{"id":25980,"date":"2021-05-05T22:01:36","date_gmt":"2021-05-05T14:01:36","guid":{"rendered":"https:\/\/swarma.org\/?p=25980"},"modified":"2021-05-05T22:01:36","modified_gmt":"2021-05-05T14:01:36","slug":"%e5%a4%8d%e6%9d%82%e4%b9%8b%e7%be%8e%ef%bc%9a%e7%ae%97%e6%b3%95%e6%95%b0%e5%ad%a6%e8%89%ba%e6%9c%af%e7%9a%8411%e5%a4%a7%e5%88%86%e6%94%af","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=25980","title":{"rendered":"\u590d\u6742\u4e4b\u7f8e\uff1a\u7b97\u6cd5\u6570\u5b66\u827a\u672f\u768411\u5927\u5206\u652f"},"content":{"rendered":"
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2. \u4e09\u7ef4\u6216\u4e09\u7ef4\u4ee5\u4e0a\u7684\u89c4\u5219\u7acb\u4f53<\/span><\/strong><\/span><\/h2>\n

3. \u5e73\u9762\u66f2\u7ebf<\/span><\/strong><\/span><\/h2>\n

4. \u5e73\u9762\u51e0\u4f55\u4e0e\u5904\u7406<\/span><\/strong><\/span><\/h2>\n

5. L-\u7cfb\u7edf\uff0c\u6d77\u9f9f\u56fe\u5f62<\/span><\/strong><\/span><\/p>\n

6. \u51fd\u6570\u7684\u56fe\u50cf<\/span><\/strong><\/span><\/h2>\n

7. \u9576\u5d4c\u56fe\u6848<\/span><\/strong><\/span><\/h2>\n

8. IFS\uff08\u8fed\u4ee3\u51fd\u6570\u7cfb\u7edf\uff09\u5206\u5f62<\/span><\/strong><\/span><\/h2>\n

9. \u66f4\u9ad8\u7ef4\u5ea6<\/span><\/strong><\/span><\/h2>\n

10. \u8fdb\u5316\u7f16\u7a0b\uff08Evolutionary Programing\uff09<\/span><\/strong><\/span><\/h2>\n

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\u539f\u6587\u6807\u9898\uff1a<\/span><\/p>\n

Algorithmic Mathematical Art<\/span><\/h1>\n

\u539f\u6587\u5730\u5740\uff1a<\/span>
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http:\/\/xahlee.info\/math\/algorithmic_math_art.html<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u4ee5\u4e0b\u662f\u7b97\u6cd5\u6570\u5b66\u827a\u672f\u768411\u4e2a\u5206\u652f\uff0c\u4ee5\u53ca\u5f53\u524d\u7684\u8fdb\u5c55\u3002<\/span><\/p>\n


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1. \u51e0\u4f55\u66f2\u9762<\/span><\/strong><\/span><\/h2>\n<\/section>\n
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\u65b9\u7a0bSin[x*y]+Sin[y*z]+Sin[z*x]=0\u7684\u56fe\u50cf<\/span><\/p>\n


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\u9ece\u66fc\u66f2\u9762\uff0c\u4f5c\u8005\uff1aRichard Palais<\/span><\/p>\n


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\u7528\u4e8e\u89c6\u89c9\u827a\u672f\u76ee\u7684\u7684\u4efb\u610f3D\u8868\u9762\u7684\u7ed8\u56fe\u8fd8\u6ca1\u6709\u88ab\u6df1\u5165\u7814\u7a76\u3002\u4f8b\u5916\u7684\u662f\u4e00\u4e9b\u7279\u6b8a\u6570\u5b66\u66f2\u9762\u7684\u53ef\u89c6\u5316\uff0c\u7279\u522b\u662f\u5728\u5fae\u5206\u51e0\u4f55\u4e2d\u3002<\/span>\uff08\u4f8b\u5982\uff0c\u6700\u5c0f\u66f2\u9762http:\/\/virtualmathmuseum.org\/Surface\/gallery_m.html\uff09<\/span><\/p>\n


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\u5230\u4eca\u5929\u4e3a\u6b62, \u6211\u4eec\u8fd8\u5f88\u5c11\u77e5\u9053\u542b\u67093\u4e2a\u53d8\u91cf\u7684\u65b9\u7a0b\u7684\u66f2\u9762\u7684\u6a21\u6837\u3002\u542b\u6709\u8d85\u8fc73\u4e2a\u53d8\u91cf\u7684\u65b9\u7a0b\u53ef\u4ee5\u88ab\u6295\u5f71\u6216\u5206\u5272\u52303\u7ef4\u7a7a\u95f4\u4e2d\uff0c\u8fd9\u662f\u5b8c\u5168\u672a\u88ab\u63a2\u7d22\u7684\u3002<\/span><\/p>\n


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2. \u4e09\u7ef4\u6216\u4e09\u7ef4\u4ee5\u4e0a\u7684\u89c4\u5219\u7acb\u4f53<\/span><\/strong><\/span><\/h2>\n<\/section>\n
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\u5728\u4e8c\u7ef4\u4e2d\uff0c\u6211\u4eec\u6709\u6b63\u591a\u8fb9\u5f62\uff0c\u5982\u6b63\u65b9\u5f62\u3001\u4e94\u8fb9\u5f62\u548c\u516d\u8fb9\u5f62\u3002\u5728\u4e09\u7ef4\u4e2d\u5219\u79f0\u4e3a\u6b63\u591a\u9762\u4f53\u3002\u6bd4\u5982\uff0c\u7acb\u65b9\u4f53\uff0c\u516b\u9762\u4f53\uff0c\u4e8c\u5341\u9762\u4f53\u3002\u4efb\u4f55\u7ef4\u5ea6\u4e2d\u6b64\u7c7b\u5bf9\u8c61\u7684\u901a\u7528\u540d\u79f0\u90fd\u79f0\u4e3a\u591a\u9762\u4f53\u3002<\/span><\/p>\n


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\u591a\u9762\u4f53\u4f5c\u4e3a\u827a\u672f\u4e3b\u9898\u5df2\u7ecf\u88ab\u5e7f\u6cdb\u63a2\u7d22\uff0c\u53ef\u4ee5\u8ffd\u6eaf\u5230\u5e0c\u814a\u65f6\u4ee3\uff0c\u4ee5\u53ca\u4e0d\u540c\u7684\u6587\u5316\uff0c\u7ecf\u5e38\u4f5c\u4e3a\u73a9\u5177\u3001\u96d5\u5851\u3001\u7eb8\u6a21<\/span>\uff08\u6298\u7eb8\uff09<\/span>\u6216\u60ac\u6302\u88c5\u9970\u5c55\u51fa\u3002\u5728\u73b0\u4ee3\uff0c\u591a\u9762\u4f53\u4e5f\u88ab\u8868\u73b0\u4e3a\u5efa\u7b51\u5143\u7d20\u3002<\/span>\uff08\u4f8b\u5982\uff1a\u8fea\u58eb\u5c3c\u7684\u6d4b\u5730\u7ebf\u7a79\u9876\uff0c\u4f0a\u7538\u56ed\u8ba1\u5212\u7684\u534a\u7403\u4f53\u7b49\uff09<\/span><\/p>\n


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\u7eb8\u6a21\u578b\u89c4\u5219\u591a\u9762\u4f53\uff0c\u4f5c\u8005Robert Webb<\/span><\/p>\n

\uff08\u56fe\u7247\u6765\u6e90http:\/\/www.software3d.com\/FedSquare.php\uff09<\/span><\/p>\n


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\u661f\u5f62\u591a\u9762\u4f53\u5f62\u72b6\u7684\u4f0a\u65af\u5170\u706f\u3002<\/span><\/p>\n

(2013\u5e74\uff0c\u6444\u4e8e\u62c9\u65af\u7ef4\u52a0\u65af\u963f\u62c9\u4e01\u9152\u5e97\u5ea6\u5047\u6751\u5165\u53e3\u5904)<\/span><\/p>\n


