{"id":24604,"date":"2016-05-12T11:14:16","date_gmt":"2016-05-12T03:14:16","guid":{"rendered":"https:\/\/case.ntu.edu.tw\/blog\/?p=24604"},"modified":"2018-08-03T14:38:57","modified_gmt":"2018-08-03T06:38:57","slug":"%e3%80%90%e6%8e%a2%e7%b4%a214-4%e3%80%91%e8%8a%b1%e8%b1%b9%e7%9a%84%e6%96%91%e7%b4%8b%e8%88%87%e6%95%b8%e5%ad%b8%e4%b8%8d%e5%be%97%e4%b8%8d%e8%aa%aa%e7%9a%84%e6%95%85%e4%ba%8b","status":"publish","type":"post","link":"https:\/\/case.ntu.edu.tw\/blog\/?p=24604","title":{"rendered":"\u3010\u63a2\u7d2215-4\u3011\u82b1\u8c79\u7684\u6591\u7d0b\u8207\u6578\u5b78\u4e0d\u5f97\u4e0d\u8aaa\u7684\u6545\u4e8b"},"content":{"rendered":"
\"\u00a9
\u00a9 Joachim S. M\u00fcller@flickr.com<\/figcaption><\/figure>\n

\u8b1b\u5e2b\uff5c<\/strong>\u4e2d\u8208\u7269\u7406\u7cfb \u5ed6\u601d\u5584\u6559\u6388
\n\u64b0\u6587\uff5c<\/strong>\u9673\u6587\u7fca<\/p>\n

\u25cf\u82b1\u8c79\u6591\u7d0b\u8ddf\u788e\u5f62<\/span>
\n<\/strong>\u82b1\u8c79\u7684\u6591\u7d0b\u662f\u600e\u9ebc\u5f62\u6210\u7684\uff1f\u4ed4\u7d30\u770b\u82b1\u8c79\u7684\u6591\u7d0b\u767c\u73fe\u5b83\u4f3c\u4e4e\u50cf\u662f\u4e4b\u524d\u4ecb\u7d39\u904e\u7684\u788e\u5f62\u3002\u5728\u554f\u82b1\u8c79\u7684\u6591\u7d0b\u662f\u4e0d\u662f\u788e\u5f62\u524d\uff0c\u9700\u8981\u5148\u4e86\u89e3\u788e\u5f62\u662f\u751a\u9ebc\uff1f\u96d6\u7136\u6578\u5b78\u4e0a\u5c0d\u788e\u5f62\u6709\u66f4\u56b4\u8b39\u7684\u5b9a\u7fa9\uff0c\u4f46\u5728\u9019\u88e1\u6211\u5011\u53ea\u8a0e\u8ad6\u788e\u5f62\u7684\u4e00\u4e9b\u7279\u6027\uff1a\u4e00\u500b\u662f\u5b83\u5728\u4e0d\u540c\u6bd4\u4f8b\u5c3a\u4e0b\u4f9d\u820a\u7dad\u6301\u8457\u5716\u5f62\u7684\u7d50\u69cb\uff0c\u4e26\u4e0d\u662f\u6beb\u7121\u898f\u5247\u7684\u51fa\u73fe\uff0c\u9019\u67d0\u7a2e\u7a0b\u5ea6\u8aaa\u660e\u4e86\u300c\u6709\u5e8f\u300d\u7684\u6982\u5ff5\uff1b\u4e8c\u662f\u5716\u5f62\u6709\u81ea\u6211\u76f8\u4f3c\u6027\u3002\u73fe\u5728\u56de\u982d\u4f86\u770b\u82b1\u8c79\u7684\u6591\u7d0b\uff0c\u767c\u73fe\u7684\u78ba\u5448\u73fe\u6709\u5e8f\u4ee5\u53ca\u81ea\u6211\u76f8\u4f3c\u7684\u7279\u6027\uff0c\u56e0\u6b64\u53ef\u4ee5\u8996\u70ba\u4e00\u7a2e\u985e\u4f3c\u788e\u5f62\u7684\u5716\u6848\u3002<\/p>\n

