff0c\u7cfb\u7edf\u663e\u793a\u8282\u70b9\u968f\u673a\u5206\u6563\u3002\u5f53\u7f29\u653e\u56e0\u5b50\u63a5\u8fd10\u65f6\uff0c\u8fd9\u4e9b\u70b9\u5728\u4efb\u610f\u5438\u5f15\u5b50\u5468\u56f4\u805a\u96c6\u6210\u96c6\u7fa4<\/span>\uff08cluster\uff0c\u96c6\u7fa4\u6216\u56e2\u7c07\uff09<\/span>\uff0c\u8986\u76d6\u6240\u6709\u5438\u5f15\u5b50\u9876\u70b9\u3002\u8fd9\u4e9b\u6d8c\u73b0\u96c6\u7fa4\u63d0\u4f9b\u4e86\u70b9\u5bf9\u70b9\u901a\u4fe1\u94fe\u8def\u6240\u9700\u7684\u62d3\u6251\uff0c\u4ee5\u53ca\u96c6\u7fa4\u95f4\u8def\u7531\u62d3\u6251\u7684\u9009\u62e9\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u8fd9\u89e3\u51b3\u4e86\u51e0\u4e2a\u95ee\u9898\uff0c\u5305\u62ec\u90a3\u4e9b\u4e0e\u62d3\u6251\u5206\u5e03\u5f0f\u7f51\u7edc\u6216\u96c6\u7fa4\u76f8\u5173\u7684\u95ee\u9898\u3002\u5b83\u8fd8\u901a\u8fc7\u4fe1\u606f\u5171\u4eab\u521b\u5efa\u6d8c\u73b0\u89e3\u51b3\u65b9\u6848\uff0c\u89e3\u51b3\u4e86\u4e00\u4e9b\u76ee\u524d\u96be\u4ee5\u89e3\u51b3\u7684\u5206\u5e03\u5f0f\u4fe1\u606f\u95ee\u9898\u3002\u5f53\u6240\u6709\u8282\u70b9\u5171\u4eab\u5c11\u91cf\u4fe1\u606f\u5bc6\u96c6\u7684\u6570\u636e<\/span>\uff08\u5728\u672c\u4f8b\u4e2d\u662f\u9876\u70b9\u4f4d\u7f6e\u548c\u7f29\u653e\u56e0\u5b50\u503c\uff09<\/span>\u65f6\uff0c\u5c31\u4f1a\u4ea7\u751f\u4e00\u4e2a\u5171\u8bc6\u4e3b\u52a8\u6027<\/strong>\u7684<\/span>\uff08stigmergic\uff09<\/span>\u89e3\u51b3\u65b9\u6848\u3002\u901a\u8fc7\u6bcf\u4e2a\u8282\u70b9\u4e86\u89e3\u8fd9\u4e9b\u7a00\u758f\u7684\u6570\u636e\u91cf\uff0c\u5b83\u4eec\u5404\u81ea\u90fd\u53ef\u4ee5\u91cd\u5efa\u590d\u6742\u7cfb\u7edf\u7684\u6574\u4e2a\u62d3\u6251\u7ed3\u6784\u3002<\/span><\/p>\n


<\/p>\n

\n
\n
## \u8bd1\u6ce8\uff1astigmergy\u5171\u8bc6\u4e3b\u52a8\u6027\uff0c\u793e\u4f1a\u7f51\u7edc\u4e2d\u751f\u7269\u4e2a\u4f53\u81ea\u6cbb\u7684\u4fe1\u606f\u534f\u8c03\u673a\u5236\u3002\u5728\u6ca1\u6709\u4e2d\u67a2\u63a7\u5236\u548c\u63a5\u89e6\u4ea4\u6d41\u7684\u6761\u4ef6\u4e0b\uff0c\u7fa4\u4f53\u901a\u8fc7\u540c\u9891\u5171\u632f\uff0c\u8fbe\u5230\u4fe1\u606f\u5bf9\u79f0\uff0c\u7136\u540e\u72ec\u7acb\u884c\u52a8\uff0c\u76f8\u4e92\u4fee\u6b63\uff0c\u81ea\u6211\u66f4\u65b0\uff0c\u9010\u6b65\u5b8c\u5584\u7fa4\u4f53\u7684\u751f\u6001\u73af\u5883\u3002\u5171\u8bc6\u4e3b\u52a8\u6027\u4e00\u822c\u8868\u73b0\u4e3a\u751f\u7269\u754c\u7684\u81ea\u7ec4\u7ec7\u6216\u4eba\u7c7b\u7684\u6c11\u4e3b\uff0c\u5728\u672c\u6587\u4e2d\u88ab\u62d3\u5c55\u5e94\u7528\u4e8e\u4fe1\u606f\u7f51\u7edc\u548c\u81ea\u7ec4\u7ec7\u96c6\u7fa4\u7b49\u3002<\/span><\/section>\n<\/section>\n<\/blockquote>\n