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\u8ba1\u7b97\u673a\u6a21\u578b\u4f5c\u4e3a\u89c6\u89c9\u827a\u672f\u5df2\u7ecf\u975e\u5e38\u6d41\u884c\u3002\u4f46\u5927\u90e8\u5206\u90fd\u662f\u5bf9\u6570\u5b66\u5bf9\u8c61\u7684\u76f4\u63a5\u6e32\u67d3\uff0c\u51e0\u4e4e\u6ca1\u6709\u827a\u672f\u4ef7\u503c\u3002\u5e38\u89c1\u7684\u662f\u7528\u6700\u65b0\u7684\u5149\u7ebf\u8ddf\u8e2a\u8ba1\u7b97\u673a\u56fe\u5f62\u6280\u672f\u6e32\u67d3\u7684\u591a\u9762\u4f53\uff0c\u5e26\u6709\u4e00\u4e9b\u661f\u5f62\u6216\u622a\u89d2\u3002\u9ad8\u5ea6\u827a\u672f\u5316\u7684\u591a\u9762\u4f53\u7684\u7b97\u6cd5\u63a2\u7d22\u51e0\u4e4e\u4e0d\u5b58\u5728\u3002\u4e0a\u6587\u4e2dMichael Trott\u7684\u56fe\u7247\u662f\u4e00\u4e2a\u5341\u4e8c\u9762\u4f53\u5448\u73b0\u4e3a\u76f8\u8fde\u7684\u4e94\u8fb9\u5f62\u73af\uff0c\u662f\u4e00\u79cd\u57fa\u672c\u7684\u827a\u672f\u63a2\u7d22\u3002<\/span><\/p>\n


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\u5bf9\u4e8e\u4e00\u4e9b\u7b97\u6cd5\u827a\u672f\u63a2\u7d22\u7684\u4f8b\u5b50\uff0c\u6211\u4eec\u53ef\u4ee5\u7cfb\u7edf\u5730\u7814\u7a76\u5982\u4f55\u901a\u8fc7\u73af\u7684\u94fe\u63a5\u6765\u5448\u73b0\u7a7a\u95f4\u3002\u4f8b\u5982\u5bf9\u4e8e\u4e2d\u5fc3\u5bf9\u79f0\u7684\u5341\u4e8c\u9762\u4f53\uff0c\u901a\u8fc7\u4e00\u4e9b\u5de7\u5999\u7684\u8fde\u63a5\uff0c\u5c31\u53ef\u4ee5\u628a\u8fd9\u4e9b\u8fde\u63a5\u5ef6\u4f38\u5230\u65e0\u9650\u8fdc\uff0c\u4ece\u800c\u7528\u8fd9\u4e9b\u8fde\u63a5\u586b\u5145\u6574\u4e2a\u7a7a\u95f4\uff0c\u5e76\u4e14\u53ef\u4ee5\u5236\u4f5c\u5256\u89c6\u56fe\u4ee5\u4ea7\u751f\u827a\u672f\u56fe\u50cf\u3002\u6216\u8005\uff0c\u53ef\u4ee5\u5c06\u591a\u8fb9\u5f62\u7ba1\u5b50\u7684\u534a\u5f84\u505a\u5f97\u66f4\u5927\uff0c\u8fd9\u6837\u7ba1\u5b50\u7684\u6bcf\u4e2a\u591a\u8fb9\u5f62\u201c\u8fb9\u201d\u90fd\u662f\u4e00\u4e2a\u5927\u7684\u5e73\u9762\u533a\u57df\uff0c\u53ef\u4ee5\u5728\u4e0a\u9762\u523b\u753b\u8ff7\u5bab\u3002\u6216\u8005\uff0c\u53ef\u4ee5\u7528\u7403\u4f53\u4ee3\u66ff\u73af\u3002\u5341\u4e8c\u9762\u4f53\u5468\u56f4\u7684\u7403\u7684\u7740\u8272\u53ef\u4ee5\u88ab\u7cfb\u7edf\u5730\u5229\u7528\uff0c\u6240\u4ee5\u5bfc\u81f4\u4e0d\u540c\u7684\u7403\u7fa4\u7684\u5bf9\u79f0\u6027\u7ec4\u4e0d\u540c\u3002\u60f3\u8c61\u4e00\u4e2a\u7531\u4e0d\u540c\u989c\u8272\u7684\u7403\u7fa4\u7ec4\u6210\u7684\u4e09\u7ef4\u7a7a\u95f4\uff0c\u8868\u73b0\u51fa\u5fae\u5999\u7684\u4e0d\u540c\u5bf9\u79f0\u7fa4\uff0c\u5c31\u50cf\u4e00\u4e2a\u7cbe\u5fc3\u5236\u4f5c\u7684\u590d\u6742\u7684\u74f7\u7816\u4f5c\u54c1\u4e00\u6837\u3002\u6216\u8005\uff0c\u60f3\u8c61\u4e00\u4e0b\u7528\u6b63\u591a\u9762\u4f53\u5747\u5300\u5e73\u94fa\u7684\u4e09\u7ef4\u7a7a\u95f4\uff0c\u5176\u4e2d\u4e00\u4e9b\u5899\u58c1\u662f\u655e\u5f00\u7684\uff0c\u4ece\u800c\u5f62\u6210\u4e00\u4e2a\u4e09\u7ef4\u8ff7\u5bab\u3002\u5982\u679c\u505a\u5f97\u597d\uff0c\u8fd9\u5c06\u662f\u4e00\u4e2a\u6781\u597d\u7684\u5256\u89c6\u56fe\u6216\u534a\u900f\u660e\u89c6\u56fe\u3002\u5728\u7535\u5b50\u6e38\u620f\u4e2d\u5b9e\u73b0\u7684\u6b65\u884c\u7a7f\u8d8a\u4e5f\u6709\u5f88\u5927\u7684\u6f5c\u529b\u3002\u7acb\u65b9\u4f53\u7684\u56fa\u4f53\u5806\u53e0\u88ab\u79f0\u4e3aPolycube<\/span>\uff08polymino\u7684\u4e09\u7ef4\u7248\u672c\uff09<\/span>\u3002\u5b9e\u4f53\u5757\u96d5\u5851\u4e0e\u5176\u4ed6\u6b63\u591a\u9762\u4f53\u57fa\u672c\u672a\u88ab\u63a2\u7d22\u3002\u5757\u72b6\u7684\u8fde\u901a\u56db\u9762\u4f53\u7279\u522b\u6709\u8da3\u3002<\/span><\/p>\n


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

\u4ee5\u4e0b\u662f\u591a\u9762\u4f53\u7684\u4e00\u4e9b\u4f8b\u5b50\uff1a<\/span><\/p>\n


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

1.Sandor Kabai\u521b\u9020\u4e86\u8bb8\u591a\u5947\u5999\u7684\u7b97\u6cd5\u6570\u5b66\u827a\u672f\uff0c\u5176\u4e2d\u8bb8\u591a\u662f\u4ee5\u6b63\u591a\u9762\u4f53\u4e3a\u4e3b\u9898\u7684\u3002<\/span><\/p>\n

\u4ed6\u7684\u4f5c\u54c1\u8bf7\u89c1\uff1ahttp:\/\/www.kabai.hu\/<\/span><\/p>\n

2.Rob\u7684\u591a\u9762\u4f53\u6a21\u578b\uff0c\u4f5c\u8005\uff0cRobert Webb\u3002<\/span><\/p>\n