\u25cf\u82b1\u8c79\u6591\u7d0b\u8ddf\u6df7\u6c8c\u7cfb\u7d71<\/span>
\n<\/strong>\u53c8\u554f\uff0c\u82b1\u8c79\u6591\u7d0b\u8ddf\u6df7\u6c8c\u7684\u95dc\u4fc2\uff1f\u6df7\u6c8c\u6700\u91cd\u8981\u7684\u7279\u5fb5\u662f\u5c0d\u521d\u59cb\u689d\u4ef6\u654f\u611f\uff0c\u4e00\u958b\u59cb\u4e00\u500b\u5c0f\u5c0f\u7684\u8b8a\u5316\uff0c\u5f8c\u4f86\u9020\u6210\u7684\u5f71\u97ff\u6703\u8d8a\u4f86\u8d8a\u5927\u7121\u6cd5\u9810\u6e2c\u3002\u6df7\u6c8c\u7cfb\u7d71\u7684\u80cc\u5f8c\u662f\u4e00\u4e9b\u5fae\u5206\u65b9\u7a0b\u5f0f\uff0c\u9019\u4e9b\u5fae\u5206\u65b9\u7a0b\u5f0f\u6703\u6709\u5947\u7570\u5438\u5b50 (strange attractors)\uff0c\u50cf\u662f Lorenz attractor\uff0c\u9019\u4e9b\u5438\u5b50\u6703\u4f7f\u6574\u500b\u7cfb\u7d71\u51fa\u73fe\u4e00\u5e7e\u4f55\u5716\u50cf\u3002\u53c8\u5947\u7570\u5438\u5b50\u662f\u600e\u9ebc\u7522\u751f\u7684\uff1f\u5b83\u53ef\u4ee5\u7531\u7c21\u55ae\u7684\u5438\u5b50\u4e4b\u9593\u7684\u7af6\u722d\u7522\u751f\uff0c\u82e5\u5e73\u9762\u4e0a\u53ea\u6709\u4e00\u500b\u5438\u5b50\u7684\u8a71\u6703\u628a\u9ede\u90fd\u5438\u904e\u53bb\uff0c\u4f46\u5982\u679c\u4e00\u500b\u5e73\u9762\u4e0a\u540c\u6642\u5b58\u5728\u597d\u5e7e\u500b\u5438\u5b50\uff0c\u53c8\u6703\u767c\u751f\u751a\u9ebc\u4e8b\u5462\uff1f\u8209\u500b\u4f8b\uff0c\u50cf\u662f\u8b1d\u723e\u8cd3\u65af\u57fa\u4e09\u89d2\u5f62(Sierpinski triangle)\uff0c\u5728\u9019\u500b\u5716\u5f62\u4e0a\u6709\u4e09\u500b\u5438\u5b50\uff0c\u6240\u6709\u9ede\u6709\u7684\u6a5f\u6703\u88ab\u4e09\u500b\u9ede\u5438\u5f15\uff0c\u51fa\u73fe\u7684\u9ede\u843d\u5728\u5f8c\u4f86\u6703\u5f62\u6210\u8b1d\u723e\u8cd3\u65af\u57fa\u4e09\u89d2\u5f62\u7684\u4f4d\u7f6e\u4e0a\uff0c\u800c\u4e14\u4e0d\u6703\u91cd\u8907\uff0c\u4e00\u958b\u59cb\u5716\u5f62\u53ef\u80fd\u9084\u4e0d\u660e\u986f\uff0c\u4f46\u7b49\u5230\u51fa\u73fe\u7684\u9ede\u5920\u591a\u5f8c\uff0c\u6f38\u6f38\u7684\u6709\u81ea\u76f8\u4f3c\u6027\u7684\u4e09\u89d2\u5f62\u5011\u5c31\u6703\u51fa\u73fe\u4e86\uff0c\u9019\u4e9b\u9ede\u8df3\u52d5\u7684\u8ecc\u8de1\u7121\u6cd5\u9810\u6e2c\uff0c\u56e0\u6b64\u662f\u500b\u6df7\u6c8c\u7684\u7cfb\u7d71\u3002\u53c8\u8b1d\u723e\u8cd3\u65af\u57fa\u4e09\u89d2\u5f62\u662f\u4e00\u7a2e\u788e\u5f62\uff0c\u8ddf\u5176\u4ed6\u7684\u788e\u5f62\u4e00\u6a23\uff0c\u53ef\u4ee5\u5f9e\u5947\u7570\u5438\u5b50\u4e2d\u7522\u751f\u3002<\/p>\n

