{"id":23015,"date":"2020-12-28T12:06:35","date_gmt":"2020-12-28T04:06:35","guid":{"rendered":"https:\/\/swarma.org\/?p=23015"},"modified":"2020-12-28T12:06:35","modified_gmt":"2020-12-28T04:06:35","slug":"%e4%bb%80%e4%b9%88%e6%98%af%e5%88%86%e5%bd%a2-%e9%9b%86%e6%99%ba%e7%99%be%e7%a7%91","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=23015","title":{"rendered":"\u4ec0\u4e48\u662f\u5206\u5f62 | \u96c6\u667a\u767e\u79d1"},"content":{"rendered":"<div class='wxsyncmain'>                                                                                                           <img class=\"rich_pages\" data-cropselx1=\"0\" data-cropselx2=\"562\" data-cropsely1=\"0\" data-cropsely2=\"316\" data-ratio=\"0.66640625\" data-s=\"300,640\"  data-type=\"jpeg\" data-w=\"1280\" style=\"height: 375px;width: 562px;box-sizing: border-box !important;overflow-wrap: break-word !important;visibility: visible !important;\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-aafc48bfcd5bf28f916e567bc737e7da.jpeg\"  \/><br \/>\u201c\u96c6\u667a\u767e\u79d1\u7cbe\u9009\u201d\u662f\u4e00\u4e2a\u957f\u671f\u4e13\u680f\uff0c\u6301\u7eed\u4e3a\u5927\u5bb6\u63a8\u9001\u590d\u6742\u6027\u79d1\u5b66\u76f8\u5173\u7684\u57fa\u672c\u6982\u5ff5\u548c\u8d44\u6e90\u4fe1\u606f\u3002\u4f5c\u4e3a\u96c6\u667a\u4ff1\u4e50\u90e8\u7684\u5f00\u6e90\u79d1\u5b66\u9879\u76ee\uff0c\u96c6\u667a\u767e\u79d1\u5e0c\u671b\u6253\u9020\u590d\u6742\u6027\u79d1\u5b66\u9886\u57df\u6700\u5168\u9762\u7684\u767e\u79d1\u5168\u4e66\uff0c\u6b22\u8fce\u5bf9\u590d\u6742\u6027\u79d1\u5b66\u611f\u5174\u8da3\u3001\u70ed\u7231\u77e5\u8bc6\u6574\u7406\u548c\u5206\u4eab\u7684\u670b\u53cb\u52a0\u5165\uff01<br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br  \/>\u672c\u6587\u662f\u5bf9\u96c6\u667a\u767e\u79d1\u4e2d\u201c\u5206\u5f62\u51e0\u4f55\u201d\u8bcd\u6761\u7684\u6458\u5f55\uff0c\u53c2\u8003\u8d44\u6599\u53ca\u76f8\u5173\u8bcd\u6761\u8bf7\u53c2\u9605\u767e\u79d1\u8bcd\u6761\u539f\u6587\u3002<\/p>\n<p>\u672c\u8bcd\u6761\u7531\u96c6\u667a\u4ff1\u4e50\u90e8\u4f17\u5305\u751f\u4ea7\uff0c\u96be\u514d\u5b58\u5728\u7eb0\u6f0f\u548c\u95ee\u9898\uff0c\u6b22\u8fce\u5927\u5bb6\u7559\u8a00\u53cd\u9988\u6216\u8005\u524d\u5f80\u5bf9\u5e94\u7684\u767e\u79d1\u8bcd\u6761\u9875\u9762\u8fdb\u884c\u4fee\u6539\uff0c\u4e00\u7ecf\u4fee\u6539\uff0c\u53ef\u4ee5\u83b7\u5f97\u5bf9\u5e94\u7684\u79ef\u5206\u5956\u52b1\u5662\uff01<\/p>\n<p>\u76ee\u5f55<br \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br \/>\u4e00\u3001\u4ec0\u4e48\u662f\u5206\u5f62<br \/>\u4e8c\u3001\u5f15\u8a00<br \/>\u4e09\u3001\u5386\u53f2<br \/>\u56db\u3001\u5b9a\u4e49\u548c\u76f8\u5173\u7279\u5f81<br \/>\u4e94\u3001\u751f\u6210\u5206\u5f62\u7684\u5e38\u7528\u6280\u672f<br \/>\u516d\u3001\u6a21\u62df\u5206\u5f62<br \/>\u4e03\u3001\u5177\u6709\u5206\u5f62\u7279\u5f81\u7684\u81ea\u7136\u73b0\u8c61<br \/>\u516b\u3001\u7531\u5206\u5f62\u800c\u8bde\u751f\u7684\u521b\u9020\u6027\u4f5c\u54c1<br \/>\u4e5d\u3001\u5728\u79d1\u6280\u4e0a\u7684\u5e94\u7528<br \/>\u5341\u3001\u8457\u540d\u5b66\u8005\u7b80\u4ecb<br \/>\u5341\u4e00\u3001\u76f8\u5173\u63a8\u8350<br \/>\u5341\u4e8c\u3001\u96c6\u667a\u767e\u79d1\u8bcd\u6761\u5fd7\u613f\u8005\u62db\u52df<br \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><\/p>\n<p><img class=\"rich_pages js_insertlocalimg\" data-cropselx1=\"0\" data-cropselx2=\"562\" data-cropsely1=\"0\" data-cropsely2=\"312\" data-ratio=\"0.5555555555555556\" data-s=\"300,640\"  data-type=\"jpeg\" data-w=\"900\" style=\"letter-spacing: 0.544px;width: 562px;height: 312px;\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-7e32befe563119d29aeff0aab145766b.jpeg\"  \/>\u5206\u5f62\u51e0\u4f55\uff1ahttps:\/\/wiki.swarma.org\/index.php?title=\u5206\u5f62\u51e0\u4f55_Fractal<\/p>\n<p><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><\/p>\n<p><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/>1. \u4ec0\u4e48\u662f\u5206\u5f62<br \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><\/p>\n<p>\u5206\u5f62\u662f\u63cf\u8ff0\u590d\u6742\u51e0\u4f55\u5f62\u4f53\u7ed3\u6784\u7684\u4e00\u79cd\u6570\u5b66\u6982\u5ff5\u3002\u5b83\u4e00\u822c\u6307\u7ef4\u6570\u53d6\u975e\u6574\u6570\u7684\u51e0\u4f55\u5f62\u4f53\u3002\u5728\u6570\u5b66\u4e2d\uff0c\u5206\u5f62\u662f\u6b27\u51e0\u91cc\u5fb7\u7a7a\u95f4 Euclidean Space\u7684\u4e00\u4e2a\u5b50\u96c6\uff0c\u5176\u5206\u5f62\u7ef4\u6570\u7684\u6570\u503c\u8fdc\u8fdc\u5927\u4e8e\u5207\u8d6b-\u52d2\u8d1d\u683c\u7ef4\u6570 Topological Dimension\uff08\u4e5f\u79f0\u8986\u76d6\u7ef4\u6570\uff09\u3002\u7ef4\u6570\u4e00\u822c\u662f\u6307\u786e\u5b9a\u6574\u4e2a\u56fe\u5f62\u4e2d\u70b9\u7684\u4f4d\u7f6e\u6240\u9700\u8981\u7684\u5750\u6807\uff08\u6216\u53c2\u6570\uff09\u7684\u4e2a\u6570\u3002<\/p>\n<p>\u5206\u5f62\u5728\u4e0d\u540c\u7684\u5c3a\u5ea6\u4e0a\u770b\u8d77\u6765\u662f\u76f8\u4f3c\u7684\uff0c\u5c31\u50cf\u66fc\u5fb7\u5e03\u6d1b\u7279\u96c6 Mandelbrot set\u7684\u8fde\u7eed\u653e\u5927\u4e00\u6837\uff0c\u56e0\u6b64\uff0c\u5206\u5f62\u5728\u81ea\u7136\u754c\u4e2d\u65e0\u5904\u4e0d\u5728\u3002<\/p>\n<p><img class=\"rich_pages js_insertlocalimg\" data-ratio=\"0.75\" data-s=\"300,640\"  data-type=\"jpeg\" data-w=\"300\" style=\"\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-d0e5979d24fb77b782e014f559e61163.jpeg\"  \/><br \/>\u66fc\u5fb7\u5e03\u6d1b\u7279\u96c6<\/p>\n<p>\u968f\u7740\u7a7a\u95f4\u5c3a\u5ea6\u4e0d\u65ad\u53d8\u5c0f\uff0c\u5206\u5f62\u5728\u67d0\u79cd\u7ed3\u6784\u6216\u8fc7\u7a0b\u7684\u7279\u5f81\u5374\u90fd\u662f\u76f8\u4f3c\u7684\u3002\u8fd9\u6837\u7684\u73b0\u8c61\u6211\u4eec\u79f0\u4e4b\u4e3a\u81ea\u76f8\u4f3c\uff0c\u4e5f\u79f0\u4e3a\u6269\u5c55\u5bf9\u79f0 Expanding Symmetry\u6216\u5c55\u5f00\u5bf9\u79f0 Unfolding Symmetry\u3002<\/p>\n<p>\u5982\u679c\u8fd9\u79cd\u4fe1\u606f\u7684\u590d\u5236\u7ed3\u679c\u5728\u6bcf\u4e2a\u7eac\u5ea6\u4e0a\u90fd\u5b8c\u5168\u76f8\u540c\uff0c\u5c31\u50cf\u95e8\u683c\u6d77\u7ef5 Menger Sponge \u4e00\u6837\uff0c\u5219\u5176\u5177\u6709\u4eff\u5c04\u81ea\u76f8\u4f3c\u6027 Affine Self-similarity\u3002\u5206\u5f62\u51e0\u4f55\u662f\u62d3\u6251\u5b66\u7684\u4e00\u4e2a\u6570\u5b66\u5206\u652f\u3002<\/p>\n<p>\u5206\u5f62\u4e0e\u6709\u9650\u51e0\u4f55\u56fe\u5f62 Geometric Figures \u7684\u4e0d\u540c\u4e4b\u5904\u5728\u4e8e\u5b83\u4eec\u7684\u7f29\u653e\u65b9\u5f0f\u3002\u5bf9\u4e8e\u6709\u9650\u51e0\u4f55\u56fe\u5f62\u800c\u8a00\uff1a\u5c06\u4e00\u4e2a\u591a\u8fb9\u5f62\u7684\u8fb9\u957f\u589e\u52a0\u4e00\u500d\uff0c\u5176\u9762\u79ef\u4f1a\u53d8\u4e3a\u539f\u6765\u7684\u56db\u500d\uff0c\u4e5f\u5c31\u662f 2^2\u500d\u3002\u5176\u4e2d2\u4e3a\u65b0\u8fb9\u957f\u4e0e\u539f\u8fb9\u957f\u4e4b\u6bd4\uff0c\u6307\u65702\u4e3a\u591a\u8fb9\u5f62\u6240\u5728\u7a7a\u95f4\u7684\u7ef4\u6570 \u3002\u540c\u6837\uff0c\u5982\u679c\u4e00\u4e2a\u7403\u4f53\u7684\u534a\u5f84\u589e\u52a0\u4e00\u500d\uff0c\u90a3\u4e48\u5b83\u7684\u4f53\u79ef\u4f1a\u53d8\u4e3a\u539f\u6765\u7684\u516b\u500d\uff0c\u4e5f\u5c31\u662f2^3\u500d\u3002\u5176\u4e2d2\u4e3a\u65b0\u65e7\u534a\u5f84\u4e4b\u6bd4\uff0c\u6307\u65703\u4e3a\u7403\u4f53\u6240\u5728\u7a7a\u95f4\u7684\u7684\u7ef4\u6570\u3002&nbsp;<\/p>\n<p>\u7136\u800c\uff0c\u5982\u679c\u4f7f\u5206\u5f62\u7684\u4e00\u7ef4\u957f\u5ea6\u589e\u52a0\u4e00\u500d\uff0c\u90a3\u4e48\u5206\u5f62\u7684\u7a7a\u95f4\u5c3a\u5ea6\u5374\u4e0d\u4e00\u5b9a\u53d8\u4e3a\u539f\u6765\u7684\u6574\u6570\u500d\u3002\u8fd9\u662f\u56e0\u4e3a\u5bf9\u4e8e\u5206\u5f62,\u5982\u6d77\u5cb8\u7ebf\u3001\u79d1\u8d6b\u66f2\u7ebf\u3001\u8c22\u5c14\u5bbe\u65af\u57fa\u6d77\u7ef5\u7b49\u7684\u590d\u6742\u6027\u65e0\u6cd5\u7528\u7ef4\u6570\u7b49\u4e8e 1\u30012\u30013 \u8fd9\u6837\u7684\u6570\u503c\u6765\u63cf\u8ff0\uff0c\u7531\u6b64\u4ea7\u751f\u4e86\u4e00\u4e2a\u65b0\u7684\u6982\u5ff5\uff1a\u5206\u5f62\u7ef4\u6570\uff0c\u5b83\u901a\u5e38\u6bd4\u5206\u5f62\u7684\u62d3\u6251\u7ef4\u6570 Topological Dimension\u8fd8\u8981\u5927\u3002<\/p>\n<p><img class=\"rich_pages __bg_gif\" data-ratio=\"0.75\" data-s=\"300,640\" data-type=\"gif\" data-w=\"128\"  style=\"box-sizing: border-box !important;overflow-wrap: break-word !important;width: 257px !important;visibility: visible !important;\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-fd50ca15652bd968309198562d737160.gif\"  \/>The Mandelbrot set<\/p>\n<p>\u5206\u5f62\u7ef4\u6570\u662f\u63cf\u8ff0\u5206\u5f62\u6700\u4e3b\u8981\u7684\u53c2\u91cf\uff0c\u5b83\u7684\u8ba1\u7b97\u516c\u5f0f\u4e3a\uff1a<br \/><img class=\"rich_pages\" data-ratio=\"0.19733333333333333\" data-s=\"300,640\"  data-type=\"png\" data-w=\"375\" style=\"width: 258px;height: 51px;\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-f5ce27c4b6be934ebb437137319de76e.png\"  \/>\u5f0f\u4e2d<img class=\"rich_pages\" data-croporisrc=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/wibWV1DB7tWLL1cEf8puFUQY8xeRzkbAdlC0tFEJJufMDY7popj87ErXB614RSwZvxgaRicnnvrI61iak5vD2P2rA\/640?wx_fmt=png\" data-cropx1=\"325.5813953488372\" data-cropx2=\"344.4767441860465\" data-cropy1=\"14.534883720930232\" data-cropy2=\"52.325581395348834\" data-ratio=\"2\" data-s=\"300,640\"  data-type=\"jpeg\" data-w=\"19\" style=\"height: 26px;text-align: center;white-space: normal;width: 13px;\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-f4aebb9b58a7568c14c7c93bb67e36dc.jpeg\"  \/>\u662f\u5c0f\u7acb\u65b9\u4f53\u4e00\u8fb9\u7684\u957f\u5ea6\uff0c<img class=\"rich_pages\" data-croporisrc=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/wibWV1DB7tWLL1cEf8puFUQY8xeRzkbAdlC0tFEJJufMDY7popj87ErXB614RSwZvxgaRicnnvrI61iak5vD2P2rA\/640?wx_fmt=png\" data-cropx1=\"162.7906976744186\" data-cropx2=\"225.2906976744186\" data-cropy1=\"8.720930232558139\" data-cropy2=\"66.86046511627907\" data-ratio=\"0.9206349206349206\" data-s=\"300,640\"  data-type=\"jpeg\" data-w=\"63\" style=\"height: 30px;text-align: center;white-space: normal;width: 33px;\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-9ebd5a4014b6f64dc76c2f59cfdbd026.jpeg\"  \/>\u662f\u7528\u6b64\u5c0f\u7acb\u65b9\u4f53\u8986\u76d6\u88ab\u6d4b\u5f62\u4f53\u6240\u5f97\u7684\u6570\u76ee\uff0c\u5206\u5f62\u7ef4\u6570\u662f\u901a\u8fc7\u7528\u8fb9\u957f\u4e3a<img class=\"rich_pages\" data-croporisrc=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/wibWV1DB7tWLL1cEf8puFUQY8xeRzkbAdlC0tFEJJufMDY7popj87ErXB614RSwZvxgaRicnnvrI61iak5vD2P2rA\/640?wx_fmt=png\" data-cropx1=\"325.5813953488372\" data-cropx2=\"344.4767441860465\" data-cropy1=\"14.534883720930232\" data-cropy2=\"52.325581395348834\" data-ratio=\"2\" data-s=\"300,640\"  data-type=\"jpeg\" data-w=\"19\" style=\"height: 26px;font-size: 15px;white-space: normal;text-align: center;width: 13px;\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-f4aebb9b58a7568c14c7c93bb67e36dc.jpeg\"  \/>\u7684\u5c0f\u7acb\u65b9\u4f53\u8986\u76d6\u88ab\u6d4b\u5f62\u4f53\u6765\u786e\u5b9a\u5f62\u4f53\u7684\u7ef4\u6570\u6765\u8fdb\u884c\u8ba1\u7b97\u7684\u3002<\/p>\n<p>\u5206\u6790\u5b66\u4e0a\uff0c\u4f5c\u4e3a\u4e00\u4e2a\u6570\u5b66\u51fd\u6570\uff0c\u5206\u5f62\u901a\u5e38\u662f\u5904\u5904\u4e0d\u53ef\u5fae\u7684\u3002\u65e0\u7a77\u5206\u5f62\u66f2\u7ebf\u53ef\u4ee5\u7406\u89e3\u4e3a\u4e00\u6761\u4e00\u7ef4\u7684\u66f2\u7ebf\u5728\u7a7a\u95f4\u4e2d\u7ed5\u884c\uff0c\u4e0e\u666e\u901a\u7684\u66f2\u7ebf\u4e0d\u540c\uff0c\u5b83\u7684\u62d3\u6251\u7ef4\u6570\u4ecd\u7136\u662f 1\uff0c\u4f46\u7531\u4e8e\u5206\u5f62\u7ef4\u6570\u5927\u4e8e1\uff0c\u8fd9\u4f7f\u5f97\u5b83\u4e5f\u6709\u7c7b\u4f3c\u66f2\u9762\u7684\u6027\u8d28\u3002<\/p>\n<p>\u6211\u4eec\u53ef\u4ee5\u4ece\u8fd9\u4e9b\u5e74\u6765\u6b63\u5f0f\u53d1\u8868\u7684\u6587\u732e\u4e2d\u8ffd\u8e2a\u5173\u4e8e\u5206\u5f62\u6982\u5ff5\u7684\u53d1\u5c55\u53f2\u3002\u4ece 17 \u4e16\u7eaa\u6709\u4e86\u9012\u5f52\u7684\u6982\u5ff5\u5f00\u59cb\uff0c\u523019\u4e16\u7eaa\u4f2f\u7eb3\u5fb7\u00b7\u6ce2\u5c14\u67e5\u8bfa Bernard Bolzano\u3001\u6ce2\u6069\u54c8\u5fb7\u00b7\u9ece\u66fc Bernhard Riemann\u548c\u5361\u5c14\u00b7\u9b4f\u5c14\u65af\u7279\u62c9\u65af Karl Weierstrass\u5bf9\u8fde\u7eed\u4e0d\u53ef\u5fae\u51fd\u6570\u5f00\u521b\u6027\u7684\u7814\u7a76\uff0c\u8fd9\u4e9b\u4e25\u8c28\u7684\u6570\u5b66\u6982\u5ff5\u63a8\u52a8\u7740\u5206\u5f62\u7684\u53d1\u5c55\u3002\u968f\u7740\u8ba1\u7b97\u673a\u5efa\u6a21\u6280\u672f\u7684\u98de\u901f\u53d1\u5c55\u548c\u5b66\u754c\u7684\u7814\u7a76\u5174\u8da3\u65e5\u76ca\u6d53\u539a\uff0c\u5206\u5f62\u8fd9\u4e2a\u8bcd\u572820\u4e16\u7eaa\u88ab\u521b\u9020\u51fa\u6765\u3002<\/p>\n<p>1975 \u5e74\u4f2f\u52aa\u00b7\u74e6\u66fc\u5fb7\u5e03\u6d1b\u7279 Beno\u00eet B. Mandelbrot\u9996\u6b21\u63d0\u51fa\u201c\u5206\u5f62 