\u7f51\u5740\uff1ahttp:\/\/www.software3d.com\/MyModels.php<\/span><\/p>\n

3.Ulrich Mikloweit\u7684\u591a\u9762\u4f53\u7684\u7f8e\u4e3d\u590d\u6742\u7684\u7269\u7406\u6a21\u578b\u3002<\/span><\/p>\n

http:\/\/www.polyedergarten.de\/e_polyseite1.htm <\/span>\uff08\u5982\u679c\u80fd\u5728\u7535\u8111\u4e0a\u7528\u7b97\u6cd5\u751f\u6210\u8fd9\u4e9b\u6a21\u578b\u5c31\u66f4\u597d\u4e86\u3002\uff09<\/span><\/p>\n

4.Russell Towle\u7684\u591a\u9762\u4f53\u7814\u7a76<\/span><\/p>\n

http:\/\/xahlee.info\/math\/russel_tower.html<\/span><\/p>\n

5.\u8d85\u7a7a\u95f4\u591a\u9762\u4f53\u5256\u5206\u5668Java\u5c0f\u7a0b\u5e8f<\/span>(2000)<\/span>\uff0c\u4f5c\u8005Mark Newbold\u3002<\/span><\/p>\n

http:\/\/dogfeathers.com\/java\/hyperslice.html<\/span><\/p>\n

6\u591a\u7ef4\u7a7a\u95f4\u6052\u661f\u591a\u9762\u4f53\u5256\u5206\u5668<\/span>\uff082000\uff09<\/span>\uff0c \u4f5c\u8005\uff1aMark Newbold\u3002<\/span><\/p>\n

http:\/\/dogfeathers.com\/java\/hyperstar.html<\/span><\/p>\n


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3. \u5e73\u9762\u66f2\u7ebf<\/span><\/strong><\/span><\/h2>\n<\/section>\n
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\u201c<\/span>\u706b\u7206\u201d\uff0c\u66f2\u7ebf\u65b9\u7a0bSin[x*Sin[y]]-Cos[y*Cos[x]]=0\u7684\u56fe\u50cf<\/span><\/p>\n


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\u5bc6\u5ea6\u56fe\u7248\u672c\u3002\uff08\u4e09\u89d2\u8868\u8fbe\u5f0f\u7684\u5bc6\u5ea6\u56fe\uff09<\/span><\/p>\n


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\u4ee5\u89c6\u89c9\u827a\u672f\u4e3a\u76ee\u7684\u7684\u4e8c\u7ef4\u56fe\u5f62\u8fd8\u6ca1\u6709\u5f97\u5230\u592a\u591a\u7684\u63a2\u7d22\u3002\u8d85\u8fc74\u6b21\u7684\u4ee3\u6570\u66f2\u7ebf\u51e0\u4e4e\u6ca1\u6709\u88ab\u63a2\u7d22\u8fc7\u3002\u6211\u4eec\u53ef\u4ee5\u521b\u5efa\u4e00\u4e2a\u7a0b\u5e8f\uff0c\u7cfb\u7edf\u5730\u6309\u6b21\u6570\u6216\u7c7b\u578b\u751f\u6210\u548c\u7ed8\u5236\u6240\u6709\u53ef\u80fd\u7684\u65b9\u7a0b\uff0c\u5305\u62ec\u975e\u4ee3\u6570\u65b9\u7a0b\u3002<\/span><\/p>\n


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\u5728\u5efa\u7b51\u6216\u5ba4\u5185\u88c5\u9970\u4e2d\uff0c\u51e0\u4e4e\u6240\u6709\u7684\u88c5\u9970\u5143\u7d20\u90fd\u4ee5\u51e0\u4f55\u4e3a\u57fa\u7840\uff0c\u5176\u4e2d\u5927\u90e8\u5206\u4ee5\u66f2\u7ebf\u4e3a\u57fa\u7840\u3002\u4ee5\u66f2\u7ebf\u4e3a\u57fa\u7840\u7684\u4f20\u7edf\u827a\u672f\u7684\u4f8b\u5b50\u6709\uff1a\u7a79\u9876\u3001\u62f1\u95e8\u3001\u62f1\u9876<\/span>\uff08\u4ee5\u5706\u5f27\u4e3a\u57fa\u7840\uff09<\/span>\u3001\u6da1\u7ebf<\/span>\uff08\u5982\u67f1\u5b50\u6216\u5c0f\u63d0\u7434\u4e0a\u7684\u5377\u8f74\uff0c\u4ee5\u5404\u79cd\u87ba\u65cb\u7ebf\u4e3a\u57fa\u7840\uff09<\/span>\u3001\u82b1\u9970<\/span>\uff08\u4ee5\u79d1\u7ebd\u87ba\u7ebf\u3001\u8fde\u9501\u87ba\u7ebf\u4e3a\u57fa\u7840\uff09\u3001<\/span>\u4e07\u82b1\u5c3a<\/span>\uff08\u4ee5\u73ab\u7470\u82b1\u3001\u5185\u5916\u65cb\u8f6e\u7ebf\u4e3a\u57fa\u7840\uff09<\/span>\u3002<\/span><\/p>\n


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\u57fa\u4e8e\u66f2\u7ebf\u7684\u827a\u672f\u4f5c\u54c1\u7684\u65b9\u6cd5\u53ef\u4ee5\u5305\u62ec\uff1a\u5207\u7ebf\u3001\u5305\u7edc\u7ebf\u3001\u7126\u6563\u7ebf<\/span>\uff08\u5f26\u827a\u672f\uff09<\/span>\uff1b\u5bc6\u5207\u5706\u4e0e\u53cd\u6f14\u3001\u6e10\u5c48\u7ebf\/\u6e10\u5f00\u7ebf\u3001\u5782\u8db3\u66f2\u7ebf\u3001\u5e73\u884c\u66f2\u7ebf\u3001\u8ffd\u9010\u66f2\u7ebf\u3002<\/span><\/p>\n


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4. \u5e73\u9762\u51e0\u4f55\u4e0e\u5904\u7406<\/span><\/strong><\/span><\/h2>\n<\/section>\n
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<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n

\u200d\u200d\u200d\u200d\u200d\u200d\u200d\u200d\u200d\u200d\u200d\u200d\u200d\u200d\u200d\u200d\u200d\u200d\u200d\u200d\u200d\u200d\u200d\u200d\u200d\u200d\u200d\u200d<\/span><\/section>\n

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\u5706\u7684\u5d4c\u5957\u53cd\u6f14\uff0c\u5d4c\u5957\u7684\u5706\u53ef\u4ee5\u4ea7\u751f\u8bb8\u591a\u7f8e\u5b66\u5f62\u8c61\u3002<\/span><\/p>\n


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\u7403\u9762\u4e0a\u7684\u5706\u5728\u5e73\u9762\u4e0a\u7684\u7acb\u4f53\u6295\u5f71\u3002 \u4f5c\u8005\uff1aViktor Massalogin<\/span><\/p>\n


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\u5706\u7684\u5d4c\u5957\u53cd\u6f14\u3002 \u4f5c\u8005\uff1aWilliam Gilbert<\/span>
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\u83ab\u6bd4\u4e4c\u65af\u53d8\u6362\u751f\u6210\u7684\u5706\uff0c\u4f5c\u8005\uff1aEd Pegg Jr.<\/span><\/p>\n


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\u57fa\u4e8e\u51e0\u4f55\u8fc7\u7a0b\u7684\u4f20\u7edf\u827a\u672f\u4f5c\u54c1\u5305\u62ec\u76f8\u5207\u5706\uff08\u963f\u6ce2\u6d1b\u5c3c\u4e4c\u65af\u5706\uff09\uff0c\u5e94\u7528\u4e8e\u7f51\u683c\u6216\u89c4\u5219\u9576\u5d4c\u7684\u5404\u79cd\u5e73\u9762\u53d8\u6362<\/span>\uff08\u7ebf\u6027\u3001\u4eff\u5c04\u3001\u5c04\u5f71\u3001\u51e0\u4f55\u53cd\u6f14\u3001\u83ab\u6bd4\u65af\u53d8\u6362\u3001\u7acb\u4f53\u6295\u5f71\u2026\u2026\uff09<\/span>\u3002<\/span><\/p>\n