\"\u8b1d\u723e\u8cd3\u65af\u57fa\u4e09\u89d2\u5f62\"
\u8b1d\u723e\u8cd3\u65af\u57fa\u4e09\u89d2\u5f62<\/figcaption><\/figure>\n

\u25cf\u82b1\u8c79\u6591\u7d0b\u5f62\u6210\u7684\u539f\u56e0<\/span>
\n<\/strong>\u73fe\u5728\u8a0e\u8ad6\u82b1\u8c79\u7684\u6591\u7d0b\u662f\u600e\u9ebc\u5f62\u6210\u7684\uff1f\u6709\u4e00\u7a2e\u89c0\u9ede\u662f\u76ee\u7684\u8ad6\uff0c\u610f\u601d\u662f\u5b83\u7684\u5f62\u6210\u662f\u6709\u8de1\u53ef\u5faa\u7684\u539f\u56e0\uff0c\u50cf\u662f\u87ba\u65cb\u8449\u5e8f\u5f62\u6210\u7684\u539f\u56e0\uff0c\u6216\u8a31\u662f\u70ba\u4e86\u8b93\u6bcf\u500b\u8449\u7247\u90fd\u53ef\u4ee5\u7167\u5230\u5145\u8db3\u7684\u967d\u5149\u3002\u5728\u9019\u88e1\u4e0d\u5f97\u4e0d\u63d0\u4e00\u500b\u8207\u4e4b\u76f8\u95dc\u6709\u8da3\u7684\u6578\u5b78\u95dc\u4fc2\uff0c\u5148\u628a\u690d\u7269\u7531\u4e0a\u5f80\u4e0b\u770b\uff0c\u8b93\u5b83\u8b8a\u6210\u4e00\u500b\u5e73\u9762\u7684\u5716\u50cf\uff0c\u5982\u679c\u6211\u5011\u628a\u8449\u7247\u7576\u4f5c\u662f\u4e00\u500b\u9ede\uff0c\u6bcf\u500b\u9ede\u8ddf\u9ede\u4e4b\u9593\u6bd4\u8f03\uff0c\u8f03\u76f8\u8fd1\u8005\u76f8\u9023\uff0c\u4e26\u4e00\u8def\u9023\u5230\u690d\u7269\u7684\u4e2d\u5fc3\uff0c\u6703\u767c\u73fe\u6bcf\u4e00\u689d\u7dda\u90fd\u4e0d\u6703\u91cd\u758a\u3002\u8981\u600e\u9ebc\u64fa\u9019\u4e9b\u8449\u7247\u624d\u53ef\u4ee5\u9019\u6a23\u5462\uff1f\u8a66\u60f3\u5982\u679c\u662f\u6bcf\u969460\u5ea6\u64fa\u4e00\u500b\uff0c\u90a3\u64fa\u516d\u500b\u8449\u7247\u5c31\u6703\u91cd\u8907\uff0c\u6240\u4ee5\