<\/p>\n

\u8fd9\u5c31\u7f29\u5c0f\u4e86\u6211\u4eec\u4f7f\u7528\u52a8\u6001\u8fed\u4ee3\u51fd\u6570\u7cfb\u7edf\u65b9\u6cd5\u7684\u8303\u56f4\u3002\u8be5\u65b9\u6cd5\u4ea7\u751f\u4f9d\u8d56\u4e8e\u4e00\u4e2a\u6216\u591a\u4e2a\u53d8\u91cf\u4e2d\u76f8\u5bf9\u8f83\u5c0f\u7684\u53d8\u5316\u7684\u6d8c\u73b0\u89e3\u51b3\u65b9\u6848\u3002\u8fd9\u4e00\u89e3\u51b3\u65b9\u6848\u8fd8\u9700\u8981\u8868\u793a\u5927\u578b\u70b9\u5bf9\u70b9\u81ea\u7ec4\u7ec7\u7f51\u7edc\u4e2d\u7684\u968f\u673a\u53d8\u5316\u3002\u6700\u540e\uff0c\u6bcf\u6b21\u5c06\u76f8\u5173\u53c2\u6570\u8bbe\u7f6e\u4e3a\u76f8\u540c\u7684\u503c\u65f6\uff0c\u7ed3\u679c\u90fd\u9700\u8981\u662f\u53ef\u91cd\u590d\u7684\u3002\u901a\u8fc7\u5c06\u7f51\u7edc\u4f20\u611f\u5668\u6570\u636e\u6dfb\u52a0\u5230\u7cfb\u7edf\u4e2d\uff0c\u975e\u9884\u5b9a\u53c2\u6570\u968f\u673a\u8fed\u4ee3\u51fd\u6570\u7cfb\u7edf<\/span>\uff08NPPR IFS\uff09<\/span>\u53ef\u4ee5\u4fee\u6539<\/span>\uff08\u9002\u5e94\uff09<\/span>\u81ea\u8eab\u4ee5\u9002\u5e94\u52a8\u6001\u53d8\u5316\u7684\u73af\u5883\u6216\u53d8\u5316\u7684\u5a01\u80c1\u884c\u4e3a\u3002\u7f51\u7edc\u5316\u7684\u667a\u80fd\u4e3b\u4f53\u4e2d\u4e4b\u95f4\u7684\u901a\u4fe1\uff0c\u5c06\u5141\u8bb8\u5171\u4eab\u77e5\u8bc6\u6765\u589e\u5f3a\u548c\u66f4\u65b0\u6bcf\u4e2a\u4e3b\u4f53\u7684\u77e5\u8bc6\u5730\u56fe[13]\uff0c\u4fc3\u8fdb\u7f51\u7edc\u73af\u5883\u4e2d\u4e00\u81f4\u5730\u5171\u4eab\u77e5\u8bc6\u3002<\/span><\/p>\n


<\/p>\n

\u975e\u9884\u5b9a\u53c2\u6570\u968f\u673a\u81ea\u9002\u5e94\u5206\u5f62\u2014\u2014\u5de5\u4f5c\u539f\u7406\u4e0e\u8f6f\u4ef6\u5de5\u5177\u5185\u5bb9\u663e\u793a<\/span><\/strong><\/h4>\n


<\/span><\/p>\n

\u7c7b\u4f3c\u4e8e\u7ebf\u7684\u7b80\u5355\u70b9\u659c\u7387\u65b9\u7a0b\uff0c\u6211\u4eec\u7ed9\u51fa\u786e\u5b9a\u6027\u6df7\u6c8c\u65b9\u7a0b\u5982\u4e0b:<\/span><\/p>\n