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\u5e26\u6709\u661f\u5f62\u56fe\u6848\u7684\u58c1\u7eb8\u56fe\u6848\uff0c\u5207\u5272\u6210\u83f1\u5f62\u8f6e\u5ed3\uff0c\u7136\u540e\u5e94\u7528\u9c7c\u773c\u900f\u955c\u53d8\u6362\u3002<\/span><\/p>\n


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\u4ee5\u4e0b\u662f\u51e0\u4e2a\u4f20\u7edf\u51e0\u4f55\u53d8\u6362\u4e86\u4f8b\u5b50\uff1a<\/span>
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5. L-\u7cfb\u7edf\uff0c\u6d77\u9f9f\u56fe\u5f62<\/span><\/strong><\/strong><\/span><\/p>\n<\/section>\n

\n

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<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n

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\u201c\u8611\u83c7\u4e09\u89d2\u5f62\u201d\uff0c\u7531\u9012\u5f52\u66ff\u6362\u751f\u6210<\/span><\/p>\n


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\u96ea\u82b1\uff0c\u7531\u9012\u5f52\u66ff\u6362\u751f\u6210\u3002\u4f5c\u8005\uff1aMichael McGuire<\/span><\/p>\n


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\u6fb3\u5927\u5229\u4e9a\u58a8\u5c14\u672c\u8054\u90a6\u5e7f\u573a<\/span><\/p>\n


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L\u7cfb\u7edf\u662f\u4e00\u4e2a\u9012\u5f52\u7b26\u53f7\u5e8f\u5217\u66ff\u6362\u7cfb\u7edf\uff0c\u6700\u521d\u662f\u4e3a\u4e86\u6a21\u62df\u690d\u7269\u751f\u957f\u800c\u8bbe\u8ba1\u7684\u3002\u5b83\u901a\u5e38\u7528\u4e8e\u901a\u8fc7\u5c06\u7b26\u53f7\u5e8f\u5217\u89e3\u91ca\u4e3a\u7ed8\u56fe\u547d\u4ee4\u6216\u51e0\u4f55\u5bf9\u8c61\u6765\u751f\u6210\u81ea\u76f8\u4f3c\u56fe\u50cf\u3002\u6d77\u9f9f\u56fe\u5f62\u6765\u81ea\u7f16\u7a0b\u8bed\u8a00Logo\uff0c\u5b83\u901a\u8fc7\u6307\u5b9a\u65b9\u5411\u548c\u7b14\u7684\u4e0a\u4e0b\u6765\u63a7\u5236\u7b14\u7684\u8fd0\u52a8\u3002<\/span><\/p>\n


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L-System\u548c\u6d77\u9f9f\u56fe\u5f62\u5728\u7a0b\u5e8f\u5458\u4e2d\u5f88\u6d41\u884c\uff0c\u7136\u800c\uff0c\u5e76\u6ca1\u6709\u5bf9\u8fd9\u4e9b\u65b9\u6cd5\u7684\u89c6\u89c9\u827a\u672f\u53ef\u80fd\u6027\u8fdb\u884c\u8ba4\u771f\u7684\u7814\u7a76\u3002\u5e38\u89c1\u7684\u6709\u6570\u5b66\u4e2d\u8457\u540d\u7684\u5e73\u9762\u586b\u5145\u66f2\u7ebf\u3001\u690d\u7269\u751f\u957f\u6a21\u578b\uff0c\u6216\u4e3a\u513f\u7ae5\u8bbe\u8ba1\u7684\u7b80\u5355\u5bf9\u79f0\u7684\u56fe\u6848\u3002\u5176\u4e2d\u5f88\u5c11\u6709\u72ec\u5177\u5320\u5fc3\u7684\u3002<\/span><\/p>\n


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\u4ee5\u4e0b\u662f\u51e0\u4e2a\u4e8c\u7ef4L\u7cfb\u7edf\uff0c\u4f5c\u8005\uff1aRobert M Dickau<\/span><\/p>\n


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\u6570\u5b66\u4e2d\u7684\u8bb8\u591a\u51fd\u6570\u90fd\u53ef\u4ee5\u7528\u7ed8\u56fe\u7684\u65b9\u5f0f\u76f4\u89c2\u5730\u8868\u73b0\u51fa\u6765\u3002\u5bf9\u4e8e\u66f2\u7ebf\u548c\u66f2\u9762\uff0c\u7ed8\u56fe\u65b9\u6848\u5f88\u7b80\u5355\u3002\u5f80\u5f80\u53ea\u662f\u5728\u4e8c\u7ef4\u7f51\u683c\u6216\u4e09\u7ef4\u7f51\u683c\u4e0a\uff0c\u7528\u6807\u8bb0\u7684\u8f74\u4f5c\u4e3a\u5750\u6807\u3002\u5982\u5411\u91cf\u503c\u51fd\u6570\u3001\u590d\u503c\u51fd\u6570\uff0c\u6570\u5b66\u5bb6\u5f00\u53d1\u4e86\u5176\u4ed6\u65b9\u6848\u6765\u53ef\u89c6\u5316\u8fd9\u4e9b\u51fd\u6570\u3002\u4ee5\u4e0b\u662f\u4e00\u4e9b\u4f8b\u5b50\u3002<\/span><\/p>\n


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\u4f5c\u8005\uff1aLinas Vepstas<\/span><\/p>\n


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\u590d\u503c\u51fd\u6570 (z-2)^2(z+1-2*i)(z+2+2*i)\/z^3 <\/span><\/p>\n

\u4f5c\u8005\uff1aHans Lundmark<\/span><\/p>\n


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\u4f20\u7edf\u7684\u51ef\u5c14\u7279\u56fe\u6848\uff0c\u4f5c\u8005\uff1aAlastair Luke\u3002<\/span><\/p>\n


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\u7740\u8272\u662f\u4e3a\u4e86\u4fbf\u4e8e\u89c2\u5bdf\u800c\u52a0\u4e0a\u7684\u3002\u4e8b\u5b9e\u4e0a\uff0c\u4e2d\u592e\u7684\u5341\u5b57\u67b6\u53ca\u5176\u5706\u5f62\u7684\u672b\u7aef\u90fd\u662f\u7531\u4e00\u6839\u7ebf\u7ec4\u6210\u7684\u3002\u6211\u53ea\u662f\u5728\u4e0d\u540c\u7684\u90e8\u5206\u7528\u4e86\u4e0d\u540c\u7684\u989c\u8272\uff0c\u5426\u5219\u5c31\u662f\u5355\u4e00\u7684\u989c\u8272\u3002<\/span><\/p>\n


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\u51ef\u5c14\u7279\u7ef3\u7ed3\u56fe\u6848\u7684\u4e3b\u8981\u5438\u5f15\u529b\u5728\u4e8e\u51e0\u4f55\u8bbe\u8ba1\uff0c\u4f46\u62d3\u6251\u65b9\u9762<\/span>\uff08\u201c\u626d\u7ed3\u201d\uff09<\/span>\u5728\u6570\u5b66\u4e0a\u4e5f\u5f88\u6709\u8da3\u3002\u4eba\u4eec\u53ef\u4ee5\u7814\u7a76\u4f20\u7edf\u7684\u51ef\u5c14\u7279\u7ef3\u7ed3\u8bbe\u8ba1\uff0c\u770b\u770b\u5b83\u4eec\u662f\u771f\u7684\u7ed3\uff0c\u8fd8\u662f\u591a\u5c11\u80a1\u7684\u7ebf\uff0c\u4ee5\u53ca\u4ed6\u4eec\u662f\u5982\u4f55\u6253\u7ed3\u7684\u3002\u6211\u4e0d\u77e5\u9053\u8fd9\u4e00\u70b9\u6709\u6ca1\u6709\u4eba\u7814\u7a76\u8fc7\u3002\u5bf9\u7b97\u6cd5\u7ed3\/\u7f16\u7ec7\u56fe\u6848\u4ee3\u7684\u7cfb\u7edf\u7814\u7a76\u5f88\u5c11\u3002<\/span>\uff08B Grunbaum\u548cG C Shephard\u5bf9\u7f16\u7ec7\u8fdb\u884c\u8fc7\u7cfb\u7edf\u7684\u6570\u5b66\u7814\u7a76\uff09<\/span>\u3002<\/span><\/p>\n