Fractal\u201d\u8fd9\u4e2a\u672f\u8bed\u3002\u636e\u66fc\u5fb7\u5e03\u6d1b\u7279\u81ea\u8ff0\uff0cFractal\u4e00\u8bcd\u662f1975\u5e74\u590f\u5929\u7684\u4e00\u4e2a\u5bc2\u9759\u591c\u665a\uff0c\u4ed6\u5728\u51a5\u601d\u82e6\u60f3\u4e4b\u4f59\u5076\u7ffb\u4ed6\u513f\u5b50\u7684\u62c9\u4e01\u6587\u5b57\u5178\u65f6\u7a81\u7136\u60f3\u5230\u7684\u3002\u6b64\u8bcd\u6e90\u4e8e\u62c9\u4e01\u6587\u5f62\u5bb9\u8bcd\u201cFractus\u201d\uff0c\u5bf9\u5e94\u7684\u62c9\u4e01\u6587\u52a8\u8bcd\u662f\u201cFrangere\u201d\uff08\u201c\u7834\u788e\u201d\u3001\u201c\u4ea7\u751f\u65e0\u89c4\u5219\u788e\u7247\u201d\uff09\u3002\u6b64\u5916\u4e0e\u82f1\u6587\u7684\u201cFraction\u201d\uff08\u201c\u788e\u7247\u201d\u3001\u201c\u5206\u6570\u201d\uff09\u53ca\u201cFragment\u201d\uff08\u201c\u788e\u7247\u201d\uff09\u5177\u6709\u76f8\u540c\u7684\u8bcd\u6839\u3002<\/p>\n<p>\u572870\u5e74\u4ee3\u4e2d\u671f\u4ee5\u524d\uff0c\u66fc\u5fb7\u5e03\u6d1b\u7279\u6559\u6388\u4e00\u76f4\u4f7f\u7528\u82f1\u6587\u201cFractional\u201d\u4e00\u8bcd\u6765\u8868\u793a\u4ed6\u7684\u5206\u5f62\u601d\u60f3\u3002\u56e0\u6b64\uff0c\u53d6\u62c9\u4e01\u8bcd\u4e4b\u5934\uff0c\u64b7\u82f1\u6587\u4e4b\u5c3e\u7684\u201cFractal\u201d\uff0c\u672c\u610f\u662f\u4e0d\u89c4\u5219\u7684\u3001\u7834\u788e\u7684\u3001\u5206\u6570\u7684\u3002\u66fc\u5fb7\u5e03\u6d1b\u7279\u662f\u60f3\u7528\u6b64\u8bcd\u6765\u63cf\u8ff0\u81ea\u7136\u754c\u4e2d\u4f20\u7edf\u6b27\u51e0\u91cc\u5fb7\u51e0\u4f55\u5b66\u6240\u4e0d\u80fd\u63cf\u8ff0\u7684\u4e00\u5927\u7c7b\u590d\u6742\u65e0\u89c4\u5219\u7684\u51e0\u4f55\u5bf9\u8c61\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u5f2f\u5f2f\u66f2\u66f2\u7684\u6d77\u5cb8\u7ebf\u3001\u8d77\u4f0f\u4e0d\u5e73\u7684\u5c71\u8109\u3001\u7c97\u7cd9\u7684\u65ad\u9762\uff0c\u53d8\u5e7b\u65e0\u5e38\u7684\u6d6e\u4e91\u3001\u4e5d\u66f2\u56de\u80a0\u7684\u6cb3\u6d41\u3001\u7eb5\u6a2a\u4ea4\u9519\u7684\u8840\u7ba1\u3001\u4ee4\u4eba\u773c\u82b1\u7f2d\u4e71\u7684\u6ee1\u5929\u7e41\u661f\u7b49\u3002\u5b83\u4eec\u7684\u7279\u70b9\u90fd\u662f\u6781\u4e0d\u89c4\u5219\u6216\u6781\u4e0d\u5149\u6ed1\u3002\u76f4\u89c2\u800c\u7c97\u7565\u5730\u8bf4\uff0c\u8fd9\u4e9b\u5bf9\u8c61\u90fd\u662f\u5206\u5f62\u3002\u4e4b\u540e\uff0c\u66fc\u5fb7\u5e03\u6d1b\u7279\u5c06\u5206\u5f62\u7684\u6982\u5ff5\u4ece\u7406\u8bba\u4e0a\u7684\u5206\u5f62\u7ef4\u6570\u62d3\u5c55\u5230\u81ea\u7136\u754c\u4e2d\u7684\u51e0\u4f55\u56fe\u5f62\u3002<\/p>\n<p>\u5728\u6570\u5b66\u4e2d\uff0c\u5206\u5f62\u7684\u751f\u6210\u662f\u57fa\u4e8e\u4e00\u4e2a\u4e0d\u65ad\u8fed\u4ee3\u7684\u65b9\u7a0b\uff0c\u5373\u4e00\u79cd\u57fa\u4e8e\u9012\u5f52\u7684\u53cd\u9988\u7cfb\u7edf\u3002\u5206\u5f62\u6709\u51e0\u79cd\u7c7b\u578b\uff0c\u53ef\u4ee5\u5206\u522b\u4f9d\u636e\u8868\u73b0\u51fa\u7684\u7cbe\u786e\u81ea\u76f8\u4f3c\u6027\u3001\u534a\u81ea\u76f8\u4f3c\u6027\u548c\u7edf\u8ba1\u81ea\u76f8\u4f3c\u6027\u6765\u5b9a\u4e49\u3002\u5982\u4f55\u826f\u597d\u5730\u5b9a\u4e49\u5206\u5f62\u8fd9\u4e00\u6982\u5ff5\uff0c\u6743\u5a01\u5b66\u8005\u4e4b\u95f4\u4ecd\u6709\u4e89\u8bba\u3002\u66fc\u5fb7\u5e03\u6d1b\u7279\u81ea\u5df1\u5c06\u5206\u5f62\u603b\u7ed3\u4e3a\uff1a\u201c\u7f8e\u4e3d\u3001\uff08\u7814\u7a76\u8d77\u6765\uff09\u6781\u5176\u56f0\u96be\u4f46\u53c8\u975e\u5e38\u5730\u6709\u7528\uff0c\u8fd9\u5c31\u662f\u5206\u5f62\u201d\u30021982 \u5e74\u66fc\u5fb7\u5e03\u6d1b\u7279\u63d0\u51fa\u4e86\u66f4\u6b63\u5f0f\u7684\u5b9a\u4e49\uff1a\u201c\u5206\u5f62\u662f\u4e00\u79cd\u5176\u8c6a\u65af\u591a\u592b\u7ef4\u6570 Hausdorff\u2013Besicovitch Dimension \u4e25\u683c\u5927\u4e8e\u62d3\u6251\u7ef4\u6570\u7684\u96c6\u5408\u201d\u3002<\/p>\n<p><img class=\"rich_pages js_insertlocalimg\" data-ratio=\"1\" data-s=\"300,640\"  data-type=\"png\" data-w=\"300\" style=\"\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-b475ceeda39e322028aaa0f8e32b0154.png\"  \/><br \/>\u4e00\u4e2a\u62d3\u6251\u7ef4\u6570\u4e3a1\uff0c\u8c6a\u65af\u591a\u592b\u7ef4\u6570\u4e3a1.893\u7684\u8c22\u5c14\u5bbe\u65af\u57fa\u5730\u6bef\uff08\u5c42\u7ea7\u4e3a6\uff09\u7684\u5206\u5f62<\/p>\n<p>\u540e\u6765\u4ed6\u8ba4\u4e3a\u8fd9\u79cd\u5b9a\u4e49\u8fc7\u4e8e\u4e25\u683c\uff0c\u4e8e\u662f\u7b80\u5316\u5e76\u6269\u5c55\u4e86\u8fd9\u4e2a\u5b9a\u4e49\uff1a\u201c\u5206\u5f62\u662f\u7531\u4e0e\u6574\u4f53\u5728\u67d0\u4e9b\u65b9\u9762\u76f8\u4f3c\u7684\u90e8\u5206\u6784\u6210\u7684\u56fe\u5f62\u3002\u201d\u53c8\u8fc7\u4e86\u4e00\u6bb5\u65f6\u95f4\uff0c\u66fc\u5fb7\u5e03\u6d1b\u7279\u51b3\u5b9a\u4f7f\u7528\u4ee5\u4e0b\u65b9\u5f0f\u6765\u63cf\u8ff0\u5206\u5f62\uff1a\u201c&#8230;\u5728\u7814\u7a76\u548c\u4f7f\u7528\u5206\u5f62\u65f6\uff0c\u4e0d\u9700\u8981\u8fc2\u8150\u7684\u5b9a\u4e49\u3002\u7528\u5206\u5f62\u7ef4\u6570\u4f5c\u4e3a\u63cf\u8ff0\u5404\u79cd\u4e0d\u540c\u5206\u5f62\u7684\u901a\u7528\u672f\u8bed\u201d\u3002\u4eba\u4eec\u4e00\u81f4\u8ba4\u4e3a\u7406\u8bba\u4e0a\u7684\u5206\u5f62\u662f\u65e0\u9650\u8fed\u4ee3\u3001\u81ea\u76f8\u4f3c\u7684\u3001\u5177\u6709\u5206\u5f62\u7ef4\u6570\u7684\u7cbe\u5bc6\u6570\u5b66\u7ed3\u6784\uff0c\u4eba\u4eec\u521b\u9020\u4e86\u8bb8\u591a\u5206\u5f62\u56fe\u6848\u5e76\u8fdb\u884c\u4e86\u5145\u5206\u7684\u7814\u7a76\u3002\u5206\u5f62\u5e76\u4e0d\u9650\u4e8e\u51e0\u4f55\u56fe\u5f62\uff0c\u5b83\u4e5f\u53ef\u4ee5\u63cf\u8ff0\u65f6\u95f4\u5e8f\u5217\u3002<\/p>\n<p>\u867d\u7136\u5206\u5f62\u662f\u4e00\u79cd\u6570\u5b66\u6784\u9020\uff0c\u5b83\u4eec\u540c\u6837\u53ef\u4ee5\u5728\u81ea\u7136\u754c\u4e2d\u88ab\u627e\u5230\uff0c\u8fd9\u4f7f\u5f97\u5b83\u4eec\u88ab\u5212\u5165\u827a\u672f\u4f5c\u54c1\u7684\u8303\u7574\u3002\u5206\u5f62\u5728\u533b\u5b66\u3001\u571f\u529b\u5b66\u3001\u5730\u9707\u5b66\u548c\u6280\u672f\u5206\u6790\u4e2d\u90fd\u6709\u5e94\u7528\u3002\u5728\u81ea\u7136\u3001\u6280\u672f\u3001\u827a\u672f\u3001\u5efa\u7b51\u548c\u6cd5\u5f8b\u7b49\u9886\u57df\uff0c\u4eba\u4eec\u5bf9\u56fe\u5f62\u3001\u7ed3\u6784\u548c\u97f3\u9891\u4e2d\u4e0d\u540c\u7a0b\u5ea6\u81ea\u76f8\u4f3c\u7684\u5206\u5f62\u56fe\u5f62\u8fdb\u884c\u4e86\u7814\u7a76\uff0c\u5e76\u53cd\u8fc7\u6765\u5229\u7528\u5206\u5f62\u7406\u8bba\u53bb\u751f\u6210\u65b0\u7684\u56fe\u5f62\u3001\u7ed3\u6784\u548c\u97f3\u9891\u3002\u6b64\u5916\uff0c\u5206\u5f62\u548c\u6df7\u6c8c\u7406\u8bba Chaos Theory\u5bc6\u5207\u76f8\u5173\uff0c\u56e0\u4e3a\u6df7\u6c8c\u8fc7\u7a0b\u7684\u56fe\u5f62\u5927\u591a\u6570\u90fd\u662f\u5206\u5f62\u3002<\/p>\n<p><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/>2. \u5386\u53f2<br \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><\/p>\n<p>\u548c\u6570\u5b66\u5bb6\u4eec\u76f8\u6bd4\uff0c\u5206\u5f62\u4e00\u8bcd\u5bf9\u5927\u4f17\u6765\u8bf4\u542b\u4e49\u4e0d\u5c3d\u76f8\u540c\u3002\u76f8\u5bf9\u4e8e\u6570\u5b66\u6982\u5ff5\u6765\u8bf4\uff0c\u5927\u4f17\u53ef\u80fd\u66f4\u719f\u6089\u5206\u5f62\u827a\u672f Fractal Art\u3002\u5373\u4f7f\u662f\u5bf9\u6570\u5b66\u5bb6\u6765\u8bf4\u5206\u5f62\u4e5f\u5f88\u96be\u8fdb\u884c\u4e00\u4e2a\u51c6\u786e\u7684\u5b9a\u4e49\u3002\u4f46\u5373\u4f7f\u6ca1\u6709\u591a\u5c11\u6570\u5b66\u80cc\u666f\uff0c\u4e5f\u53ef\u4ee5\u7406\u89e3\u5206\u5f62\u7684\u6838\u5fc3\u7279\u5f81\u3002<\/p>\n<p><img class=\"rich_pages js_insertlocalimg\" data-ratio=\"0.5\" data-s=\"300,640\"  data-type=\"png\" data-w=\"450\" style=\"\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-32fa32798b55403224bae76aa22b346c.png\"  \/>\u901a\u8fc7 javascript \u521b\u5efa\u4e00\u4e2a\u7b80\u5355\u7684\u5206\u5f62\u6811<\/p>\n<p>\u81ea\u76f8\u4f3c\u6027 Self-Similarity \u7684\u7279\u5f81\u5f88\u5bb9\u6613\u7406\u89e3\uff0c\u5b83\u7c7b\u4f3c\u4e8e\u7528\u955c\u5934\u6216\u5176\u5b83\u88c5\u7f6e\u653e\u5927\u56fe\u50cf\uff0c\u4ee5\u4fbf\u53d1\u73b0\u66f4\u7cbe\u7ec6\u7684\u3001\u4ee5\u524d\u770b\u4e0d\u89c1\u7684\u65b0\u7ed3\u6784\u3002\u7136\u800c\uff0c\u5982\u679c\u653e\u5927\u4e00\u4e2a\u5206\u5f62\u7684\u56fe\u50cf\uff0c\u5c31\u4e0d\u4f1a\u51fa\u73b0\u65b0\u7684\u7ec6\u8282; \u56fe\u50cf\u6ca1\u6709\u4efb\u4f55\u53d8\u5316\uff0c\u76f8\u540c\u7684\u56fe\u6848\u4e00\u904d\u904d\u5730\u91cd\u590d\u51fa\u73b0\u3002<\/p>\n<p>\u6216\u8005\u5bf9\u4e8e\u67d0\u4e9b\u5206\u5f62\u6765\u8bf4\uff0c\u51e0\u4e4e\u76f8\u540c\u7684\u56fe\u6848\u4e00\u904d\u904d\u5730\u91cd\u590d\u51fa\u73b0\u3002\u81ea\u76f8\u4f3c\u6027\u672c\u8eab\u5e76\u4e0d\u4e00\u5b9a\u8fdd\u53cd\u76f4\u89c9\u3002\u4eba\u4eec\u5728\u751f\u6d3b\u4e2d\u4e5f\u80fd\u770b\u5230\u81ea\u6211\u76f8\u4f3c\u7684\u73b0\u8c61\uff0c\u4f8b\u5982\uff1a\u4e24\u9762\u5e73\u884c\u7684\u955c\u5b50\u95f4\u7684\u65e0\u9650\u91cd\u590d\u3001\u5c71\u4e0a\u5e99\u91cc\u8001\u548c\u5c1a\u7684\u6545\u4e8b\u91cc\u7684\u5c71&#8230;&#8230;\u5206\u5f62\u7684\u4e0d\u540c\u4e4b\u5904\u5728\u4e8e\u91cd\u590d\u7684\u56fe\u6848\u4e00\u5b9a\u6709\u7740\u8be6\u5c3d\u7684\u7ec6\u8282\u3002<\/p>\n<p>\u8fd9\u79cd\u7ec6\u8282\u5316\u7684\u6982\u5ff5\u6d89\u53ca\u5230\u53e6\u4e00\u4e2a\u4e0d\u9700\u8981\u6570\u5b66\u80cc\u666f\u5c31\u53ef\u4ee5\u7406\u89e3\u7684\u7279\u5f81: 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3\uff0c\u5219\u4f1a\u4ea7\u751f9\u4e2a\u788e\u7247\u3002\u800c\u5bf9\u4e8e\u666e\u901a\u7684\u81ea\u76f8\u4f3c\u7269\u4f53\uff0c\u5176\u7ef4\u6570\u4e3an\uff0c\u5c06\u5176\u91cd\u65b0\u5e73\u94fa\u6210\u4e00\u4e2a\u4e2a\u7247\u6bb5\uff0c\u6bcf\u4e2a\u7247\u6bb5\u6309\u90fd\u7f29\u5c0f1 \/ r \u500d\uff0c\u5219\u4f1a\u4ea7\u751f rn\u4e2a\u7247\u6bb5\u3002\u73b0\u5728\uff0c\u8003\u8651\u79d1\u8d6b\u66f2\u7ebf Koch curve \uff0c \u5b83\u662f\u5f62\u6001\u4f3c\u96ea\u82b1\u7684\u4e00\u79cd\u5206\u5f62\uff0c\u5b83\u53ef\u4ee5\u901a\u8fc7\u7f29\u5c0f\u4e3a\u539f\u6765\u76841 \/ 3\u7684\u65b9\u5f0f\u8fdb\u884c\u5e73\u94fa\uff0c\u4ece\u800c\u5f62\u6210\u56db\u4e2a\u5b50\u96ea\u82b1\u66f2\u7ebf\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u901a\u8fc7\u8fdb\u884c\u4e25\u683c\u7684\u7c7b\u6bd4\uff0c\u6211\u4eec\u53ef\u4ee5\u628a\u79d1\u8d6b\u66f2\u7ebf\u7684\u201c\u7ef4\u6570\u201dD\u8ba1\u7b97\u51fa\u6765\uff0c\u5b83\u6ee1\u8db33^D=4\u3002\u8fd9\u8bf4\u660e\uff0cD\u51b3\u4e0d\u662f\u4e00\u4e2a\u6574\u6570\u3002D\u5176\u5b9e\u5c31\u662f\u6570\u5b66\u5bb6\u4eec\u6240\u8bf4\u7684\u79d1\u8d6b\u66f2\u7ebf\u7684\u5206\u5f62\u7ef4\u6570\u3002\u7531\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u51fa\u4ee5\u4e0b\u7ed3\u8bba\uff1a\u7531\u4e8e\u79d1\u8d6b\u66f2\u7ebf\u5177\u6709\u975e\u6574\u6570\u7684\u5206\u5f62\u7ef4\u6570\uff0c\u6240\u4ee5\u79d1\u8d6b\u66f2\u7ebf\u662f\u4e00\u79cd\u5206\u5f62\u3002<br \/><img class=\"rich_pages js_insertlocalimg\" data-ratio=\"1.04\" data-s=\"300,640\"  data-type=\"gif\" data-w=\"300\" style=\"\" 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style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/>3.\u5b9a\u4e49\u548c\u76f8\u5173\u7279\u5f81<br \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><\/p>\n<p>\u5206\u5f62\u7684\u5386\u53f2\u53ef\u4ee5\u4ece\u4e3b\u8981\u7406\u8bba\u7684\u7814\u7a76\u8ffd\u6eaf\u5230\u73b0\u4ee3\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u4e2d\u7684\u5e94\u7528\uff0c\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\u6709\u51e0\u4e2a\u8457\u540d\u7684\u4eba\u7269\u5bf9\u5178\u578b\u7684\u5206\u5f62\u5f62\u5f0f\u7684\u7814\u7a76\u505a\u51fa\u4e86\u8d21\u732e\u3002<\/p>\n<p>\u6839\u636e\u76ae\u79d1\u5f17 Pickover\u7684\u8bf4\u6cd5\uff1a17 \u4e16\u7eaa\u65f6\uff0c\u6570\u5b66\u5bb6\u517c\u54f2\u5b66\u5bb6\u83b1\u5e03\u5c3c\u8328 Gottfried Leibniz\u601d\u8003\u8fc7\u9012\u5f52\uff08\u53ef\u7528\u4e8e\u63cf\u8ff0\u4ee5\u81ea\u76f8\u4f3c\u65b9\u6cd5\u91cd\u590d\u4e8b\u7269\u7684\u8fc7\u7a0b\uff09\uff0c\u5206\u5f62\u7684\u6570\u5b66\u4ece\u90a3\u65f6\u5f00\u59cb\u6e10\u6e10\u5730\u6210\u5f62\uff08\u867d\u7136\u4ed6\u8bef\u8ba4\u4e3a\u53ea\u6709\u76f4\u7ebf\u4f1a\u5728\u9012\u5f52\u7684\u60c5\u51b5\u4e0b\u6709\u81ea\u76f8\u4f3c\u7684\u73b0\u8c61\uff09\u3002<\/p>\n<p>\u5728\u4ed6\u7684\u8457\u4f5c\u4e2d\uff0cGottfried Leibniz\u4f7f\u7528\u4e86\u201c\u5206\u5f62\u6307\u6570\u201d\u8fd9\u4e2a\u672f\u8bed\uff0c\u4f46\u662f\u9057\u61be\u7684\u662f\u5728\u201c\u51e0\u4f55\u201d\u5b66\u4e0a\u5f88\u591a\u6570\u5b66\u5bb6\u672a\u80fd\u63a5\u53d7\u6216\u4e86\u89e3\u8fd9\u4e00\u65b0\u6982\u5ff5\u3002\u6839\u636e\u5404\u79cd\u5386\u53f2\u8bb0\u8f7d\uff0c\u5728\u90a3\u4e4b\u540e\uff0c\u5f88\u5c11\u6709\u6570\u5b66\u5bb6\u5904\u7406\u8fd9\u4e9b\u95ee\u9898\uff0c\u5373\u4f7f\u6709\uff0c\u5904\u7406\u8fd9\u4e9b\u95ee\u9898\u7684\u7814\u7a76\u5de5\u4f5c\u4ecd\u7136\u542b\u7cca\u4e0d\u6e05\u3002\u8fd9\u4e3b\u8981\u662f\u56e0\u4e3a\u5f53\u65f6\u7684\u6570\u5b66\u5bb6\u4eec\u62b5\u5236\u8fd9\u4e9b\u964c\u751f\u7684\u65b0\u6982\u5ff5\uff08\u8fd9\u4e9b\u6982\u5ff5\u6709\u65f6\u88ab\u79f0\u4e3a\u6570\u5b66\u4e2d\u7684\u201c\u602a\u7269\u201d\uff09\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u76f4\u5230\u4e24\u4e2a\u4e16\u7eaa\u4e4b\u540e\uff0c\u5361\u5c14\u00b7\u9b4f\u5c14\u65af\u7279\u62c9\u65af Karl Weierstrass \u624d\u4e8e1872\u5e747\u670818\u65e5\u5728\u7687\u5bb6\u666e\u9c81\u58eb\u79d1\u5b66\u9662\u7ed9\u51fa\u5206\u5f62\u7684\u7b2c\u4e00\u4e2a\u5b9a\u4e49\uff1a\u5206\u5f62\u662f\u4e00\u79cd\u5177\u6709\u53cd\u76f4\u89c9\u6027\u8d28\u7684\u51fd\u6570\u56fe\u5f62\u3002\u8fd9\u79cd\u6027\u8d28\u8868\u73b0\u5728\u5b83\u5904\u5904\u8fde\u7eed\u5374\u53c8\u5904\u5904\u4e0d\u53ef\u5fae\u3002\u6b64\u5916\uff0c\u5176\u5546\u5dee\u968f\u7740\u6c42\u548c\u6307\u6570\u7684\u589e\u52a0\u800c\u4efb\u610f\u5927\u3002<\/p>\n<p>\u4e0d\u4e45\u4e4b\u540e\uff0c1883\u5e74\uff0c\u53c2\u52a0Karl Weierstrass \u8bb2\u5ea7\u7684\u5eb7\u6258\u5c14 Georg Cantor\u4e5f\u7ed9\u51fa\u4e00\u4e2a\u5177\u6709\u53cd\u76f4\u89c9\u6027\u8d28\u7684\u4f8b\u5b50\uff1a\u5b9e\u76f4\u7ebf\u4e0a\u7684\u5b50\u96c6\u2014\u2014\u5eb7\u6258\u5c14\u96c6\uff0c\u73b0\u5728\u4e5f\u88ab\u8ba4\u4e3a\u662f\u5206\u5f62\u3002\u572819\u4e16\u7eaa\u672b\uff0c\u8d39\u5229\u514b\u65af \u00b7 \u514b\u83b1\u56e0 Felix Klein \u548c\u4ea8\u5229 \u00b7 \u5e9e\u52a0\u83b1 Henri Poincar\u00e9\u4e5f\u63d0\u51fa\u4e86\u201c\u81ea\u9006\u201d\u5206\u5f62\uff08\u5206\u5f62\u7684\u4e00\u79cd\uff09\u3002<\/p>\n<p><img class=\"rich_pages\" data-ratio=\"0.5362318840579711\" data-s=\"300,640\" data-type=\"png\" data-w=\"414\"  style=\"box-sizing: border-box !important;overflow-wrap: break-word !important;width: 414px !important;visibility: visible !important;\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-0777e93aed2529e240ad9d3758832588.png\"  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br \/>\u5eb7\u6258\u5c14\u96c6\uff08Cantor set\uff09\u7684\u4e00\u90e8\u5206&nbsp;\u5f62\u4f3c\u9053\u5bb6\u7684\u5366\u56fe<\/p>\n<p>\u5206\u5f62\u53d1\u5c55\u7684\u4e00\u4e2a\u91cc\u7a0b\u7891\u5728 1904 \u5e74\uff0c\u5f53\u65f6\u6d77\u91cc\u683c\u00b7\u51af\u00b7\u79d1\u8d6b Helge Von Koch\u4e0d\u6ee1\u610f Weierstrass\u7684\u62bd\u8c61\u53c8\u57fa\u4e8e\u5206\u6790\u6982\u5ff5\u4e0a\u7684\u5b9a\u4e49\u3002\u4ed6\u6269\u5c55\u4e86Poincar\u00e9\u7684\u5b9a\u4e49\uff0c\u7ed9\u51fa\u4e86\u66f4\u52a0\u51e0\u4f55\u5316\u7684\u5b9a\u4e49\u5e76\u9644\u4e0a\u4e86\u4e00\u4e2a\u7c7b\u4f3c\u51fd\u6570\u7684\u624b\u7ed8\u56fe\u5f62\uff0c\u4e5f\u5c31\u662f\u73b0\u5728\u6240\u8bf4\u7684\u79d1\u8d6b\u96ea\u82b1\u3002<\/p>\n<p>\u53e6\u4e00\u4e2a\u91cc\u7a0b\u7891\u5728\u5341\u4e00\u5e74\u4e4b\u540e\uff0c1915\u5e74\uff0c\u74e6\u8328\u74e6\u592b\u00b7\u8c22\u5c14\u5bbe\u65af\u57fa Wac\u0142aw Sierpi\u0144ski\u6784\u9020\u51fa\u4e86\u8c22\u5c14\u5bbe\u65af\u57fa\u4e09\u89d2\u5f62\uff1b\u6b21\u5e74\uff0c\u53c8\u9020\u51fa\u4e86\u8c22\u5c14\u5bbe\u65af\u57fa\u5730\u6bef\u3002\u52301918\u5e74\uff0c\u4e24\u4f4d\u6cd5\u56fd\u6570\u5b66\u5bb6\u76ae\u57c3\u5c14 \u00b7 \u6cd5\u56fe Pierre Fatou\u548c\u52a0\u65af\u987f \u00b7 \u6731\u5229\u4e9a Gaston Julia\u901a\u8fc7\u5404\u81ea\u7684\u72ec\u7acb\u5de5\u4f5c\uff0c\u57fa\u672c\u4e0a\u540c\u65f6\u5f97\u51fa\u76f8\u540c\u7684\u7ed3\u8bba\u3002\u8be5\u7ed3\u8bba\u63cf\u8ff0\u4e86\u590d\u6570\u6620\u5c04\u4ee5\u53ca\u51fd\u6570\u8fed\u4ee3\u76f8\u5173\u5206\u5f62\u884c\u4e3a\uff0c\u5e76\u7531\u6b64\u5f15\u51fa\u4e86\u5173\u4e8e\u5947\u5f02\u5438\u5f15\u5b50(\u5373\u5438\u5f15\u6216\u6392\u65a5\u5176\u4ed6\u70b9\u7684\u70b9)\u7684\u7406\u8bba\uff0c\u8be5\u7406\u8bba\u5728\u5206\u5f62\u7814\u7a76\u4e2d\u5df2\u53d8\u5f97\u975e\u5e38\u91cd\u8981\u3002<\/p>\n<p><img class=\"rich_pages js_insertlocalimg\" data-ratio=\"1\" data-s=\"300,640\"  data-type=\"gif\" data-w=\"300\" style=\"\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-c001d9c547e17a77043f8e96a84944fe.gif\"  \/><br \/>\u5229\u7528\u5206\u5f62\u6811\u751f\u6210\u8c22\u5c14\u5bbe\u65af\u57fa\u57ab\u7247<\/p>\n<p>\u5728\u5173\u4e8e\u5947\u5f02\u5438\u5f15\u5b50 Strange Attractors\u7684\u7ed3\u8bba\u63d0\u51fa\u540e\u4e0d\u4e45\uff0c\u52301918\u5e743\u6708\uff0c\u8d39\u5229\u514b\u65af \u00b7 \u8c6a\u65af\u591a\u592b Felix Hausdorff\u6269\u5c55\u4e86\u201c\u7ef4\u6570\u201d\u7684\u5b9a\u4e49\uff0c\u8fd9\u4f7f\u5f97\u5206\u5f62\u7684\u5b9a\u4e49\u66f4\u52a0\u660e\u786e\uff0c\u4f7f\u96c6\u5408\u5177\u6709\u975e\u6574\u6570\u7ef4\u6570\u3002<\/p>\n<p>1938\u5e74\uff0c\u4fdd\u7f57\u00b7\u76ae\u57c3\u5c14\u00b7\u83b1\u7ef4 Paul L\u00e9vy\u5728\u4ed6\u7684\u8bba\u6587\u300a\u5e73\u9762\u3001\u7a7a\u95f4\u66f2\u7ebf\u548c\u7531\u4e0e\u6574\u4f53\u81ea\u76f8\u4f3c\u90e8\u4ef6\u7ec4\u6210\u7684\u66f2\u9762 Plane or Space Curves and Surfaces Consisting of Parts Similar to the Whole\u300b\u4e2d\u8fdb\u4e00\u6b65\u660e\u786e\u4e86\u81ea\u76f8\u4f3c\u66f2\u7ebf\u7684\u6982\u5ff5\uff0c\u8fd8\u5728\u6587\u4e2d\u63cf\u8ff0\u4e86\u4e00\u4e2a\u65b0\u7684\u5206\u5f62\u66f2\u7ebf\u2014\u2014\u83b1\u7ef4C\u5f62\u66f2\u7ebf\u3002<\/p>\n<p>\u4e0d\u540c\u7814\u7a76\u9886\u57df\u7684\u5b66\u8005\u90fd\u8bf4\uff1a\u5982\u679c\u6ca1\u6709\u73b0\u4ee3\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u7684\u5e2e\u52a9\uff0c\u4ec5\u51ed\u65e9\u671f\u7684\u7814\u7a76\u4eba\u5458\u901a\u8fc7\u624b\u5de5\u63cf\u7ed8\u56fe\u5f62\uff0c\u5219\u4e0d\u53ef\u80fd\u5c06\u7f8e\u4e3d\u7684\u56fe\u5f62\u8fdb\u884c\u53ef\u89c6\u5316\uff0c\u4e5f\u65e0\u6cd5\u53d1\u73b0\u5728\u56fe\u5f62\u4e2d\u6240\u8574\u542b\u7684\u4fe1\u606f\u3002(\u4f8b\u5982\uff0c Julia\u96c6\u53ea\u80fd\u901a\u8fc7\u51e0\u6b21\u8fed\u4ee3\u5c06\u56fe\u5f62\u53ef\u89c6\u5316)\u3002<\/p>\n<p><img class=\"rich_pages js_insertlocalimg\" data-ratio=\"0.75\" data-s=\"300,640\"  data-type=\"png\" data-w=\"300\" style=\"\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-41647723e8dc7d83c54fffb00a424198.png\"  \/><br \/>\u6731\u5229\u5a05\u96c6\uff0c\u4e00\u4e2a\u4e0e\u66fc\u5fb7\u5c14\u5e03\u6d1b\u96c6\u76f8\u5173\u7684\u5206\u5f62<\/p>\n<p>\u7136\u800c\uff0c\u8fd9\u79cd\u60c5\u51b5\u572820\u4e16\u7eaa60\u5e74\u4ee3\u53d1\u751f\u4e86\u6539\u53d8\uff0c\u5f53\u65f6\u66fc\u5fb7\u5e03\u6d1b\u7279\u5f00\u59cb\u7814\u7a76\u81ea\u76f8\u4f3c\uff0c\u5728\u8def\u6613\u65af\u00b7\u5f17\u83b1\u00b7\u7406\u67e5\u5fb7\u68ee Lewis Fry Richardson\u4e4b\u524d\u5de5\u4f5c\u7684\u57fa\u7840\u4e0a\uff0c\u5199\u4e0b\u4e86\u4e00\u7bc7\u8bba\u6587\u300a\u82f1\u56fd\u6d77\u5cb8\u6709\u591a\u957f\uff1f\u7edf\u8ba1\u81ea\u76f8\u4f3c\u548c\u5206\u5f62\u7ef4\u5ea6\u300b\u3002<\/p>\n<p>\u6700\u7ec8\uff0c\u57281975\u5e74\uff0c\u66fc\u5fb7\u5e03\u6d1b\u7279\u603b\u7ed3\u4e86\u6570\u767e\u5e74\u6765\u5173\u4e8e\u5206\u5f62\u7684\u601d\u60f3\u53ca\u6570\u5b66\u4e0a\u76f8\u5173\u7684\u7ed3\u8bba\uff0c\u63d0\u51fa\u4e86&#8221;\u5206\u5f62&#8221;\u4e00\u8bcd\uff0c\u5e76\u7528\u9ad8\u8d85\u7684\u8ba1\u7b97\u673a\u53ef\u89c6\u5316\u6784\u9020\u6765\u8bf4\u660e\u4ed6\u7684\u6570\u5b66\u5b9a\u4e49\u3002\u5305\u62ec\u4ed6\u81ea\u5df1\u5b9a\u4e49\u7684\u66fc\u5fb7\u52c3\u7f57\u96c6\u5728\u5185\u7684\u56fe\u50cf\uff0c\u6fc0\u52b1\u5927\u4f17\u5c55\u5f00\u4e86\u4e30\u5bcc\u7684\u60f3\u8c61; \u5176\u4e2d\u8bb8\u591a\u56fe\u50cf\u662f\u57fa\u4e8e\u9012\u5f52\u7684\uff0c\u4ece\u800c\u4f7f\u201c\u5206\u5f62\u201d\u5f62\u6210\u4e86\u73b0\u5728\u7684\u5b9a\u4e49\u3002<\/p>\n<p><img class=\"rich_pages js_insertlocalimg\" data-ratio=\"1\" data-s=\"300,640\"  data-type=\"gif\" data-w=\"200\" style=\"\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-cb005d09a6c04bd80aae92d4afbca794.gif\"  \/><br \/>\u4e00\u4e2a\u5177\u6709\u591a\u91cd\u5206\u5f62\u7ef4\u5ea6\u7684\u5947\u5f02\u5438\u5f15\u5b50<br  \/>1980 \u5e74\uff0c\u6d1b\u4f26\u00b7\u5361\u5f6d\u7279 Loren