<\/span><\/p>\n

<\/p>\n


<\/p>\n

X(n-1)\u662f\u5f53\u524d\u70b9\uff0cX(n)\u662f\u4e0b\u4e00\u4e2a\u70b9\uff0cM\u662f\u6807\u5ea6\u7f29\u653e\u53c2\u6570<\/span>\uff08scale parameter\uff09<\/span>\uff0c\u5b83\u63a7\u5236\u5f53\u524d\u8282\u70b9\u751f\u6210\u4e0b\u4e00\u4e2a\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\uff0cZ\u5bf9\u5e94\u4e8e\u968f\u673a\u9009\u62e9\u7684\u201c\u9876\u70b9\u201d\u4e4b\u4e00\uff0c\u8fd9\u4e9b\u9876\u70b9\u662f\u7ea6\u675f\u6240\u6709\u7f51\u7edc\u8282\u70b9\u7684\u4e00\u7ec4\u521d\u59cb\u70b9\uff0c\u5728\u6211\u4eec\u7684\u4f8b\u5b50\u4e2d\u53ef\u4ee5\u8868\u793a\u7f51\u7edc\u96c6\u7ebf\u5668\u3002\u5982\u679c\u9700\u8981\uff0c\u521d\u59cb\u70b9\u7684\u6570\u91cf\u53ef\u4ee5\u4ece3\u4e2a\u5230\u8d85\u8fc7100\u4e2a\u4e0d\u7b49\uff0c\u5c3d\u7ba1\u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff0c\u5927\u591a\u6570\u72ec\u7279\u7684\u6d8c\u73b0\u884c\u4e3a\u662f\u752812\u4e2a\u6216\u66f4\u5c11\u7684\u521d\u59cb\u70b9\u89c2\u5bdf\u5230\u7684\u3002\u7279\u5b9a\u7684Z\u662f\u4ece\u8fd9\u7ec4\u521d\u59cb\u70b9\u4e2d\u968f\u673a\u9009\u62e9\u7684\u3002M\u7684\u503c\u4e3a0 < |M| < 1\uff0c\u9700\u8981\u5b9e\u9a8c\u53d1\u73b0\u624d\u80fd\u786e\u5b9a\u4ec0\u4e48\u6837\u7684M\u503c\u80fd\u7ed9\u51fa\u671f\u671b\u7684\u6d8c\u73b0\u884c\u4e3a\u3002\u4e00\u65e6\u786e\u5b9a\u4e86\u8fd9\u4e9b\u503c\uff0c\u5728\u76f8\u4f3c\u7684\u62d3\u6251\u4e2d\uff0c\u7528\u9009\u5b9a\u7684M\u548c\u76f8\u540c\u6570\u91cf\u7684\u521d\u59cb\u70b9\u5bf9\u8be5\u65b9\u7a0b\u8fdb\u884c\u7684\u4efb\u4f55\u968f\u673a\u8fd0\u884c\uff0c\u90fd\u5c06\u4ea7\u751f\u76f8\u540c\u7684\u6574\u4f53\u62d3\u6251\u7ed3\u6784\u3002\u8fd9\u662f\u7279\u522b\u6709\u8da3\u7684\uff0c\u56e0\u4e3a\u6539\u53d8\u968f\u673a\u6570\u79cd\u5b50\u51e0\u4e4e\u4e0d\u4f1a\u5bf9\u751f\u6210\u7684\u62d3\u6251\u4ea7\u751f\u660e\u663e\u7684\u5f71\u54cd\uff0c\u5c3d\u7ba1\u4e8b\u5b9e\u4e0a\u6240\u6709\u7684\u70b9\u90fd\u662f\u65b0\u751f\u6210\u7684\u3002\u8fd9\u8fd8\u8bc1\u660e\u4e86\u8be5\u6570\u5b66\u51fd\u6570\u662f\u5c5e\u4e8e\u786e\u5b9a\u6027\u6df7\u6c8c\u7684\u3002\u53d8\u91cfM\u548c\u53d8\u91cfZ\u90fd\u5177\u6709\u5f71\u54cd\u6574\u4e2a\u7f51\u7edc\u62d3\u6251\u7684\u76f8\u4e92\u4f9d\u8d56\u6027\uff0c\u5305\u62ec\u63a7\u5236\u96c6\u7fa4\u7684\u7a0b\u5ea6\uff0c\u4ee5\u53ca\u5728\u4e0d\u540c\u5c3a\u5ea6\u4e0a\u7279\u5b9a\u96c6\u7fa4\u5b50\u96c6\u4e4b\u95f4\u7684\u9690\u5f0f\u6620\u5c04\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u8be5\u7b97\u6cd5\u5177\u6709\u201c\u53ef\u8c03\u201d\u503c\uff0c\u53ef\u63a7\u5236\u4ece\u6709\u5e8f\u5230\u6df7\u6c8c\u7684\u53ef\u91cd\u590d\u8f6c\u53d8\u3002\u8fd9\u662f\u7531\u4e0e\u521d\u59cb\u9876\u70b9\u96c6\u8026\u5408\u7684\u53d8\u91cfM\u63a7\u5236\u7684\u3002\u9664\u4e86\u4e3a\u7f51\u7edc\u8def\u7531\u751f\u6210\u62d3\u6251\u56fe\u4e4b\u5916\uff0c\u751f\u6210\u7684\u6570\u636e\u70b9\u8fd8\u53ef\u7528\u4e8e\u521b\u5efa\u51e0\u7c7b\u4fe1\u606f\u3002\u8fd9\u4e9b\u4fe1\u606f\u53ef\u4ee5\u6765\u81ea\u4f20\u611f\u5668\u6570\u636e\uff0c\u5305\u62ec\u4e0e\u7279\u5f81\u7c7b\u522b\u76f8\u5173\u8054\u7684\u51e0\u4e2a\u7279\u5f81\uff0c\u5e76\u4e14\u53ef\u4ee5\u7531\u62d3\u6251\u5173\u7cfb\u6765\u8868\u793a\u3002\u5982\u679c\u4f4d\u4e8e\u4e0d\u540c\u4f4d\u7f6e\u7684\u51e0\u4e2a\u4f20\u611f\u5668\u68c0\u6d4b\u5230\u540c\u4e00\u4e2a\u4f4d\u7f6e\u7684\u4e1c\u897f\uff0c\u4f46\u5bf9\u5176\u8fdb\u884c\u4e86\u4e0d\u540c\u7684\u5206\u7c7b\uff0c\u90a3\u4e48\u4f20\u611f\u5668\u7684\u6570\u636e\u5c06\u6620\u5c04\u5230\u591a\u4e2a\u76f8\u5173\u7684\u7c7b\u522b\u4e2d\u3002\u201c\u62d3\u6251\u5730\u56fe\u201d<\/span>\uff08topological map\uff09<\/span>\u5c06\u5305\u542b\u4f20\u611f\u5668\u4f4d\u7f6e\u548c\u6570\u636e\uff0c\u5e76\u5c06\u5b83\u4eec\u4e4b\u95f4\u7684\u5173\u7cfb\u8054\u7cfb\u8d77\u6765\uff0c\u540c\u65f6\u4fdd\u7559\u5dee\u5f02\u3002\u8fd9\u5141\u8bb8\u5171\u4eab\u4fe1\u606f\u5b9a\u4e49\u90a3\u4e9b\u4e0d\u540c\u4f46\u53c8\u5e38\u89c1\u7684\u7279\u5f81\u3002\u4f20\u611f\u5668\u5143\u4ef6\u4e4b\u95f4\u4f20\u8f93\u7684\u5c11\u91cf\u6570\u636e\u53ef\u7528\u4e8e\u5171\u4eab\u4f20\u611f\u5668\u8282\u70b9\u7684\u5168\u5c40\u56fe\u50cf\uff0c\u5373\u5171\u8bc6\u4e3b\u52a8\u6027\u5173\u7cfb\u3002\u5927\u81ea\u7136\u4e5f\u4f7f\u7528\u7c7b\u4f3c\u7684\u7814\u7a76\u65b9\u6cd5\uff0c\u6bd4\u5982\u8682\u8681\u548c\u5176\u4ed6\u7fa4\u5c45\u6606\u866b\u6807\u8bb0\u4e00\u4e2a\u611f\u5174\u8da3\u7684\u5730\u70b9\u3002\u5f53\u5176\u4ed6\u8682\u8681\u7ecf\u8fc7\u6807\u8bb0\u7684\u4f4d\u7f6e\uff0c\u5b83\u4eec\u4e5f\u4f1a\u6807\u8bb0\u5b83\uff0c\u8db3\u591f\u591a\u7684\u6807\u8bb0\u4f1a\u4f7f\u6240\u6709\u8682\u8681\u8ddf\u968f\u5730\u6807\u7684\u8e2a\u8ff9\u3002\u8fd9\u4e00\u5c0f\u5757\u4fe1\u606f\u4f1a\u53d8\u5f97\u975e\u5e38\u5f3a\u5927\uff0c\u7c7b\u4f3c\u4e8e\u975e\u9884\u5b9a\u53c2\u6570\u968f\u673a\u7b97\u6cd5\u4e2d\u7528\u4e8e\u5b9a\u4e49\u884c\u4e3a\u7684\u7a00\u758f\u6570\u636e\u5143\u7d20\u3002\u4e3a\u4e86\u7814\u7a76\u975e\u9884\u5b9a\u53c2\u6570\u968f\u673a\u7b97\u6cd5\uff0c\u5728Mathematica\u00ae\u4e2d\u6784\u5efa\u4e86\u4e00\u4e2a\u5de5\u5177\uff0c\u7528\u4e8e\u663e\u793a\u7528\u6237\u52a8\u6001\u8fdb\u884c\u7684\u53c2\u6570\u66f4\u6539\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u5bf9\u6bd4\u56fe1\u4e2d\u7684\u4e24\u5e45\u56fe\uff0c\u53ef\u4ee5\u770b\u5230\u521d\u59cb\u70b9\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u4e5f\u53ef\u4ee5\u8ba4\u4e3a\u662f\u4e94\u4e2a\u7c7b\u522b\u7684\u62d3\u6251\u8868\u793a\uff0c\u6bcf\u4e2a\u5438\u5f15\u5b50\/\u9876\u70b9\u4ee3\u8868\u4e00\u4e2a\u7c7b\u522b\u3002\u5982\u524d\u6240\u8ff0\uff0c\u6bcf\u5f20\u56fe\u7247\u4e2d\u5de6\u4e0a\u89d2<\/span>\uff08\u8f83\u5c0f\uff09<\/span>\u7684\u77e9\u5f62\u5305\u542b\u4e94\u4e2a\u70b9\uff0c\u8868\u793a\u7a7a\u95f4\u5206\u79bb\u7684\u521d\u59cb\u7c7b\u522b<\/span>\uff08\u5728\u672c\u6570\u636e\u5206\u6790\u793a\u4f8b\u4e2d\uff09<\/span>\u3002\u6bcf\u5f20\u56fe\u7247\u4e2d\u7684\u5927\u77e9\u5f62\u4e2d\u7684\u4e00\u7ec4\u805a\u7c7b\u70b9\u4ee3\u8868\u6570\u636e\u3002\u5de6\u56fe\u663e\u793a\u4e86\u7531\u7c7b\u522b\u7684\u5bf9\u79f0\u5e03\u5c40\u4ea7\u751f\u7684\u5bf9\u79f0\u96c6\u7fa4<\/span>\uff08symmetric clusters\uff0c\u5bf9\u79f0\u96c6\u7fa4\uff09<\/span>\u3002\u5f53\u5de6\u4e0b\u7c7b\u522b\u9876\u70b9\u79fb\u52a8\u5230\u66f4\u9760\u8fd1\u5176\u4ed6\u7c7b\u522b\u65f6\uff0c\u805a\u7c7b\u6570\u636e\u70b9\u4f1a\u53d1\u751f\u53d8\u5316\uff0c\u4ee5\u5339\u914d\u76f8\u5bf9\u7684\u7c7b\u522b\u4f4d\u7f6e\u3002<\/span><\/p>\n