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\uff08Islamic Designs for artists and craftspeople\uff09\uff0cEva Wilson\u8457<\/span><\/p>\n

\uff08\u6d82\u8272\u4ee5\u4fbf\u663e\u793a\u7f16\u5236\u7eb9\u8def\uff09<\/span>
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\u4e00\u4e2a\u67f3\u6761\u7f16\u7ec7\u56fe\u6848\uff0c\u901a\u5e38\u89c1\u4e8e\u4e9a\u6d32\u7684\u85e4\u6905\u4e0a\u3002<\/span><\/p>\n


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\u5bf9\u4e8e\u5e73\u9762\u56fe\u6848\uff0c\u4ece\u4e0a\u4e2a\u4e16\u7eaa\u5f00\u59cb\u5c31\u77e5\u9053\u670917\u79cd\u5bf9\u79f0\u6027\u3002<\/span>\uff08\u8bf7\u53c2\u8003Branko Gr\u00fcnbaum\u7b49\u4eba\u7684\u8bba\u6587\uff0cSymmetry in Moorish and Other Ornaments\uff0c1986\uff09<\/span>\u5e76\u4e0d\u662f\u6240\u6709\u7684\u7c7b\u578b\u90fd\u80fd\u5728\u963f\u5c14\u7f55\u5e03\u62c9\u5bab\u4e2d\u627e\u5230\uff0c\u8fd9\u4e0e\u5927\u4f17\u7684\u770b\u6cd5\u76f8\u53cd\u3002\u4f7f\u5728\u4eca\u5929\uff0c\u5bf9\u9576\u5d4c\u56fe\u6848\u7684\u6570\u5b66\u7406\u89e3\u4e5f\u76f8\u5bf9\u8f83\u5dee\u3002\u5b83\u57fa\u672c\u4e0a\u662f\u4e00\u4e2a\u672a\u88ab\u63a2\u7d22\u7684\u9886\u57df\u3002\u5bf9\u7f16\u7ec7\u7684\u6570\u5b66\u5206\u6790\u51e0\u4e4e\u5b8c\u5168\u6ca1\u6709\u63a5\u89e6\u8fc7\u3002<\/span>\uff08\u7f16\u7ec7\uff0c\u4f5c\u4e3a\u51ef\u5c14\u7279\u7ef3\u7ed3\u548c\u4f0a\u65af\u5170\u56fe\u6848\u7684\u6570\u5b66\u5185\u5bb9\u3002\u5728\u62d3\u6251\u7ed3\u6784\u4e0a\uff0c\u5b83\u53ef\u4ee5\u88ab\u8ba4\u4e3a\u662f\u626d\u7ed3\u548c\u8fab\u5b50\uff0c\u4e5f\u53ef\u4ee5\u770b\u4f5c\u662f\u5177\u6709\u51e0\u4f55\u5e03\u5c40\u7684\u5e26\u6709\u6807\u8bb0\u8282\u70b9\u548c\u8fb9\u7684\u67d0\u79cd\u5747\u5300\u7684\u683c\u5b50\u7f51\u7edc\u3002\uff09<\/span><\/p>\n


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\u5f6d\u7f57\u65af\u9576\u5d4c<\/span><\/p>\n


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\u5f6d\u7f57\u65af\u9576\u5d4c\u662f\u4e00\u79cd\u975e\u5468\u671f\u9576\u5d4c\u3002\u5f6d\u7f57\u65af\u9576\u5d4c\u7684\u53d1\u73b0\u662f\u6570\u5b66\u548c\u6676\u4f53\u5b66\u4e0a\u7684\u4e00\u4e2a\u7a81\u7834\uff0c\u5f71\u54cd\u5f88\u5927<\/span>\uff08\u6bd4\u5982\u6750\u6599\u79d1\u5b66\uff09<\/span>\u3002\u975e\u5468\u671f\u9576\u5d4c\u7684\u7f8e\u611f\u5728\u4e8e\u5176\u6709\u5e8f\u6027\u662f\u5fae\u5999\u7684\u3002\u8fd9\u79cd\u7c7b\u578b\u7684\u7f8e\u5728\u8fc7\u53bb\u672a\u66fe\u89c1\u5230\u3002<\/span><\/p>\n


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\u4e00\u79cd\u9576\u5d4c\u56fe\u6848\uff0c\u4f5c\u8005\uff1aOlaf Delgado Friedrichs<\/span><\/p>\n


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\u53cc\u66f2\u9762\u9576\u5d4c\uff0c\u4f5c\u8005\uff1ahsaka<\/span><\/p>\n


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\u53cc\u66f2\u9762\u534a\u89c4\u5219\u9576\u5d4c<\/span><\/p>\n


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\u51e0\u4f55\u6846\u67b6\u4e2d\u7684\u7ef3\u7ed3\uff0c<\/span><\/p>\n

http:\/\/knotplot.com\/<\/span><\/p>\n


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8. IFS\uff08\u8fed\u4ee3\u51fd\u6570\u7cfb\u7edf\uff09\u5206\u5f62<\/span><\/strong><\/span><\/h2>\n<\/section>\n
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\u5bfb\u6839\u7b97\u6cd5\u56fe\u3002\u725b\u987f\u5206\u5f62\u3002\u4f5c\u8005\uff1aBen Haller<\/span><\/p>\n


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\u8fed\u4ee3\u8fc7\u7a0b\u7684\u56fe\uff0c\u4f5c\u8005\uff1aBen Haller<\/span><\/p>\n


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\u975e\u6b27\u51e0\u4f55\u5b66\u3001\u9ad8\u7ef4\u51e0\u4f55\u5b66\u3001\u62d3\u6251\u5b66\u5728\u4e16\u754c\u4e0a\u53ea\u6709\u5c11\u6570\u6570\u5b66\u5bb6\u7406\u89e3\u3002<\/span>\uff08\u4e5f\u8bb8\u6709\u51e0\u5343\u4eba\uff0c\u5982\u679c\u662f\u4e13\u4e1a\u6570\u5b66\u9886\u57df\u7684\u4eba\u58eb\uff0c\u53ef\u80fd\u66f4\u5c11\u3002\uff09<\/span>\u56e0\u6b64\uff0c\u901a\u8fc7\u5bf9\u5b83\u4eec\u7684\u7406\u89e3\u6765\u8fdb\u884c\u827a\u672f\u521b\u4f5c\u57fa\u672c\u4e0a\u662f\u4e0d\u5b58\u5728\u7684\u3002\u672c\u9875\u6240\u8ba8\u8bba\u7684\u51e0\u4e4e\u6240\u6709\u89c2\u70b9\u90fd\u53ef\u4ee5\u5728\u66f4\u9ad8\u7ef4\u5ea6\u548c\u6216\u975e\u6b27\u51e0\u91cc\u5f97\u7a7a\u95f4\u4e2d\u8fdb\u884c\u601d\u8003\u3002\u5728\u66f4\u9ad8\u7ef4\u5ea6\u4e0a\uff0c\u6709\u4e00\u4e9b\u5168\u65b0\u7684\u6982\u5ff5\u5728\u4f4e\u7ef4\u5ea6\u4e0a\u662f\u4e0d\u5b58\u5728\u7684\u3002<\/span>\uff08\u53ef\u5b9a\u5411\u6027\u3001\u5d4c\u5165\u6027\u3001\u5404\u5411\u540c\u6027\u7b49\uff09<\/span>\u968f\u7740\u6570\u5b66\u548c\u6280\u672f\u7684\u53d1\u5c55\uff0c\u6211\u4eec\u53ef\u80fd\u4f1a\u770b\u5230\u66f4\u591a\u7684\u89c6\u89c9\u827a\u672f\u5728\u9ad8\u7ef4\u5ea6\u4e0a\u7684\u63a2\u7d22\u3002<\/span><\/p>\n