Carpenter\u5728\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u9876\u7ea7\u5e74\u4f1aSIGGRAPH\u4e0a\u53d1\u8868\u4e86\u4e00\u6b21\u6f14\u8bb2\uff0c\u6f14\u8bb2\u4e2d\u4ed6\u4ecb\u7ecd\u4e86\u4ed6\u57fa\u4e8e\u5206\u5f62\u7406\u8bba\u5f00\u53d1\u7684\u7528\u4e8e\u4ea7\u751f\u666f\u89c2\u7684\u8f6f\u4ef6\u3002<\/p>\n<p>\u800c\u5bf9\u4e8e\u4e2d\u56fd\u800c\u8a00\uff0c\u6700\u65e9\u628a\u5206\u5f62\u51e0\u4f55\u5f15\u8fdb\u4e2d\u56fd\u7684\u53ef\u80fd\u662f\u4e2d\u79d1\u9662\u6c88\u9633\u91d1\u5c5e\u7814\u7a76\u6240\u7684\u9f99\u671f\u5a01\u7814\u7a76\u5458\uff0c\u4ed6\u66fe\u662f\u4e2d\u56fd\u79d1\u5b66\u6280\u672f\u5927\u5b66\u6559\u6388\u5e76\u4efb\u4e2d\u79d1\u9662\u56fd\u9645\u6750\u6599\u7269\u7406\u4e2d\u5fc3\u4e3b\u4efb\u3002\u4ed6\u7387\u5148\u628a\u5206\u5f62\u7406\u8bba\u5e94\u7528\u4e8e\u91d1\u5c5e\u65ad\u88c2\u7814\u7a76\uff0c\u5e76\u57f9\u517b\u4e86\u628a\u5206\u5f62\u65b9\u6cd5\u5f15\u5165\u5230\u88c2\u9699\u5ca9\u4f53\u975e\u8fde\u7eed\u53d8\u5f62\u3001\u5f3a\u5ea6\u548c\u65ad\u88c2\u7834\u574f\u884c\u4e3a\u7814\u7a76\u7684\u4e00\u4f4d\u4f18\u79c0\u5b66\u751f\uff0c\u4e5f\u5c31\u662f\u56db\u5ddd\u5927\u5b66\u524d\u4efb\u6821\u957f\u8c22\u548c\u5e73\u9662\u58eb\u3002<\/p>\n<p><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/>4. \u751f\u6210\u5206\u5f62\u7684\u5e38\u7528\u6280\u672f<br \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/>&nbsp;<br  \/>\u5728\u66fc\u5fb7\u5e03\u6d1b\u7279\u53d1\u8868\u7684\u4e00\u7bc7\u63cf\u8ff0\u51e0\u4f55\u5206\u5f62\u7684\u6587\u7ae0\u4e2d\uff0c\u5bf9\u4e8e\u5206\u5f62\u7684\u63cf\u8ff0\u7ecf\u5e38\u88ab\u5f15\u7528\uff1a\u201c\u4e00\u79cd\u7c97\u7cd9\u6216\u7834\u788e\u7684\u51e0\u4f55\u5f62\u72b6\uff0c\u53ef\u4ee5\u88ab\u5206\u5272\u6210\u51e0\u4e2a\u90e8\u5206\uff0c\u4e14\u6bcf\u4e00\u4e2a\u90e8\u5206(\u81f3\u5c11\u5927\u81f4\u4e0a)\u90fd\u662f\u6574\u4f53\u7684\u7f29\u5c0f\u7248\u672c\u201d\uff1b&nbsp;\u8fd9\u4e2a\u5b9a\u4e49\u6709\u52a9\u4e8e\u6211\u4eec\u7406\u89e3\u5206\u5f62\uff0c\u4f46\u4e5f\u6709\u5c40\u9650\u6027\u3002\u4f5c\u8005\u4e0d\u540c\u610f\u5bf9\u5206\u5f62\u8fdb\u884c\u786e\u5207\u5b9a\u4e49\uff0c\u4f46\u7ecf\u5e38\u9610\u8ff0\u81ea\u76f8\u4f3c\u7684\u57fa\u672c\u601d\u60f3\u3001\u5177\u6709\u53cd\u76f4\u89c9\u6027\u7684\u5206\u5f62\u4ee5\u53ca\u4ed6\u4eec\u6240\u5d4c\u5165\u7684\u7a7a\u95f4\u3002<\/p>\n<p><img class=\"rich_pages js_insertlocalimg\" data-ratio=\"1\" data-s=\"300,640\"  data-type=\"gif\" data-w=\"300\" style=\"\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-8eae12e0fbe3c7d132ab056b5576e1f8.gif\"  \/><br \/>\u5747\u5300\u8d28\u5fc3\u4e09\u89d2\u5f62\u7684\u5206\u5f62\u56fe\u6848<\/p>\n<p>\u6709\u4e00\u70b9\u662f\u53ef\u4ee5\u786e\u5b9a\u7684\uff0c\u5206\u5f62\u56fe\u6848\u5177\u6709\u5206\u5f62\u7ef4\u6570\u7684\u7279\u6027\u3002\u8fd9\u4e9b\u7ef4\u6570\u91cf\u5316\u4e86\u590d\u6742\u6027(\u4f8b\u5982\uff0c\u968f\u7740\u89c4\u6a21\u7684\u53d8\u5316\u800c\u6539\u53d8\u7ec6\u8282) \uff0c\u5b83\u4eec\u6ca1\u6709\u7279\u522b\u63cf\u8ff0\u548c\u8be6\u7ec6\u8bf4\u660e\u5982\u4f55\u6784\u5efa\u7279\u5b9a\u7684\u5206\u5f62\u56fe\u6848\u30021975\u5e74\uff0c\u5f53\u66fc\u5fb7\u5e03\u6d1b\u7279\u63d0\u51fa\u201c\u5206\u5f62\u201d\u8fd9\u4e2a\u8bcd\u65f6\uff0c\u662f\u4e3a\u4e86\u6807\u8bb0\u4e00\u4e2a\u8c6a\u65af\u591a\u592b-\u8d1d\u897f\u79d1\u7ef4\u5947\u7ef4\u6570 Hausdorff\u2013Besicovitch dimension\u5927\u4e8e\u62d3\u6251\u7ef4\u6570\u7684\u5bf9\u8c61\u3002\u7136\u800c\uff0c\u50cf\u5e0c\u5c14\u4f2f\u7279\u66f2\u7ebf\u8fd9\u6837\u7684\u7a7a\u95f4\u586b\u5145\u66f2\u7ebf\u5e76\u4e0d\u80fd\u6ee1\u8db3\u8fd9\u4e00\u8981\u6c42\u3002<\/p>\n<p>\u56e0\u4e3a\u5728\u4e3a\u5206\u5f62\u627e\u5230\u4e00\u4e2a\u786e\u5207\u5b9a\u4e49\u7684\u8fc7\u7a0b\u4e2d\u9047\u5230\u4e86\u5f88\u591a\u56f0\u96be\uff0c\u6709\u4e9b\u4eba\u8ba4\u4e3a\u5206\u5f62\u6839\u672c\u4e0d\u5e94\u8be5\u88ab\u4e25\u683c\u5b9a\u4e49\u3002\u6839\u636e \u798f\u5c14\u514b\u7eb3 Falconer \u7684\u89c2\u70b9\uff1a\u5206\u5f62\u9664\u4e86\u5904\u5904\u4e0d\u53ef\u5fae\u5e76\u4e14\u53ef\u4ee5\u6709\u5206\u5f62\u7ef4\u6570\u4e4b\u5916\uff0c\u8fd8\u5e94\u8be5\u5177\u6709\u4ee5\u4e0b\u53ef\u80fd\u7684\u7279\u5f81\uff1a<\/p>\n<p>1.\u81ea\u76f8\u4f3c\u6027\uff0c\u53ef\u80fd\u5305\u62ec\uff1a<br \/>\u5177\u6709\u5b8c\u5168\u81ea\u76f8\u4f3c\u6027\uff08\u5373\u5728\u6240\u6709\u5c3a\u5ea6\u4e0a\u90fd\u5b8c\u5168\u76f8\u540c\uff09\uff0c\u8b6c\u5982\u79d1\u8d6b\u96ea\u82b1<br \/>\u51c6\u81ea\u76f8\u4f3c\u6027\uff1a\u5728\u4e0d\u540c\u5c3a\u5ea6\u4e0a\u62e5\u6709\u8fd1\u4f3c\u76f8\u540c\u7684\u5f62\u72b6; \u53ef\u80fd\u5305\u542b\u626d\u66f2\u548c\u9000\u5316\u7684\u5b8c\u6574\u5206\u5f62\u7684\u7f29\u5c0f\u526f\u672c;\u4f8b\u5982\u66fc\u5fb7\u52c3\u7f57\u96c6\u4e2d\u7684\u536b\u661f\u96c6\uff08\u4e5f\u5c31\u662f\u9644\u5c5e\u96c6\uff09\u4e0e\u6574\u4e2a\u96c6\u5408\u662f\u76f8\u4f3c\u7684\uff0c\u4f46\u5b83\u4e0d\u662f\u6574\u4e2a\u96c6\u5408\u7684\u7cbe\u786e\u526f\u672c<br \/>\u7edf\u8ba1\u81ea\u76f8\u4f3c\u6027:\u968f\u673a\u91cd\u590d\u4e00\u4e2a\u56fe\u6848\uff0c\u4ee5\u4fbf\u5728\u4e0d\u540c\u5c3a\u5ea6\u4e0a\u4fdd\u7559\u5176\u6570\u503c\u6216\u7edf\u8ba1\u5ea6\u91cf;\u4f8b\u5982\uff0c\u5bf9\u4e8e\u50cf\u82f1\u56fd\u6d77\u5cb8\u7ebf\u4e00\u6837\u968f\u673a\u751f\u6210\u7684\u5206\u56fe\u6848\u6765\u8bf4\uff0c\u4eba\u4eec\u65e0\u6cd5\u627e\u5230\u50cf\u79d1\u8d6b\u96ea\u82b1\u4e2d\u5206\u6bb5\u7f29\u653e\u4e14\u6574\u9f50\u91cd\u590d\u7684\u5355\u5143<br \/>\u5b9a\u6027\u81ea\u76f8\u4f3c\u6027: \u5982\u5728\u65f6\u95f4\u5e8f\u5217\u4e2d<br \/>\u591a\u91cd\u5206\u5f62\u7f29\u653e: \u5177\u6709\u591a\u4e2a\u5206\u5f62\u7ef4\u6570\u6216\u591a\u79cd\u7f29\u653e\u89c4\u5219<br \/>2.\u5728\u4efb\u610f\u5c0f\u7684\u5c3a\u5ea6\u4e0a\u90fd\u80fd\u6709\u7cbe\u7ec6\u7684\u7ed3\u6784\uff1b\u8fd9\u4f7f\u5f97\u5206\u5f62\u53ef\u80fd\u5177\u6709\u7a81\u73b0\u7684\u6027\u8d28\uff08\u4e0e\u8fd9\u4e2a\u5217\u8868\u4e2d\u7684\u4e0b\u4e00\u4e2a\u51c6\u5219\u76f8\u5173\uff09<br \/>3.\u4f20\u7edf\u7684\u6b27\u51e0\u91cc\u5fb7\u51e0\u4f55\u8bed\u8a00\u5f88\u96be\u63cf\u8ff0\u5c40\u90e8\u548c\u5168\u5c40\u7684\u4e0d\u89c4\u5219\u6027\u3002\u5bf9\u4e8e\u5206\u5f62\u56fe\u6848\uff0c\u53ef\u4ee5\u7528\u201c\u5149\u6ed1\u7684\u5806\u79ef\u8868\u9762\u201d\u548c\u201c\u6f29\u6da1\u4e2d\u7684\u6f29\u6da1\u201d\u8fd9\u6765\u63cf\u8ff0<br \/>4.\u591a\u6570\u5b9a\u4e49\u8f83\u4e3a\u7b80\u5355\uff0c\u4e14\u53ef\u80fd\u57fa\u4e8e\u9012\u5f52\u6982\u5ff5\uff1b\uff08\u53c2\u89c1\u751f\u6210\u5206\u5f62\u7684\u5e38\u7528\u65b9\u6cd5)<br \/>5.\u4e00\u822c\u5730\uff0c\u5176\u201c\u5206\u5f62\u7ef4\u6570\u201d\uff08\u901a\u5e38\u4e3a\u8c6a\u65af\u591a\u592b\u7ef4\u6570\uff09\u4f1a\u5927\u4e8e\u62d3\u6251\u7ef4\u6570\uff08\u4f46\u5728\u7a7a\u95f4\u586b\u5145\u66f2\u7ebf\u5982\u5e0c\u5c14\u4f2f\u7279\u66f2\u7ebf\u4f8b\u5916\uff09<\/p>\n<p><img class=\"rich_pages js_insertlocalimg\" data-ratio=\"0.79\" data-s=\"300,640\"  data-type=\"jpeg\" data-w=\"300\" style=\"\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-917ccb6050da21956e5d435354cd13ff.jpeg\"  \/><br \/>\u9012\u5f52\u5ea6<\/p>\n<p>\u6309\u7167\u8fd9\u4e9b\u6807\u51c6\uff0c\u53ef\u4ee5\u6392\u9664\u67d0\u4e9b\u4e0d\u786e\u5b9a\u5176\u662f\u4e0d\u662f\u5206\u5f62\u7684\u60c5\u51b5\u3002\u6bd4\u5982\u90a3\u4e9b\u53ef\u80fd\u81ea\u76f8\u4f3c\u4f46\u6ca1\u6709\u5176\u4ed6\u5178\u578b\u7684\u5206\u5f62\u7279\u5f81\u7684\u60c5\u51b5\u3002\u4ee5\u4e00\u6761\u76f4\u7ebf\u4e3e\u4f8b\uff0c\u5b83\u662f\u81ea\u76f8\u4f3c\u7684\uff0c\u4f46\u4e0d\u662f\u5206\u5f62\uff0c\u56e0\u4e3a\u5b83\u7f3a\u4e4f\u7ec6\u8282\uff0c\u800c\u4e14\u53ef\u4ee5\u7528\u6b27\u51e0\u91cc\u5fb7\u8bed\u8a00\u8fdb\u884c\u7b80\u5355\u63cf\u8ff0\uff0c\u5177\u6709\u4e0e\u62d3\u6251\u7ef4\u6570\u76f8\u540c\u7684\u5206\u5f62\u7ef4\u6570\uff0c\u5e76\u4e14\u5b8c\u5168\u4e0d\u9700\u8981\u9012\u5f52\u8fdb\u884c\u51c6\u786e\u5b9a\u4e49\u3002<\/p>\n<p><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/>5.