<\/p>\n

<\/p>\n

\u56fe1. \u4e00\u4e2a\u9876\u70b9\u88ab\u79fb\u52a8<\/span><\/p>\n


<\/p>\n

\u4e3a\u4e86\u89c2\u5bdf\u53c2\u6570M\u5bf9\u62d3\u6251\u7ed3\u6784\u7684\u5f71\u54cd\uff0c\u5728\u56fe2\u4e2d\uff0cM\u88ab\u9009\u4e3a\u5927\u4e8e0.5\u7684\u503c\uff0c\u4e94\u4e2a\u521d\u59cb\u70b9\u7684\u7ed3\u679c\u6a21\u5f0f\u662f\u968f\u673a\u6563\u5c04\uff0c\u8fd9\u5c06\u662f\u9ed8\u8ba4\u6a21\u5f0f\uff0c\u4efb\u4f55\u4eba\u90fd\u53ef\u4ee5\u4f7f\u7528\u975e\u9884\u5b9a\u53c2\u6570\u968f\u673a\u7b97\u6cd5\u7684\u968f\u673a\u65b9\u9762\u7684\u7b80\u5355\u51fd\u6570\u3002\u73b0\u5728\uff0c\u5728\u56fe3\u4e2d\uff0cM\u53d8\u4e3a0.33\u5de6\u53f3\uff0c\u5176\u7ed3\u679c\u4e0e\u7ecf\u5178\u7535\u5b50\u6e38\u620f\u300a\u592a\u7a7a\u5165\u4fb5\u8005\u300b\u76f8\u4f3c\u3002\u672c\u7ae0\u672b\u5c3e\u8fd8\u5305\u62ec\u5176\u4ed6\u793a\u4f8b\u6a21\u5f0f\u3002<\/span><\/p>\n