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\u4f8b\u5982\uff0c\u521b\u5efa\u9576\u5d4c\u56fe\u6848\u7684\u4e00\u4e2a\u60f3\u6cd5\u662f\u5207\u5f00\u4e00\u4e9b\u9ad8\u7ef4\u6d41\u5f62\u7684\u89c4\u5219\u7f51\u683c\u3002\u6b64\u5916\uff0c\u6211\u4eec\u53ef\u80fd\u4f1a\u95ee\uff0c\u662f\u5426\u6709\u53ef\u80fd\u901a\u8fc7\u89c6\u89c9\u5c55\u793a\u6765\u7f16\u7801\u4e00\u4e9b\u9ad8\u7ef4\u6d41\u5f62\u5c5e\u6027\u3002<\/span>\uff08\u4f8b\u5982\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5c55\u793a\u77e9\u5f62\u7f51\u683c\u7684\u524d\u540e\u56fe\u50cf\u6765\u8bf4\u660e\u53cd\u8f6c\u7684\u89d2\u5ea6\u4e0d\u53d8\u7279\u6027\u3002\u6211\u4eec\u4e5f\u53ef\u4ee5\u901a\u8fc7\u7ebf\u6027\u53d8\u6362\u548c\u4eff\u5c04\u53d8\u6362\u5e94\u7528\u5230\u7f51\u683c\u4e0a\u65f6\u7684\u6837\u5b50\u6765\u5c55\u793a\u5b83\u4eec\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u9634\u5f71\u6765\u663e\u793a\u6295\u5f71\u53d8\u6362\u548c\u5706\u9525\u622a\u9762\u7684\u7279\u6027\u3002\u60f3\u8c61\u4e00\u4e0b\u5927\u6559\u5802\u91cc\u7f8e\u4e3d\u7684\u5f69\u8272\u73bb\u7483\u3002\uff09<\/span>\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u52a8\u753b\u5c55\u793a\u540c\u80da\u6216\u8fde\u7eed\u53d8\u6362\uff0c\u5c24\u5176\u662f\u5728\u9576\u5d4c\u4e0a\u3002\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u66f2\u9762\u7684\u66f2\u7387\u7ed9\u66f2\u9762\u7740\u8272\uff0c\u6cbf\u5e38\u66f2\u7387\u7ebf\u7ed8\u5236\u7f51\u683c\u7ebf\uff0c\u5e76\u663e\u793a\u66f2\u7387\u4e0d\u53d8\u6027\uff0c\u5982\u87ba\u65cb\u66f2\u9762\uff0c\u60ac\u94fe\u66f2\u9762\u65cf\u3002<\/span><\/p>\n


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\u9ad8\u7ef4\u6b63\u591a\u9762\u4f53\u7684\u4e09\u7ef4\u5207\u5272\uff0c\u4f5c\u8005\uff1aMark Newbold<\/span><\/p>\n


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\u4e09\u7ef4\u6d41\u5f62\u7684\u53ef\u89c6\u5316\uff0c\u4f5c\u8005\uff1aJeff Weeks<\/span><\/p>\n


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10. \u8fdb\u5316\u7f16\u7a0b\uff08Evolutionary Programing\uff09<\/span><\/strong><\/span><\/h2>\n<\/section>\n
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\u7ec6\u80de\u81ea\u52a8\u673a\u7684\u4e00\u4e2a\u4f8b\u5b50\uff0c<\/span><\/p>\n

\u6458\u81ea\u300a\u4e00\u79cd\u65b0\u7684\u79d1\u5b66\u300b\uff08A New Kind of Science\uff09\uff0cS.Wolfram\u8457<\/span><\/p>\n


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\u7ec6\u80de\u81ea\u52a8\u673a\u4e5f\u53ef\u4ee5\u7528\u4e8e\u6570\u5b66\u89c6\u89c9\u827a\u672f\u3002\u4f8b\u5982\uff0cStephen Wolfram\u7684\u300a\u4e00\u79cd\u65b0\u7684\u79d1\u5b66\u300b<\/span>\uff08A New Kind of Science\uff09<\/span>\u4e00\u4e66\u4e2d\u5c31\u5305\u542b\u4e86\u8bb8\u591a\u8d4f\u5fc3\u60a6\u76ee\u7684\u7ec6\u80de\u81ea\u52a8\u673a\u56fe\u50cf\uff0c\u5c3d\u7ba1\u5e76\u4e0d\u662f\u4ee5\u89c6\u89c9\u827a\u672f\u4e3a\u660e\u786e\u76ee\u7684\u3002<\/span><\/p>\n


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\u4f8b\u5982\uff0c\u4eba\u4eec\u7ecf\u5e38\u5f15\u7528\u6d77\u8d1d\u4e0a\u7684\u56fe\u6848\u5c31\u662f\u7ec6\u80de\u81ea\u52a8\u673a\u7684\u7ed3\u679c\uff08\u4e0b\u56fe\uff09\u3002\u8fd9\u662f\u4e00\u4e2a\u5c06\u7ec6\u80de\u81ea\u52a8\u673a\u7528\u4e8e\u975e\u6570\u5b66\u827a\u672f\u7684\u4f8b\u5b50\u3002<\/span><\/p>\n


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11. \u57c3\u820d\u5c14\u7684\u6570\u5b66\u827a\u672f<\/span><\/strong><\/span><\/h2>\n<\/section>\n
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\u57c3\u820d\u5c14<\/span>\uff08M C Escher\uff0c1898-1972\uff09<\/span>\u662f\u8377\u5170\u827a\u672f\u5bb6\uff0c\u4ed6\u7684\u4f5c\u54c1\u4ee5\u6570\u5b66\u4e3b\u9898\u4e3a\u4e3b\uff0c\u5176\u4e2d\u5f88\u591a\u662f\u7eaf\u7b97\u6cd5\u7684\u827a\u672f\u3002\u4e0d\u8fc7\uff0c\u57c3\u820d\u5c14\u662f\u4e00\u4f4d\u4f20\u7edf\u827a\u672f\u5bb6\uff0c\u4ed6\u7684\u7b97\u6cd5\u827a\u672f\u662f\u624b\u5de5\u5b8c\u6210\u7684\uff0c\u5e76\u4e0d\u662f\u8ba1\u7b97\u673a\u7a0b\u5e8f\u6765\u5b8c\u6210\uff0c\u4e5f\u6ca1\u6709\u660e\u786e\u7684\u7b97\u6cd5\u89c4\u8303\u3002<\/span><\/p>\n


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\u4ece\u7b97\u6cd5\u5230\u89c6\u89c9\u56fe\u50cf\u5f88\u5bb9\u6613\uff0c\u4f46\u662f\u7ed9\u5b9a\u4e00\u4e2a\u7b97\u6cd5\u4f5c\u54c1\uff0c\u5f88\u96be\u4ee5\u7cbe\u786e\u7684\u53ef\u8fd0\u884c\u7a0b\u5e8f\u7684\u5f62\u5f0f\u63d0\u53d6\u7b97\u6cd5\u3002\u57c3\u820d\u5c14\u7684\u4ee5\u4e0b\u4e24\u5e45\u4f5c\u54c1\u8bf4\u660e\u4e86\u8fd9\u4e00\u70b9:<\/span><\/p>\n