u89d2\u5ea6\u4e0d\u80fd\u64fa360\u5ea6\u7684\u56e0\u6578\uff0c\u751a\u81f3\u662f\u9078\u7121\u7406\u6578\u7576\u4f5c\u89d2\u5ea6\u3002\u5176\u4ed6\u4e5f\u6703\u5448\u73fe\u87ba\u65cb\u7dda\u7684\uff0c\u8209\u4f8b\u677e\u679c\uff0c\u677e\u679c\u53ef\u4ee5\u756b\u51fa\u5de6\u65cb\u8ddf\u53f3\u65cb\u7684\u87ba\u65cb\u7dda\uff0c\u66f4\u5de7\u7684\u662f\uff0c\u5de6\u53f3\u87ba\u65cb\u7684\u6578\u91cf\u5206\u5225\u662f8\u8ddf13\u689d\uff0c\u9019\u4ee4\u4eba\u60f3\u8d77\u8cbb\u5e03\u90a3\u897f\u6578\u5217 (Fibonacci number)\uff0c\u8cbb\u5e03\u90a3\u897f\u6578\u5217\u4e5f\u6709\u4e00\u4e9b\u6709\u8da3\u7684\u7279\u6027\uff0c\u50cf\u662f\u5982\u679c\u628a\u76f8\u9130\u5169\u6578\uff0c\u524d\u8005\u9664\u4ee5\u5f8c\u8005\u7684\u7d50\u679c\u53d6\u6975\u9650\uff0c\u6703\u5f97\u5230\u4e00\u500b\u7121\u7406\u6578\uff0c\u63db\u7b97\u6210\u89d2\u5ea6\u5c31\u6703\u662f\u9ec3\u91d1\u89d2\uff0c\u5e38\u5e38\u5169\u5169\u87ba\u65cb\u8449\u76f8\u9130\u7684\u89d2\u5ea6\u6703\u63a5\u8fd1\u9019\u500b\u89d2\u5ea6\u3002\u53e6\u4e00\u7a2e\u82b1\u8c79\u6703\u5f62\u6210\u6591\u7d0b\u7684\u89c0\u9ede\u662f\u5f9e\u9054\u723e\u6587\u51fa\u767c\uff0c\u62b1\u6301\u7684\u8ad6\u9ede\u662f\uff0c\u5929\u64c7\u7684\u57fa\u672c\u55ae\u4f4d\u662f\u57fa\u56e0\uff0c\u7136\u5f8c\u57fa\u56e0\u662f\u81ea\u79c1\u7684\uff0c\u5b83\u5011\u6703\u904b\u7528\u81ea\u79c1\u8207\u5229\u4ed6\u7684\u5404\u7a2e\u7b56\u7565\uff0c\u4f7f\u81ea\u5df2\u6210\u70ba\u6700\u5177\u7af6\u722d\u529b\u7684\u8907\u88fd\u8005\u3002<\/p>\n