<\/p>\n

<\/p>\n

\u56fe2. M>0.5<\/span><\/p>\n


<\/p>\n

<\/p>\n

\u56fe3. M~0.33<\/span><\/p>\n


<\/p>\n

\u4ece\u4e0a\u9762\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0c\u56fe3\u4e2d\u51fa\u73b0\u7684\u96c6\u7fa4\u6a21\u5f0f\u662f\u7531\u56fe2\u4e2d\u770b\u4f3c\u968f\u673a\u7684\u70b9\u4e91\u4ea7\u751f\u7684\u3002\u56e0\u6b64\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5bf9\u4e8e5\u4e2a\u9876\u70b9\uff0c\u5c06\u6807\u5ea6\u7f29\u653e\u53c2\u6570M\u4ece\u5927\u7ea60.5\u6216\u66f4\u5927\u6539\u53d8\u5230\u5927\u7ea60.33\u4f1a\u5bfc\u81f4\u8be5\u987a\u5e8f\u51fa\u73b0\u3002\u5c06\u56fe\u7247\u5212\u5206\u4e3a\u5e73\u94fa\u90e8\u5206\u7684\u7ebf\u6761\u662f\u5bf9\u5c4f\u5e55\u4e0a\u7684\u70b9\u5e94\u7528Voronoi \u51fd\u6570\u6620\u5c04\u7684\u7ed3\u679c\u3002Voronoi \u9576\u5d4c\u63d0\u4f9b\u4e86\u4e00\u79cd\u65e0\u504f\u7684\u65b9\u6cd5\u6765\u786e\u5b9a\u54ea\u4e9b\u70b9\u6620\u5c04\u5230\u4e00\u4e2a\u7279\u5b9a\u805a\u7c7b\u3002\u8fd9\u907f\u514d\u4e86\u7531\u4e8e\u4f30\u8ba1\u96c6\u7fa4\u5f00\u59cb\u548c\u7ed3\u675f\u7684\u4f4d\u7f6e\u6216\u96c6\u7fa4\u4f4d\u4e8e\u67d0\u4e2a\u4f4d\u7f6e\u7684\u9519\u89c9<\/span>\uff08\u5373pareidolia\uff09<\/span>\u800c\u5bfc\u81f4\u7684\u4eba\u4e3a\u9519\u8bef\u6216\u504f\u89c1\u3002Voronoi \u5e76\u975e\u4e07\u65e0\u4e00\u5931\uff0c\u56e0\u4e3a\u6709\u65f6\u96c6\u7fa4\u7684\u67d0\u4e9b\u90e8\u5206\u4f1a\u51fa\u73b0\u5728\u4e24\u4e2a\u9576\u5d4c\u76d8\u4e4b\u95f4\u7684\u8fb9\u7ebf\u4e0a\u3002\u4f46\u5b83\u4e3a\u96c6\u7fa4\u4f55\u65f6\u6613\u4e8e\u5206\u79bb\u63d0\u4f9b\u4e86\u4e00\u4e2a\u901a\u7528\u6307\u6807\u3002<\/span><\/p>\n


<\/span><\/p>\n

1.3\u5efa\u8bae\u7684\u89e3\u51b3\u65b9\u6848\uff1a\u5e94\u7528\u975e\u9884\u5b9a\u53c2\u6570\u968f\u673a\u7b97\u6cd5\u89e3\u51b3\u81ea\u7ec4\u7ec7\u8def\u7531\u95ee\u9898<\/span><\/strong><\/span><\/h4>\n


<\/p>\n

\u6211\u4eec\u73b0\u5728\u6709\u8db3\u591f\u7684\u4fe1\u606f\u6765\u89e3\u51b3\u6211\u4eec\u7684\u5927\u578b\u81ea\u7ec4\u7ec7\u7f51\u7edc\u8def\u7531\u95ee\u9898\u3002\u4f7f\u7528\u56fe3\u4e2d\u6240\u793a\u7684\u5148\u524d\u9ad8\u5ea6\u7ed3\u6784\u5316\u7684\u62d3\u6251\uff0c\u6211\u4eec\u73b0\u5728\u6dfb\u52a0\u8def\u7531\uff0c\u5e76\u5b9a\u4e49\u901a\u4fe1\u8ddd\u79bb\u3002\u8fd9\u4e2a\u7ed3\u679c\u6211\u4eec\u6807\u8bb0\u4e3a\u56fe4\uff0c\u5c31\u50cf\u6807\u8bb0\u4e3a\u56fe3\u4e00\u6837\u3002<\/span><\/p>\n