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\u57c3\u820d\u5c14\u7684\u300a\u6f29\u6da1\u300b\u3002\u8fd9\u5e45\u753b\u4e5f\u662f\u7b97\u6cd5\u827a\u672f\u3002\u4e00\u6761\u6761\u4e00\u6a21\u4e00\u6837\u7684\u9c7c\uff0c\u7f20\u7ed5\u6210\u4e00\u4e2a\u53cc\u87ba\u65cb\u3002\u8981\u7528\u7b97\u6cd5\u751f\u6210\u8fd9\u4e2a\u56fe\u50cf\uff0c\u53ef\u4ee5\u4ece\u4e00\u53ea\u9c7c\u5f00\u59cb\uff0c\u901a\u8fc7\u53cd\u5c04\u548c\u6ed1\u79fb\u53cd\u5c04\u5f97\u5230\u4e00\u4e32\u9c7c\uff0c\u7136\u540e\u4f7f\u7528\u4e00\u4e2a\u51fd\u6570\u5c06\u6761\u5e26\u6620\u5c04\u6210\u87ba\u65cb\uff0c\u518d\u901a\u8fc7\u955c\u50cf\u5f97\u5230\u53e6\u4e00\u4e2a\u87ba\u65cb\u3002<\/span>(\u6216\u8005\u4f7f\u7528\u5c06\u6761\u5e26\u6620\u5c04\u6210\u8fd9\u6837\u7684\u53cc\u87ba\u65cb\u7684\u51fd\u6570\u3002)<\/span>\u627e\u5230\u8fd9\u4e2a\u51fd\u6570\u53ef\u80fd\u5e76\u4e0d\u5bb9\u6613\u3002\u4e5f\u8bb8\u4e00\u4e2a\u66f4\u4f18\u96c5\u4f46\u66f4\u96be\u7684\u65b9\u6cd5\u7528\u9012\u5f52\u63cf\u8ff0\u5b83\uff0c\u8fd9\u5c06\u66f4\u597d\u5730\u5904\u7406\u6bcf\u4e2a\u87ba\u65cb\u4e2d\u5fc3\u7684\u5947\u70b9\u3002<\/span><\/p>\n


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\u57c3\u820d\u5c14\u7684\u300a\u53d8\u5f62\u300b\u3002\u57fa\u4e8e\u7b97\u6cd5\u7684\u9576\u5d4c\u53d8\u5f62\u662f\u4e00\u79cd\u7279\u6b8a\u7684\u7b97\u6cd5\u6570\u5b66\u827a\u672f\u3002\u4faf\u4e16\u8fbe<\/span>\uff08Douglas Hofstadter\uff09<\/span>\u5bf9\u6b64\u9887\u6709\u7814\u7a76\u3002<\/span><\/p>\n


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\u57c3\u820d\u5c14\u7684\u53e6\u4e00\u5e45\u7b97\u6cd5\u6570\u5b66\u827a\u672f\u4f5c\u54c1\u300a\u86c7\u300b\u3002\u5b83\u7531\u4e0d\u540c\u5927\u5c0f\u7684\u76f8\u4e92\u8fde\u63a5\u7684\u5706\u5708\u7ec4\u6210\u7684\u7f16\u7ec7\uff0c\u5728\u4e00\u4e2a\u5706\u5708\u5185\u6709\u7279\u5b9a\u7684\u51e0\u4f55\u5e03\u5c40\u3002\u86c7\u7684\u5f62\u8c61\u4ec5\u4ec5\u662f\u4e3a\u827a\u672f\u54c1\u589e\u6dfb\u60c5\u8da3\u7684\u88c5\u9970\u54c1\u3002<\/span><\/p>\n

\u8981\u7528\u7b97\u6cd5\u751f\u6210\u8fd9\u4e2a\u4f5c\u54c1\uff0c\u9700\u8981\u5bf9\u626d\u7ed3\u8fdb\u884c\u7f16\u7801\u3002<\/span>\uff08\u5373\u5f53\u4e24\u4e2a\u5706\u76f8\u4ea4\u65f6\uff0c\u54ea\u4e00\u4e2a\u5728\u4e0a\u9762\u3002\uff09<\/span>\u8fd8\u9700\u8981\u5bf9\u51e0\u4f55\u5e03\u5c40\u8fdb\u884c\u7f16\u7801\uff0c\u5373\u5706\u7684\u4f4d\u7f6e\u548c\u5927\u5c0f\u3002\u6ce8\u610f\uff0c\u5706\u5728\u9760\u8fd1\u4e2d\u5fc3\u7684\u5730\u65b9\u53d8\u5c0f\uff0c\u4f46\u5728\u9760\u8fd1\u8fb9\u7f18\u7684\u5730\u65b9\u4e5f\u4f1a\u53d8\u5c0f\u3002\u8fd9\u79cd\u5927\u5c0f\u53d8\u5316\u4e0d\u662f\u7ebf\u6027\u7684\u3002\u53e6\u5916\u8bf7\u6ce8\u610f\uff0c\u5706\u5708\u67093\u79cd\u4e0d\u540c\u7684\u989c\u8272\u3002\u5f53\u5b83\u4eec\u5411\u8fb9\u7f18\u6269\u6563\u65f6\uff0c\u7740\u8272\u57fa\u672c\u4e0a\u662f\u5faa\u73af\u5f80\u590d\u7684\u3002\u53e6\u5916\uff0c\u6bcf\u4e2a\u5706\u73af\u90fd\u8584\u539a\u4e0d\u4e00\uff0c\u7a84\u7684\u4e00\u8fb9\u8981\u4e48\u671d\u5411\u4e2d\u5fc3\uff0c\u8981\u4e48\u671d\u5411\u8fb9\u7f18\u3002<\/span><\/p>\n


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\u76f8\u5173\u94fe\u63a5\u4e0e\u6587\u732e:<\/span><\/strong><\/h2>\n

\u4ee5\u4e0b\u662f\u4e00\u4e9b\u4ece\u4e8b\u7b97\u6cd5\u827a\u672f\u3001\u6570\u5b66\u827a\u672f\u6216\u5176\u827a\u672f\u4f5c\u54c1\u4e0e\u6570\u5b66\u5bc6\u5207\u76f8\u5173\u7684\u4eba\u7684\u540d\u5355:<\/span><\/strong><\/p>\n


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\u00b7Michael Trott\u4ece20\u4e16\u7eaa90\u5e74\u4ee3\u521d\u5c31\u5f00\u59cb\u7528Mathematica\u63a2\u7d22\u6570\u5b66\u827a\u672f\u3002\u8457\u6709\u300aMathematica Guidebook\u300b\uff0c\u4ed6\u7684\u4f5c\u54c1\u8bf7\u89c1http:\/\/www.mathematicaguidebooks.org\/gallery\/<\/span><\/p>\n

\u00b7Sandor Kabai\u521b\u9020\u4e86\u8bb8\u591a\u5947\u5999\u7684\u7b97\u6cd5\u6570\u5b66\u827a\u672f\u3002\u4ed6\u662f\u8fd9\u65b9\u9762\u5353\u6709\u6210\u679c\u7684\u4eba\u4e4b\u4e00\u3002\u4ed6\u7684\u4f5c\u54c1\u8bf7\u89c1 http:\/\/www.kabai.hu\/<\/span><\/p>\n

\u00b7Hop David\uff0c\u4e00\u4f4d\u521b\u4f5c\u4e86\u8bb8\u591a\u521b\u9020\u6027\u6570\u5b66\u63d2\u56fe\u7684\u4f20\u7edf\u827a\u672f\u5bb6\uff0c\u4ed6\u7684\u4f5c\u54c1\u8bf7\u89c1http:\/\/clowder.net\/hop\/index.html<\/span><\/p>\n

\u00b7Craig S Kaplan\uff0c\u4e00\u4f4d\u8ba1\u7b97\u51e0\u4f55\u4e13\u5bb6\uff0c\u505a\u4e86\u8bb8\u591a\u9576\u5d4c\u56fe\u6848\u65b9\u9762\u827a\u672f\u54c1 http:\/\/www.cgl.uwaterloo.ca\/~csk\/phd\/<\/span><\/p>\n