\u25cf\u6591\u7d0b\u7684\u6210\u9577\u8207\u578b\u614b<\/span>
\n<\/strong>\u5728\u9019\u88e1\u4e0d\u5f97\u4e0d\u63d0\u7531\u827e\u502b\u00b7\u5716\u9748\u63d0\u51fa\uff0c\u4e26\u7531 Hans Meinhardt\u3001Alfred Gierer \u7b49\u5f8c\u4f86\u7684\u79d1\u5b78\u5bb6\u6301\u7e8c\u4fee\u6b63\u7684\u6578\u5b78\u6a21\u578b<\/p>\n

\"0512\"<\/p>\n

\u5716\u9748\u539f\u672c\u7684\u60f3\u6cd5\u985e\u4f3c\u9019\u6a23\uff1a\u4e00\u500b\u539f\u672c\u662f\u5713\u5f62\u7684\u99ac\u80da\u80ce\uff0c\u5982\u679c\u4e0d\u7d93\u904e\u53cd\u61c9\u8ddf\u64f4\u6563\uff0c\u662f\u4e0d\u6703\u5f62\u6210\u99ac\u7684\u5f62\u72c0\u7684\u3002\u4e5f\u5c31\u662f\u8aaa\u4e00\u500b\u539f\u672c\u53ef\u80fd\u662f\u5747\u52fb\u3001\u5c0d\u7a31\u7684\u7269\u9ad4\u5728\u7d93\u904e reaction-diffusion system \u5f8c\uff0c\u53ef\u4ee5\u6539\u8b8a\u7269\u9ad4\u539f\u672c\u7684\u5f62\u72c0\u3002\u5728\u9019\u500b\u6a21\u578b\u88e1\u9762\u6709\u5169\u7a2e\u4e0d\u540c\u7684\u5206\u5b50\uff0c\u7a31\u4f5c morphogens\uff0c\u5b83\u6703\u900f\u904e reaction-diffusion system \u5efa\u7acb\u8d77\u4e0d\u540c\u7684\u5316\u5b78\u68af\u5ea6(gradients)\u3002\u70ba\u4e86\u8981\u5f97\u5230\u6700\u5f8c\u53ef\u4ee5\u7a69\u5b9a\u4e00\u6bb5\u6642\u9593\u7684\u5716\u5f62\uff0c\u5fc5\u9808\u8981\u5c0d\u9019\u500b\u7cfb\u7d71\u4f5c\u5047\u8a2d\uff0c\u5047\u8a2d morphogen A \u53ef\u4ee5\u81ea\u6211\u50ac\u5316\uff0c\u6240\u4ee5A\u7522\u751f\u7684\u901f\u7387\u6703\u6b63\u6bd4\u65bcA\u73fe\u5728\u7684\u6578\u91cf\uff0c\u53c8A\u5b83\u4e5f\u6703\u4fc3\u9032\u53e6\u4e00\u500b morphogen B \u7684\u5f62\u6210\uff0cB\u7684\u529f\u80fd\u662f\u6291\u5236A\u7684\u5f62\u6210\uff0c\u56e0\u6b64\u9019\u500b\u7cfb\u7d71\u662f\u5728A\u7684\u81ea\u6211\u50ac\u5316\u8ddfB\u7684\u6291\u5236\u4e2d\u7af6\u722d\uff0c\u5982\u679c\u8981\u5f62\u6210\u4e00\u500b\u7a69\u5b9a\u7684\u5716\u5f62\uff0c\u5247B\u7684\u64f4\u6563\u901f\u5ea6\u8981\u6bd4A\u9084\u8981\u5feb\uff0c\u9019\u610f\u5473\u8457A\u7684\u81ea\u6211\u50ac\u5316\u6703\u8b93A\u5728\u67d0\u4e9b\u4f4d\u7f6e\u6578\u91cf\u662f\u4f54\u6709\u512a\u52e2\u7684\uff0c\u4f46\u5728\u9060\u96e2\u9019\u4e9b\u4f4d\u7f6e\u4e00\u4e9b\u8ddd\u96e2\u5f8c\u6703\u88abB\u7d66\u6291\u5236\uff0cB\u6709\u8f03\u5feb\u7684\u64f4\u6563\u901f\u5ea6\u78ba\u4fdd\u5728\u5c0f\u7bc4\u570d\u88e1\u4e0d\u6703\u6291\u5236A\u7684\u7522\u751f\uff0c\u56e0\u70baB\u6d88\u6563\u7684\u592a\u5feb\u4e86\u3002\u56e0\u6b64A\u8ddfB\u5728\u6574\u500b\u5716\u4e0a\u4e0d\u540c\u7684\u4f4d\u7f6e\u6709\u4e0d\u540c\u7684\u6578\u91cf\uff0c\u4f7f\u6574\u500b\u7cfb\u7d71\u4e0d\u518d\u50cf\u662f\u539f\u5148\u90a3\u6a23\u5747\u8cea\u3002\u5716\u9748\u63d0\u51fa\u7684\u6578\u5b78\u6a21\u578b\u63d0\u4f9b\u4e00\u500b\uff0c\u8a0e\u8ad6\u82b1\u8c79\u6591\u7d0b\u600e\u9ebc\u5f62\u6210\u7684\u65b9\u5411\uff0c\u5ed6\u601d\u5584\u6559\u6388\u5229\u7528\u6b64\u65b9\u7a0b\u5f0f\uff0c\u5206\u6210\u5169\u968e\u6bb5\u8a2d\u5b9a\u53c3\u6578\uff0c\u6a21\u64ec\u51fa\u8fd1\u4f3c\u82b1\u8c79\u6591\u7d0b\u5f62\u6210\u7684\u904e\u7a0b\u3002<\/p>\n