<\/p>\n

<\/p>\n

\u56fe4. \u56fe3\u7684\u8def\u7531\u6807\u8bb0<\/span><\/p>\n


<\/span><\/p>\n

\u56fe\u4e2d\u7684\u4e94\u4e2a\u4e3b\u8981\u96c6\u7fa4\uff0c\u5373\u6bcf\u4e2aVoronoi\u56fe\u5757\u4e3a\u4e00\u4e2a\u4e3b\u8981\u96c6\u7fa4<\/span>\uff08clusters\uff09<\/span>\uff0c\u5176\u88ab\u5212\u5206\u4e3a\u4e94\u4e2a\u5b50\u96c6\u7fa4<\/span>\uff08sub-clusters\uff09<\/span>\uff0c\u5176\u4e2d\u4e00\u4e2a\u5b50\u96c6\u7fa4\u4ee5\u7d2b\u8272\u5708\u4e3a\u4f8b\u3002\u7531\u4e8e\u8fed\u4ee3\u51fd\u6570\u7cfb\u7edf\u7684\u81ea\u76f8\u4f3c\u6027\u8d28\uff0c\u8fd9\u4e9b\u5b50\u96c6\u7fa4\u518d\u6b21\u88ab\u5212\u5206\u4e3a\u5b50\u5b50\u96c6\u7fa4<\/span>\uff08sub-sub-clusters\uff09<\/span>\uff0c\u5e76\u8fdb\u4e00\u6b65\u7ec6\u5206\u3002\u8ba9\u6211\u4eec\u5047\u8bbe\u5305\u542b\u96c6\u7fa4\u7684\u7a97\u53e3\u662f\u6307\u5411\u8fd9\u4e9b\u70b9\u6240\u5728\u7684\u533a\u57df\u4e00\u4e2a\u4e8c\u7ef4\u6620\u5c04\u3002\u8ba9\u6211\u4eec\u5047\u8bbe\u5c4f\u5e55\u4e0a\u7684\u6bcf\u4e00\u4e2a\u6700\u5c0f\u70b9\u90fd\u5bf9\u5e94\u4e8e\u4e00\u4e2a\u81ea\u7ec4\u7ec7\u65e0\u7ebf\u7535<\/span>\uff08\u6216\u7269\u8054\u7f51\u8bbe\u5907\uff09<\/span>\uff0c\u8fd9\u4e2a\u8bbe\u5907\u53ef\u80fd\u4f4d\u4e8e\u67d0\u4e2a\u667a\u80fd\u4e3b\u4f53\u6216\u65e0\u4eba\u673a\u5185\u3002\u8bf7\u6ce8\u610f\uff0c\u8fd9\u5f20\u56fe\u7247\u4e2d\u7684\u6bcf\u4e2a\u5355\u72ec\u7684\u70b9\u90fd\u4e0d\u662f\u663e\u5f0f\u53ef\u89c1\u7684\uff0c\u56e0\u4e3a\u8be5\u5de5\u5177\u6b64\u6b21\u8fd0\u884c\u7ed8\u5236\u4e8620,000\u4e2a\u552f\u4e00\u7684\u70b9\uff0c\u5176\u4e2d\u8bb8\u591a\u70b9\u662f\u7d27\u5bc6\u805a\u96c6\u7684\u3002\u5bf9\u4e8e\u7528\u7d2b\u8272\u5708\u8d77\u6765\u7684\u5b50\u96c6\u7fa4\uff0c\u8ba9\u6211\u4eec\u5047\u8bbe\u5706\u7684\u76f4\u5f84\u662f\u4e24\u4e2a\u8282\u70b9\u4e4b\u95f4\u70b9\u5bf9\u70b9\u901a\u4fe1\u7684\u4e00\u822c\u8303\u56f4\u3002\u6700\u540e\uff0c\u9009\u62e9\u4e24\u4e2a\u8282\u70b9<\/span>\uff08\u5b9e\u9645\u4e0a\u4e3a\u4e86\u4fbf\u4e8e\u67e5\u770b\uff0c\u9009\u62e9\u4e86\u4e24\u4e2a\u5b50\u96c6\u7fa4\uff09<\/span>\uff0c\u5e76\u7528\u7eff\u8272\u5708\u6807\u8bb0\u3002\u4e3a\u4e86\u663e\u793a\u8def\u7531\uff0c\u5728\u7a97\u53e3\u7684\u5bf9\u89d2\u4e24\u7aef\u9009\u62e9\u4e86\u7eff\u8272\u5706\u5708\u8282\u70b9\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u7531\u4e8e\u6bcf\u4e2a\u8282\u70b9\u90fd\u80fd\u591f\u8ba1\u7b97\u51fa\u6240\u6709\u5176\u4ed6\u8282\u70b9\u7684\u603b\u4f53\u5e03\u5c40\uff0c\u56e0\u6b64\u5b83\u80fd\u591f\u51b3\u5b9a\u5c06\u81ea\u5df1\u7684\u6d88\u606f\u54ea\u4e2a\u65b9\u5411\uff0c\u4ee5\u7528\u4e8e\u5176\u8def\u7531\u7684\u4e0b\u4e00\u7ad9\u6216\u4e0b\u4e00\u8df3\uff0c\u5982\u56fe4\u4e2d\u7684\u7ea2\u8272\u5f27\u7ebf\u6240\u793a\u3002\u6d8c\u73b0\u7684\u81ea\u76f8\u4f3c\u6027\u4f7f\u5176\u66f4\u5bb9\u6613\uff0c\u56e0\u4e3a\u5c3d\u7ba1\u8282\u70b9\u662f\u968f\u673a\u8fed\u4ee3\u7684\uff0c\u4f46\u603b\u4f53\u62d3\u6251\u5c06\u4fdd\u6301\u81ea\u76f8\u4f3c\uff0c\u81f3\u5c11\u5bf9\u4e8e\u6807\u5ea6\u7f29\u653e\u53c2\u6570M\u7684\u67d0\u4e9b\u503c\u800c\u8a00\u662f\u5982\u6b64\u3002\u5982\u679c\u6bcf\u4e2a\u8282\u70b9\u90fd\u77e5\u9053\u5176\u8303\u56f4\u9650\u5236\uff0c\u5373\u7d2b\u8272\u5706\u5708\u7684\u76f4\u5f84\uff0c\u90a3\u4e48\u5b83\u5c06\u5728\u5176\u8303\u56f4\u8fb9\u7f18\u4ee5\u9002\u5f53\u7684\u65b9\u5411\u5411\u5b50\u96c6\u7fa4\u5e7f\u64ad\uff0c\u4ee5\u5230\u8fbe\u76ee\u6807\u8282\u70b9\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u6bcf\u4e2a\u8282\u70b9\u90fd\u6709\u8ba1\u7b97\u6240\u6709\u5176\u4ed6\u8282\u70b9\u7684\u4f4d\u7f6e\u6240\u9700\u7684\u4fe1\u606f\uff0c\u5728\u672c\u4f8b\u4e2d\uff0c\u8fd9\u4e9b\u4fe1\u606f\u7531\u4e94\u4e2a\u9876\u70b9\u7684\u4f4d\u7f6e\u548c\u6807\u5ea6\u7f29\u653e\u53c2\u6570M\u7684\u503c\u7ec4\u6210\u3002\u968f\u7740\u9876\u70b9\u4f4d\u7f6e\u7684\u6539\u53d8\u6216M\u7684\u6539\u53d8\uff0c\u8fd9\u4e9b\u503c\u53ef\u4ee5\u5728\u77ed\u65f6\u95f4\u5185\u5e7f\u64ad\u5230\u6240\u6709\u8282\u70b9\u3002\u5bf9\u4e8e\u4efb\u4f55\u73b0\u4ee3\u5316\u7684\u5904\u7406\u8282\u70b9\u6765\u8bf4\uff0c\u91cd\u65b0\u8ba1\u7b97\u90fd\u662f\u5fae\u4e0d\u8db3\u9053\u7684\uff0c\u56e0\u4e3a\u5b83\u7531\u4e00\u4e2a\u7ebf\u6027\u52a0\u6cd5\u548c\u4e00\u4e2a\u6d6e\u70b9\u6570\u4f5c\u4e3a\u4e58\u6cd5\u5668\u7ec4\u6210\u3002\u8fd9\u4e9b\u8282\u70b9\u62d3\u6251\u7684\u5185\u90e8\u8ba1\u7b97\u4e3a\u6240\u6709\u8282\u70b9\u63d0\u4f9b\u4e86\u521b\u5efa\u4e0e\u6574\u4f53\u62d3\u6251\u4e00\u81f4\u7684\u5185\u90e8\u4e16\u754c\u6a21\u578b\u7684\u80fd\u529b\uff0c\u56e0\u6b64\u80fd\u591f\u6d3e\u751f\u51fa\u4e00\u4e2a\u5171\u4eab\u4e16\u754c\u6a21\u578b\u3002\u8fd9\u5c31\u4e3a\u8282\u70b9\u4e4b\u95f4\u7684\u901a\u4fe1\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5171\u540c\u7684\u7406\u89e3\uff0c\u5373\u4f7f\u53c2\u6570\u52a8\u6001\u53d8\u5316\u3002<\/span><\/p>\n