\u00b7\u4faf\u4e16\u8fbe\uff0c\u4ed6\u6700\u51fa\u540d\u7684\u4f5c\u54c1\u662f\u300a\u54e5\u5fb7\u5c14\u3001\u57c3\u820d\u5c14\u3001\u5df4\u8d6b\uff1a\u96c6\u5f02\u74a7\u4e4b\u5927\u6210\u300b\u3002\u4ed6\u4e00\u76f4\u5bf9\u4eba\u5de5\u667a\u80fd\u53ca\u5176\u4e0e\u827a\u672f\u7684\u5173\u7cfb\u611f\u5174\u8da3\u3002\u4ed6\u5728\u300a\u79d1\u5b66\u7f8e\u56fd\u4eba\u300b\u4e0a\u53d1\u8868\u4e86\u4e00\u7bc7\u5173\u4e8e\u9576\u5d4c\u53d8\u5f62\u7684\u6587\u7ae0\u3002\u6211\u4e0d\u77e5\u9053\u4ed6\u662f\u5426\u50cf\u8fd9\u91cc\u8ba8\u8bba\u7684\u90a3\u6837\u505a\u4e86\u5f88\u591a\u827a\u672f\u54c1\u3002<\/span><\/p>\n

\u00b7Ed Pegg Jr’s\uff0c\u6570\u5b66\u5bb6\uff0cmathpuzzle.com\u7f51\u7ad9\u7684\u521b\u5efa\u8005\u3002\u8be5\u7f51\u7ad9\u5305\u542b\u5927\u91cf\u9ad8\u8d28\u91cf\u7684\u6570\u5b66\u63d2\u56fe\u3002\u4f46\u5927\u591a\u90fd\u4e0d\u662f\u901a\u8fc7\u7f16\u7a0b\u5b8c\u6210\u7684\uff0c\u800c\u662f\u7b80\u5355\u7684\u63d2\u753b\uff0c\u4f46\u4e5f\u6709\u827a\u672f\u6027\u7684\u3002\u4f8b\u5982\u4ed6\u7684\u9576\u5d4c\u4f5c\u54c1 http:\/\/www.mathpuzzle.com\/Mitre2.html<\/span><\/p>\n


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\u00b7\u300a\u9576\u5d4c\u4e0e\u56fe\u6848\u300b\uff08Tiling and Patterns\uff09\uff0c1987\u5e74\uff0c\u4f5c\u8005 B Grunbaum \u548cG C Shephard\uff0c\u5173\u4e8e\u8fd9\u4e2a\u4e3b\u9898\u7684\u6700\u6743\u5a01\u548c\u4fe1\u606f\u6700\u4e30\u5bcc\u7684\u4f5c\u54c1\u3002<\/span><\/p>\n

\u00b7\u300a\u4e00\u79cd\u65b0\u79d1\u5b66\u300b\uff08A New Kind Of Science\uff09\uff0c2002\u5e74\uff0c\u4f5c\u8005Stephen Wolfram\uff0c\u8bb2\u8ff0\u4e86\u7ec6\u80de\u81ea\u52a8\u673a\u4e4b\u7f8e\u3002<\/span><\/p>\n

\u00b7\u300a\u8d1d\u58f3\u7684\u7b97\u6cd5\u4e4b\u7f8e\u300b\uff08The Algorithmic Beauty of Sea Shells\uff09\uff0c\u4f5c\u8005Hans Meinhardt, Przemyslaw Prusinkiewicz, Deborah R Fowler\uff0c\u8fd8\u6709\u4e00\u672c\u5173\u4e8e\u690d\u7269\u7684\u7c7b\u4f3c\u4e66\u7c4d\u300a\u690d\u7269\u7684\u7b97\u6cd5\u4e4b\u7f8e\u300b\uff08The Algorithmic Beauty of Plants\uff09\u3002<\/span><\/p>\n

\u00b7\u300a\u5bf9\u79f0\u7684\u5f62\u8c61\u300b\uff0c1990\u5e74\uff0c\u4f5c\u8005Doris Schattschneider\uff0c\u4e00\u672c\u5173\u4e8e\u57c3\u820d\u5c14\u9576\u5d4c\u4f5c\u54c1\u7684\u753b\u518c\uff0c\u975e\u5e38\u7cbe\u7f8e\u3002<\/span><\/p>\n


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\u4ee5\u4e0b\u662f\u51e0\u672c\u5173\u4e8e\u4f0a\u65af\u5170\u51e0\u4f55\u56fe\u6848\u7684\u4e66\uff1a<\/span><\/strong><\/span><\/p>\n


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\u00b7\u300a\u4ece\u4f0a\u65af\u6cd5\u7f55\u5230\u6cf0\u59ec\u9675\u7684\u4f0a\u65af\u5170\u827a\u672f\u548c\u5efa\u7b51\u300b\uff08Islamic Art and Architecture from Isfahan to Taj Mahal\uff09\uff0c2002\u5e74\uff0c\u4f5c\u8005Thames and Hudson<\/span><\/p>\n

\u00b7\u300a\u4f0a\u65af\u5170\u827a\u672f\u300b\uff08The Art of Islam \uff09\uff0c1992\u5e74\uff0c\u4f5c\u8005Nurhan Atasoy, Afif Bahnassi, Michael Rogers\uff0c\u4e3b\u8981\u662f\u5e26\u8bf4\u660e\u7684\u7167\u7247\uff0c\u5305\u62ec\u5efa\u7b51\u548c\u5899\u58c1\u88c5\u9970\u3002<\/span><\/p>\n

\u00b7\u300a\u4f0a\u65af\u5170\u7684\u8f89\u714c\uff1a\u5efa\u7b51\u3001\u88c5\u9970\u548c\u8bbe\u8ba1\u300b\uff08Splendors of Islam \u201cArchitecture, Decorations and design\u201d\uff09\uff0c2000\u5e74\uff0c\u4f5c\u8005Dominique Clevenot\uff0c Gerard Degeorge\u3002\u4e66\u4e2d\u6709\u5927\u91cf\u4f0a\u65af\u5170\u5efa\u7b51\u548c\u88c5\u9970\u7684\u7cbe\u7f8e\u7167\u7247\u3002<\/span><\/p>\n

\u00b7\u300a\u4f0a\u65af\u5170\u827a\u672f\u4e0e\u5efa\u7b511250-1800\u300b\uff08The Art and Architecture of Islam 1250 to 1800\uff09\uff0c\u4f5c\u8005Sheila S Blair, Jonathan M Bloom\u3002\u4e00\u672c\u753b\u518c\uff0c\u91cc\u9762\u6709\u5f88\u591a\u6587\u5b57\u548c\u7167\u7247\u3002<\/span><\/p>\n

\u00b7\u300a\u4f0a\u65af\u5170\u827a\u672f\u300b\uff08Islamic arts\uff09\uff0c\u4f5c\u8005Sheila S Blair, Jonathan M Bloom\u3002\u8fd9\u672c\u4e0d\u662f\u753b\u518c\uff0c\u662f\u5b66\u672f\u6027\u4e66\u7c4d\uff0c\u4ee5\u6587\u5b57\u4e3a\u4e3b\uff0c\u4e66\u4e2d\u9644\u6709\u7cbe\u7f8e\u7684\u56fe\u7247\u3002<\/span><\/p>\n

\u00b7\u300a\u4f0a\u65af\u5170\u51e0\u4f55\u56fe\u6848\u7684\u5bf9\u79f0\u6027\u300b\uff08Symmetries of Islamic Geometrical Patterns\uff09\uff0c1995\u5e74\uff0c\u4f5c\u8005Syed Jan Abas, Amer Shaker Salman\u3002\u5305\u542b\u4e86\u5927\u7ea6250\u79cd\u4f0a\u65af\u5170\u5bf9\u79f0\u56fe\u6848\u7684\u9ed1\u767d\u56fe\u6848\u3002<\/span><\/p>\n


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