\u25cf\u7d50\u8a9e<\/span>
\n<\/strong>\u4f46\u82b1\u8c79\u6591\u7d0b\u7684\u5f62\u6210\u5c31\u662f\u9019\u6a23\u55ce\uff1f\u6240\u6709\u5f62\u72c0\u3001\u6591\u7d0b\u4e0d\u80fd\u53ea\u662f\u5f9e\u8868\u9762\u4e0a\u770b\u5230\u7684\u5c31\u53bb\u81c6\u6e2c\uff0c\u61c9\u8a72\u8981\u591a\u53bb\u4ed4\u7d30\u7814\u7a76\u80cc\u5f8c\u7684\u539f\u56e0\u662f\u751a\u9ebc\uff0c\u9054\u723e\u6587\u7684\u5929\u64c7\u8aaa\uff0c\u5f62\u5f0f\u6e90\u81ea\u529f\u80fd\u4e0a\u7684\u9700\u6c42\uff0c\u4f46\u5929\u64c7\u4e26\u4e0d\u80fd\u56de\u7b54\u300c\u5982\u4f55\u300d\u7684\u554f\u984c\uff0c\u82b1\u8c79\u6591\u7d0b\u7684\u5f62\u6210\u53ef\u80fd\u6709\u5f88\u591a\u7a2e\u7b54\u6848\uff0c\u800c\u8ddf\u7269\u7a2e\u6f14\u5316\u6709\u95dc\u7684\u57fa\u56e0\uff0c\u4e26\u4e0d\u662f\u751f\u7269\u554f\u984c\u7684\u7d42\u7d50\uff0c\u800c\u53ea\u662f\u500b\u958b\u59cb\u3002\u6700\u5f8c\uff0c\u6709\u6c92\u6709\u751a\u9ebc\u8a9e\u8a00\u53ef\u4ee5\u63cf\u8ff0\u9019\u4e9b\u5716\u5f62\u3001\u5f62\u72c0\u5462\uff1f\u6216\u8a31\u5f62\u72c0\u7684\u81ea\u7136\u8a9e\u8a00\u662f\u6578\u5b78\uff0c\u800c\u5f62\u72c0\u7684\u5f62\u6210\u6a5f\u5236\u662f\u7269\u7406\u3002<\/p>\n

\u53c3\u8003\u8cc7\u6599\uff1a<\/strong>
\n1.Nature\u2019s Patterns <\/em>\u2013 A Tapestry in Three Parts<\/em>, Philip Ball, Oxford (2009)
\n2.Two-stage Turing model for generating pigment patterns on the leopard and the jaguar, S. S. Liaw et al, Physical Review E 74<\/strong>, 011914 (2006)
\n3.Nonlinear Dynamics and Chaos, Steven H. Strogatz
\n4. \u751f\u7269\u4e16\u754c\u7684\u6578\u5b78\u904a\u6232\uff0cIan Stewart\u8457\uff0c\u8521\u4fe1\u884c\u8b6f\uff0c\u5929\u4e0b\u6587\u5316 (2000)<\/p>\n

--
\n\u672c\u6587\u6574\u7406\u81ea\uff1a105\/4\/30\u00a0<\/strong>\u7531\u5ed6\u601d\u5584\u6559\u6388\u5728\u81fa\u5927\u601d\u4eae\u9928\u570b\u969b\u6703\u8b70\u5ef3\u6240\u4e3b\u8b1b\u4e4b\u300c\u82b1\u8c79\u7684\u6591\u7d0b\u8207\u6578\u5b78\u4e0d\u5f97\u4e0d\u8aaa\u7684\u6545\u4e8b<\/a>\u300d\u6f14\u8b1b\u5167\u5bb9\u3002<\/strong><\/p>\n

 <\/p>\n

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