<\/h4>\n

\u904d\u5386\u70b9\u5bf9\u70b9\u7f51\u7edc\u8fde\u63a5<\/span><\/strong><\/h4>\n


<\/span><\/p>\n

\u5f53\u6211\u4eec\u6cbf\u7740\u4ece\u6e90\u8282\u70b9\u5230\u76ee\u7684\u5730\u7684\u8def\u7ebf\u79fb\u52a8\u65f6\uff0c\u6700\u5bb9\u6613\u7684\u65b9\u6cd5\u662f\u6309\u67d0\u79cd\u987a\u5e8f\u5bf9\u96c6\u7fa4\u548c\u5b50\u96c6\u7fa4\u8fdb\u884c\u7f16\u53f7\u3002\u4efb\u610f\u5730\uff0c\u8ba9\u6211\u4eec\u5728\u6bcf\u4e2a\u96c6\u7fa4\u548c\u5b50\u96c6\u7fa4\u5185\u987a\u65f6\u9488\u79fb\u52a8\uff0c\u4ece\u5de6\u4e0b\u89d2\u5f00\u59cb\uff0c\u5230\u53f3\u4e0b\u89d2\u7ed3\u675f\u3002\u56e0\u6b64\uff0c\u5bf9\u4e8e\u5de6\u4e0b\u65b9\u7684\u7eff\u8272\u5706\u5708\u8282\u70b9\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u4e09\u4e2a\u6570\u5b57<\/span>\uff08cluster\u96c6\u7fa4\u3001sub\u5b50\u96c6\u7fa4\u3001sub-sub\u5b50\u5b50\u96c6\u7fa4\uff09<\/span>\u6765\u8868\u793a\u8fd9\u4e9b\u96c6\u7fa4\u5143\u7d20\uff0c\u59821\uff0c2\uff0c1\u3002\u7ea2\u8272\u5f27\u7ebf\u8868\u793a\u6bcf\u4e2a\u8282\u70b9\u8303\u56f4\u9650\u5236\u5185\u7684\u6bcf\u4e00\u8df3\u7684\u8def\u5f84\u3002\u4ece1\uff0c2\uff0c1\u4e2d\u7684\u7eff\u8272\u5706\u5708\u8282\u70b9\u52304\uff0c4\uff0c5\u4e2d\u7684\u76ee\u7684\u5730\u7eff\u8272\u5706\u5708\u8282\u70b9\u7684\u5927\u81f4\u8df3\u8dc3\u987a\u5e8f\u5982\u4e0b\uff1a<\/span><\/p>\n