\u6a21\u62df\u5206\u5f62<br \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><\/p>\n<p>\u5206\u5f62\u7684\u56fe\u50cf\u53ef\u4ee5\u901a\u8fc7\u5206\u5f62\u751f\u6210\u8f6f\u4ef6\u751f\u6210\u3002<\/p>\n<p>\u8fed\u4ee3\u51fd\u6570\u7cfb\u7edf\uff08IFS\uff09\uff1a\u4f7f\u7528\u56fa\u5b9a\u7684\u51e0\u4f55\u66ff\u6362\u539f\u5219\uff1b\u53ef\u4ee5\u662f\u968f\u673a\u7684\u6216\u786e\u5b9a\u6027\u7684\uff1b\u4f8b\u5982\uff0c\u79d1\u8d6b\u96ea\u82b1\uff0c\u5eb7\u6258\u96c6\uff0c\u54c8\u5f17\u66fc\u5730\u6bef Haferman Carpet\uff0c\u8c22\u5c14\u5bbe\u65af\u57fa\u5730\u6bef Sierpinski Carpet\uff0c\u8c22\u5c14\u5bbe\u65af\u57fa\u57ab\u7247 Sierpinski Gasket\uff0c\u76ae\u4e9a\u8bfa\u66f2\u7ebf Peano Curve\uff0c\u54c8\u7279\u6d77\u5a01\u9f99\u66f2\u7ebf Harter-Heighway Dragon Curve\uff0cT-\u65b9\u5f62 T-Square\uff0c\u95e8\u683c\u6d77\u7ef5 Menger Sponge\u3002<br \/>\u5947\u5f02\u5438\u5f15\u5b50\uff1a\u4f7f\u7528\u6620\u5c04\u7684\u8fed\u4ee3\u6216\u8868\u793a\u51fa\u6df7\u6c8c\u7684\u521d\u503c\u5fae\u5206\u6216\u5dee\u5206\u65b9\u7a0b\u7cfb\u7edf\u7684\u89e3(\u4f8b\u5982\uff0c\u53c2\u89c1\u591a\u91cd\u5206\u5f62\u56fe\u50cf\u6216\u903b\u8f91\u6620\u5c04)\u3002<br \/>L-\u7cfb\u7edf\uff1a\u53ef\u80fd\u7c7b\u4f3c\u4e8e\u690d\u7269\u3001\u751f\u7269\u7ec6\u80de\uff08\u5982\u795e\u7ecf\u5143\u548c\u514d\u75ab\u7cfb\u7edf\uff09\u7ec6\u80de\u3001\u8840\u7ba1\u3001\u80ba\u7ed3\u6784\u3001\u7b49\u7684\u5206\u652f\u6a21\u5f0f\uff0c\u6216\u6d77\u9f9f\u56fe\u5f62\u6a21\u5f0f\uff0c\u5982\u7a7a\u95f4\u586b\u5145\u66f2\u7ebf\u548c\u5206\u5272\u9003\u9038\u65f6\u95f4\u5206\u5f62\u2014\u2014\u5728\u7a7a\u95f4\u7684\u6bcf\u4e2a\u70b9\uff08\u5982\u590d\u5e73\u9762\uff09\u4e0a\u4f7f\u7528\u516c\u5f0f\u6216\u9012\u63a8\u5173\u7cfb\uff1b\u901a\u5e38\u662f\u51c6\u81ea\u76f8\u4f3c\u7684 Quasi-Self-Similar\uff1b\u4e5f\u88ab\u79f0\u4e3a\u201c\u8f68\u9053\u201d\u5206\u5f62\uff1b\u4f8b\u5982\uff0c\u66fc\u5fb7\u5e03\u6d1b\u7279\u96c6 Mandelbrot set\uff0c\u6731\u5229\u4e9a\u96c6 Julia set\uff0c\u71c3\u70e7\u8239\u5206\u5f62 Burning Ship Fractal\uff0c\u65b0\u661f\u5206\u5f62 Nova Fractal\u548c\u674e\u4e9a\u666e\u8bfa\u592b\u5206\u5f62 Lyapunov Fractal\u3002<\/p>\n<p><img class=\"rich_pages js_insertlocalimg\" data-ratio=\"1.0066666666666666\" data-s=\"300,640\"  data-type=\"jpeg\" data-w=\"300\" style=\"\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-22a544e2e75d6c3f60e13695b7ee656d.jpeg\"  \/><br \/>\u7528 L \u7cfb\u7edf\u539f\u7406\u5728\u7845\u6811\u8102\u4e2d\u6a21\u62df\u81ea\u76f8\u4f3c\u5206\u652f\u6a21\u5f0f<\/p>\n<p>\u7531\u9003\u9038\u65f6\u95f4\u516c\u5f0f\u7684\u4e00\u4e2a\u6216\u4e24\u4e2a\u8fed\u4ee3\u4ea7\u751f\u7684\u4e8c\u7ef4\u77e2\u91cf\u573a\uff0c\u5f53\u70b9\uff08\u6216\u50cf\u7d20\u6570\u636e\uff09\u91cd\u590d\u901a\u8fc7\u8be5\u573a\u65f6\uff0c\u4e5f\u4f1a\u4ea7\u751f\u5206\u5f62\u5f62\u5f0f\u3002<br \/>\u968f\u673a\u5206\u5f62-\u4f7f\u7528\u968f\u673a\u89c4\u5219\uff1a\u4f8b\u5982:\u5bf9\u83b1\u7ef4\u98de\u884c Levy Flight\u3001\u6e17\u900f\u96c6\u7fa4 Percolation Clusters\uff0c\u81ea\u56de\u907f\u884c\u8d70 Self &#8211; Avoiding walks\u3001\u5206\u5f62\u666f\u89c2\u3001\u5e03\u6717\u8fd0\u52a8\u8f68\u8ff9\u548c\u5e03\u6717\u6811\uff08\u5373\u901a\u8fc7\u6a21\u62df\u6269\u6563\u53d7\u9650\u805a\u96c6\u6216\u53cd\u5e94\u53d7\u9650\u805a\u96c6\u7c07\u751f\u6210\u7684\u6811\u679d\u72b6\u5206\u5f62\uff09\u3002<br \/>\u6709\u9650\u7ec6\u5206\u89c4\u5219\uff1a\u4f7f\u7528\u9012\u5f52\u62d3\u6251\u7b97\u6cd5\u6765\u7ec6\u5316\u5206\u5272\uff0c\u5b83\u4eec\u7c7b\u4f3c\u4e8e\u7ec6\u80de\u5206\u88c2\u7684\u8fc7\u7a0b\u3002\u5728\u521b\u5efa\u5eb7\u6258\u5c14\u96c6\u548c\u8c22\u5c14\u5bbe\u65af\u57fa\u5730\u6bef\u7684\u8fed\u4ee3\u8fc7\u4e2d\u7a0b\u8fd0\u7528\u5230\u8be5\u89c4\u5219\uff0c\u5177\u4f53\u4f8b\u5b50\u5982\u91cd\u5fc3\u7ec6\u5206\u3002<\/p>\n<p><br  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/>6. \u5177\u6709\u5206\u5f62\u7279\u5f81\u7684\u81ea\u7136\u73b0\u8c61<br \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br  \/>\u7531\u4e8e\u7269\u7406\u65f6\u95f4\u548c\u7a7a\u95f4\u7684\u5b9e\u9645\u9650\u5236\uff0c\u5df2\u6709\u5f88\u591a\u6a21\u62df\u5206\u5f62\u7684\u6a21\u578b\uff08\u5c3d\u7ba1\u662f\u5728\u4e00\u5b9a\u8303\u56f4\u5185\u800c\u4e0d\u662f\u65e0\u9650\u8303\u56f4\u5185\uff09\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u6a21\u578b\u53ef\u4ee5\u6a21\u62df\u5177\u6709\u5206\u5f62\u7279\u5f81\u7684\u7406\u8bba\u5206\u5f62\u6216\u81ea\u7136\u73b0\u8c61\u3002\u5728\u5efa\u6a21\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u9ad8\u5ea6\u827a\u672f\u5316\u7684\u6548\u679c\u56fe\u3001\u4e00\u4e9b\u8c03\u67e5\u7684\u7ed3\u679c\u3001\u7528\u4e8e\u5206\u5f62\u5206\u6790\u7684\u57fa\u51c6\u3002\u4e0b\u9762\u5217\u51fa\u4e86\u5206\u5f62\u5728\u6280\u672f\u4e0a\u7684\u4e00\u4e9b\u5177\u4f53\u5e94\u7528\u3002<\/p>\n<p>\u56fe\u50cf\u548c\u5efa\u6a21\u7684\u4e00\u4e9b\u7ed3\u679c\u901a\u5e38\u88ab\u79f0\u4e3a\u201c\u5206\u5f62\u201d\uff0c\u5373\u4f7f\u5b83\u4eec\u6ca1\u6709\u4e25\u683c\u7684\u5206\u5f62\u7279\u5f81\uff0c\u6b64\u65f6\u53ef\u80fd\u662f\u56e0\u4e3a\u5df2\u7ecf\u653e\u5927\u5230\u4e00\u4e2a\u4e0d\u663e\u793a\u4efb\u4f55\u5206\u5f62\u7279\u6027\u7684\u5206\u5f62\u56fe\u50cf\u533a\u57df\uff0c\u4e5f\u53ef\u80fd\u662f\u56e0\u4e3a\u5305\u542b\u4e86\u8ba1\u7b97\u6216\u663e\u793a\u4eba\u5de5\u5236\u54c1\u7b49\u7279\u5f81\uff08\u8fd9\u4e9b\u7279\u5f81\u5e76\u4e0d\u662f\u771f\u6b63\u7684\u5206\u5f62\u7279\u5f81\uff09\u3002\u6a21\u62df\u7684\u5206\u5f62\u53ef\u4ee5\u662f\u58f0\u97f3\u3001\u6570\u5b57\u56fe\u50cf\u3001\u7535\u5316\u5b66\u6a21\u5f0f\u3001\u663c\u591c\u8282\u5f8b\u7b49\u3002\u5206\u5f62\u56fe\u6848\u5df2\u7ecf\u5728\u7269\u7406\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u91cd\u65b0\u8fdb\u884c\u6784\u9020\uff08\u8fd9\u901a\u5e38\u88ab\u79f0\u4e3a\u7845\u5668\u4ef6\u5efa\u6a21\uff09\u3002<\/p>\n<p>\u5206\u5f62\u6a21\u578b\u901a\u5e38\u662f\u901a\u8fc7\u5206\u5f62\u751f\u6210\u8f6f\u4ef6\u521b\u5efa\u7684\uff0c\u8fd9\u4e9b\u5206\u5f62\u751f\u6210\u8f6f\u4ef6\u8fd0\u7528\u5230\u4e0a\u8ff0\u6240\u8bf4\u7684\u6280\u672f\u3002\u8b6c\u5982\uff0c\u5229\u7528\u9012\u5f52\u7b97\u6cd5\u548cL\u7cfb\u7edf