<\/span><\/p>\n

1, 2, 1 to 1, 3, 3 to 2, 5, 1 to 2, 4, {3, 4, or 5} to 3, 2, 1 to 3, 3, 2 to 3, 4, {1 or 2} to 4, 2, 2 to 4, 3, 2 to 4, 4, {3, 4, 5}\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u5927\u62ec\u53f7\u8868\u793a\u8fd1\u4f3c\u7684\u8df3\u6570\uff0c\u56e0\u4e3a\u5927\u62ec\u53f7\u4e2d\u7684\u6240\u6709\u8282\u70b9\u90fd\u5728\u8303\u56f4\u5185\uff0c\u6240\u4ee5\u5982\u679c\u4e00\u4e9b\u8282\u70b9\u4e0d\u53ef\u7528\uff0c\u5176\u4ed6\u8282\u70b9\u53ef\u4ee5\u4ee3\u66ff\u5b83\u4eec\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u867d\u7136\u9009\u62e9\u7684\u786e\u5207\u8def\u7531\u53ef\u80fd\u5e76\u975e\u6bcf\u6b21\u90fd\u662f\u6700\u4f18\u7684\uff0c\u4f46\u8fd9\u79cd\u7c7b\u578b\u7684\u8def\u7531\u62d3\u6251\u4e3a\u8fb9\u7f18\u8282\u70b9\u548c\u66f4\u96c6\u4e2d\u7684\u8282\u70b9\u63d0\u4f9b\u4e86\u5f39\u6027\u80fd\u529b\u7684\u5ea6\u91cf\u3002\u56e0\u4e3a\u5373\u4f7f\u67d0\u4e9b\u5b50\u96c6\u7fa4\u548c\u5b50\u96c6\u7fa4\u4e22\u5931\u4e86\u591a\u8fbe\u4e00\u534a\u7684\u8282\u70b9\uff0c\u901a\u4fe1\u8def\u7531\u4e5f\u53ef\u4ee5\u5de5\u4f5c\u3002\u4e0e\u73b0\u6709\u7684\u81ea\u7ec4\u7ec7\u8def\u7531\u534f\u8bae\u76f8\u6bd4\uff0c\u5b83\u6709\u4e00\u4e2a\u660e\u663e\u7684\u4f18\u52bf\u3002\u4f8b\u5982AODV\u534f\u8bae<\/span>\uff08ad-hoc On Demand Distance V-Vector routing\uff09<\/span>\uff0c\u5728\u8def\u7531\u53d1\u73b0\u8fc7\u7a0b\u4e2d\u5b58\u5728\u8f83\u5927\u7684\u5ef6\u8fdf\u65f6\u95f4\u3002\u76f8\u53cd\uff0c\u8fd9\u79cd\u4f7f\u7528\u975e\u9884\u5b9a\u53c2\u6570\u968f\u673a\u7684\u65b9\u6cd5\u53ea\u9700\u8981\u8ba1\u7b97\u51e0\u4e2a\u8def\u7531\u6392\u5217\uff0c\u5c31\u53ef\u4ee5\u627e\u5230\u4e00\u6761\u9ad8\u6548<\/span>\uff08\u5c3d\u7ba1\u4e0d\u662f\u6700\u4f18\uff09<\/span>\u7684\u8def\u7531\u3002<\/span><\/p>\n


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1. Library of Congress, Congressional Research Service. Network centric operations: background and oversight issues for Congress (Report Order Code RL32411) (2007). https:\/\/www.fas.org\/ sgp\/crs\/natsec\/RL32411.pdf. Accessed 02 Jan 2015<\/span><\/p>\n

2. Bar-Y am, Y .: About engineering complex systems: multiscale analysis and evolutionary engineering (2005). https:\/\/necsi.edu\/research\/multiscale\/ESOA04.pdf. Accessed 01 Apr 2017<\/span><\/p>\n

3. Stygmergy. https:\/\/en.wikipedia.org\/wiki\/Stygmergy. Accessed 01 May 2016<\/span><\/p>\n

4. Masoumi, B., Meybodi, M.R.: Speeding up learning automata based multi agent systems using the concepts of stigmergy and entropy. Expert Syst. Appl. 38(7), 8105\u20138118 (2011)<\/span><\/p>\n

5. Dagon, D., Guofei, G., Lee, C.P ., Wenke, L.: A taxonomy of botnet structures. In: Computer Security Applications Conference, 2007, ACSAC 2007, pp. 325\u2013339. ACSAC (2007)<\/span><\/p>\n

6. Kleinberg, J., Sandler, M., Slivkins, A.: Network failure detection and graph connectivity. In: SODA \u201804 Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 76\u201385. Society for Industrial and Applied Mathematics, Philadelphia (2004)<\/span><\/p>\n

7. Dorogovtsev, S., Mendes, J.: The shortest path to complex networks. Am. J. Med. Genet. 71, 47\u201353 (2004)<\/span><\/p>\n

8. Shargel, B., Sayama, H., Epstein, I., Bar-Y am, Y .: Optimization of robustness and connectivity in complex networks. Phys. Rev. Lett. 90(6) (2003)<\/span><\/p>\n

9. Bak, P ., Tang, C., Wiesenfeld, K.: Self-organized criticality: an explanation of 1\/f noise. Phys. Rev. Lett. 59, 381\u2013384 (1987)<\/span><\/p>\n

10. Park, K., Willinger, W.: The internet as a large-scale complex system. In: Santa Fe Institute Studies on the Sciences of Complexity, Oxford University Press, New Y ork (2005)<\/span><\/p>\n

11. Barnsley, M.F.: Fractals Everywhere. Academic Press, San Diego, CA (1988)<\/span><\/p>\n

12. Demko, S., Hodges, S., Naylor, B.: Construction of fractal objects with IFS. Comput. Graph. 19(3), 271\u2013278 (1985)<\/span><\/p>\n

13. Peitgen, H., Jurgens, H., Saupe, D.: Chaos and Fractals: New Frontiers of Science. Springer (1992)<\/span><\/p>\n

14. Barnsley, M.F., Vince, A.: The chaos game on a general iterated function system. Ergodic Theory Dyn. Syst. 31(4), 1073\u20131079 (2010)<\/span><\/p>\n

15. Schaff, J.: Creating human-like behavior in a UA V: a counter-terrorism model. In: Proceedings of the Fourteenth Annual Software Technology Conference (2002)<\/span><\/p>\n

16. Diacu, F.: The solution of the n-body problem. Math. Intell. 18(3), 66\u201370 (1996)<\/span><\/p>\n

17. Reynolds, C.: Flocks, herds and schools: a distributed behavioral model. In: SIGGRAPH \u201887: Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques, pp. 25\u201334. Association for Computing Machinery (1987)<\/span><\/p>\n

18. Office of the Deputy Under Secretary of Defense for Acquisition and Technology: Systems and software engineering. Systems engineering guide for systems of systems, version 1.0. ODUSD(A&T) SSE, Washington, DC (2008)<\/span><\/p>\n

19. McKelvey, B.: Complexity science as order-creation science: new theory, new method. ECO 6(4), 2\u201327 (2004)<\/span><\/p>\n

20. Brooks, R.A.: Intelligence without reason. In: IJCAI\u201991 Proceedings of the 12th International Joint Conference on Artificial Intelligence, vol. 1, pp. 569\u2013595. Sydney (1991)<\/span><\/p>\n


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