L-systems\u6280\u672f\uff0c\u53ef\u4ee5\u5728\u8ba1\u7b97\u673a\u4e0a\u6a21\u62df\u6811\u6728\u3001\u8568\u7c7b\u690d\u7269\u3001\u795e\u7ecf\u7cfb\u7edf\u7ec6\u80de \u3001\u8840\u6db2\u548c\u80ba\u8840\u7ba1\u7cfb\u7edf\u53ca\u5176\u4ed6\u81ea\u7136\u754c\u7684\u5206\u652f\u56fe\u5f62\u3002\u67d0\u4e9b\u56fe\u5f62\u7684\u9012\u5f52\u6027\u8d28\u662f\u5f88\u660e\u663e\u7684\u2014\u2014\u6bd4\u5982\u4e00\u68f5\u6811\u7684\u6811\u679d\u6216\u8568\u7c7b\u690d\u7269\u7684\u53f6\u5b50\u662f\u6574\u4e2a\u6a21\u5f0f\u7684\u5fae\u7f29\u590d\u5236\u54c1:\u5b83\u4eec\u4e0d\u5b8c\u5168\u76f8\u540c\uff0c\u4f46\u5728\u672c\u8d28\u4e0a\u662f\u76f8\u4f3c\u7684\u3002<\/p>\n<p><img class=\"rich_pages js_insertlocalimg\" data-ratio=\"1.01\" data-s=\"300,640\"  data-type=\"png\" data-w=\"300\" style=\"\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-31185887b74d150b8b051ccd6e2869de.png\"  \/><br \/>\u4ea4\u9519\u94fe\u8def\u6709\u9650\u7ec6\u5206\u6cd5\u751f\u6210\u7684\u5206\u5f62<\/p>\n<p>\u7c7b\u4f3c\u5730\uff0c\u968f\u673a\u5206\u5f62\u88ab\u7528\u6765\u63cf\u8ff0\/\u521b\u9020\u8bb8\u591a\u9ad8\u5ea6\u4e0d\u89c4\u5219\u7684\u771f\u5b9e\u4e16\u754c\u5bf9\u8c61\u3002\u4f46\u5206\u5f62\u5efa\u6a21\u4e5f\u6709\u5c40\u9650\u6027\uff1a\u5c3d\u7ba1\u5206\u5f62\u6a21\u578b\u751f\u6210\u7684\u7ed3\u679c\u4e0e\u81ea\u7136\u73b0\u8c61\u6709\u76f8\u4f3c\u6027\uff0c\u4f46\u5e76\u4e0d\u80fd\u8bc1\u660e\u7c7b\u4f3c\u7684\u5efa\u6a21\u7b97\u6cd5\u53ef\u4ee5\u81ea\u7136\u751f\u6210\u6211\u4eec\u4eba\u4e3a\u5efa\u7acb\u7684\u6a21\u578b\u3002<\/p>\n<p><br  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/>7. \u5e94\u7528<br \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><\/p>\n<p>\u81ea\u7136\u754c\u4e2d\u53d1\u73b0\u7684\u8fd1\u4f3c\u5206\u5f62\u5728\u53ef\u6269\u5c55\u5374\u6709\u9650\u7684\u5c3a\u5ea6\u8303\u56f4\u5185\u663e\u793a\u51fa\u81ea\u76f8\u4f3c\u6027\u3002\u4f8b\u5982\uff0c\u5206\u5f62\u4e0e\u6811\u53f6\u4e4b\u95f4\u7684\u8054\u7cfb\uff0c\u76ee\u524d\u6b63\u88ab\u7528\u6765\u786e\u5b9a\u6811\u6728\u4e2d\u542b\u6709\u591a\u5c11\u78b3\u3002\u5df2\u77e5\u5177\u6709\u5206\u5f62\u7279\u5f81\u7684\u73b0\u8c61\u5305\u62ec\uff1a<br  \/>\u4f5c\u7528\u6027\u7ec6\u80de\u9aa8\u67b6\u3001\u85fb\u7c7b\u3001\u52a8\u7269\u7684\u7740\u8272\u56fe\u6848\u3001\u8840\u7ba1\u548c\u80ba\u8840\u7ba1\u3001\u4e91\u5c42\u548c\u96e8\u91cf\u533a\u3001\u6d77\u5cb8\u7ebf\u3001\u9668\u77f3\u5751\u3001\u6c34\u6676\u3001DNA\u3001\u5730\u9707\u3001\u65ad\u5c42\u7ebf\u3001\u51e0\u4f55\u5149\u5b66\u3001\u5fc3\u7387\u3001\u5fc3\u97f3\u3001\u95ea\u7535\u3001\u5c71\u7f8a\u89d2\u3001\u5c71\u8109\u3001\u6d77\u6d6a\u3001\u83e0\u841d\u3001\u5fc3\u7406\u4e3b\u89c2\u77e5\u89c9\u3001\u86cb\u767d\u8d28\u3001\u571f\u661f\u73af\u3001\u6cb3\u7f51\u3001\u5b9d\u5854\u82b1\u83dc\u3001\u96ea\u82b1\u3001\u571f\u58e4\u5b54\u9699\u3001\u6e4d\u6d41\u8868\u9762\u3001\u6811\u6728\u3001\u5e03\u6717\u8fd0\u52a8\uff08\u7531\u4e00\u7ef4\u7ef4\u7eb3\u8fc7\u7a0b\u4ea7\u751f\uff09<br  \/><img class=\"rich_pages js_insertlocalimg\" data-ratio=\"0.6659619450317125\" data-s=\"300,640\"  data-type=\"jpeg\" data-w=\"473\" style=\"width: 348px;height: 232px;\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-88e99767a14411d94605555814127c78.jpeg\"  \/>\u51b7\u73bb\u7483\u4e0a\u81ea\u7136\u5f62\u6210\u7684\u971c\u6676\u5448\u73b0\u5206\u5f62\u56fe\u6848<br  \/><img class=\"rich_pages js_insertlocalimg\" data-ratio=\"0.75\" data-s=\"300,640\"  data-type=\"jpeg\" data-w=\"420\" style=\"width: 350px;height: 263px;\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-5880d08e4313718dd55b1401633e765c.jpeg\"  \/>\u51e0\u4f55\u5149\u5b66\u7cfb\u7edf\u4e2d\u7684\u5206\u5f62\u6d41\u57df\u8fb9\u754c<br  \/><img class=\"rich_pages js_insertlocalimg\" data-ratio=\"0.75\" data-s=\"300,640\"  data-type=\"jpeg\" data-w=\"420\" style=\"width: 350px;height: 263px;\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-0f973465294728ba8845da74f9541a2f.jpeg\"  \/>\u62c9\u5f00\u4e24\u4e2a\u88ab\u80f6\u6c34\u8986\u76d6\u7684\u4e19\u70ef\u9178\u7247\u65f6\u4ea7\u751f\u7684\u5206\u5f62<br  \/><img class=\"rich_pages js_insertlocalimg\" data-ratio=\"0.9077809798270894\" data-s=\"300,640\"  data-type=\"png\" data-w=\"347\" style=\"\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-148c07f74ca820a71cc15e52c88678c9.png\"  \/>\u9ad8\u538b\u51fb\u7a7f4\u82f1\u5bf8(100\u6beb\u7c73)\u7684\u4e19\u70ef\u9178\u73bb\u7483\u5757\u521b\u5efa\u4e00\u4e2a\u7535\u82b1\u5206\u5f62\u56fe<br  \/><img class=\"rich_pages js_insertlocalimg\" data-ratio=\"0.75\" data-s=\"300,640\"  data-type=\"jpeg\" data-w=\"420\" style=\"width: 357px;height: 268px;\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-01f2ccb1389d9bb30c3a706685aeabe1.jpeg\"  \/>\u5b9d\u5854\u82b1\u83dc\uff0c\u4ee5\u81ea\u76f8\u4f3c\u7684\u5f62\u5f0f\u6784\u6210\u4e86\u8fd1\u4f3c\u7684\u81ea\u7136\u5206\u5f62<br  \/><img class=\"rich_pages js_insertlocalimg\" data-ratio=\"0.8333333333333334\" data-s=\"300,640\"  data-type=\"jpeg\" data-w=\"378\" style=\"width: 354px;height: 295px;\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-ae7e6ea00091d01bbaa60bbc8b9fb8e9.jpeg\"  \/>\u6781\u5730\u706b\u661f\u7684\u5206\u5f62\u878d\u971c\u6a21\u5f0f,\u51b7\u51bb\u7684\u4e8c\u6c27\u5316\u78b3\u5347\u534e\u5f62\u6210\u4e86\u8fd9\u4e9b\u56fe\u6848<br  \/><img class=\"rich_pages js_insertlocalimg\" data-ratio=\"0.7482185273159145\" data-s=\"300,640\"  data-type=\"jpeg\" data-w=\"421\" style=\"width: 363px;height: 272px;\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-d0d48cff514ec1b8b63d1281fd09a4b7.jpeg\"  \/>\u5728\u6728\u5934\u4e0a\u4ee5\u5206\u5f62\u65b9\u5f0f\u751f\u957f\u7684\u6700\u5927\u7c98\u83cc<\/p>\n<p><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/>8. \u7531\u5206\u5f62\u800c\u8bde\u751f\u7684\u521b\u9020\u6027\u4f5c\u54c1<br \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br  \/>\u81ea1999\u5e74\u4ee5\u6765\uff0c\u8d85\u8fc710\u4e2a\u79d1\u5b66\u56e2\u961f\u5bf9\u6770\u514b\u900a\u00b7\u6ce2\u6d1b\u514b Jackson Pollock\uff081912-1956\uff09\u768450\u591a\u5e45\u6cb9\u753b\u8fdb\u884c\u4e86\u5206\u5f62\u5206\u6790\uff0c\u8fd9\u4e9b\u6cb9\u753b\u662f\u76f4\u63a5\u5c06\u989c\u6599\u5012\u5728\u6c34\u5e73\u753b\u5e03\u4e0a\u521b\u4f5c\u51fa\u6765\u7684\u3002\u5206\u5f62\u5206\u6790\u540e\u6765\u88ab\u7528\u6765\u533a\u5206 Jackson Pollock \u7684\u771f\u54c1\u548c\u8d5d\u54c1\uff0c\u8fa8\u8ba4\u6210\u529f\u7387\u8fbe\u5230\u4e8693% \u3002\u8ba4\u77e5\u795e\u7ecf\u79d1\u5b66\u5bb6\u5df2\u7ecf\u8bc1\u5b9e\uff0cJackson Pollock\u7684\u5206\u5f62\u53ef\u4ee5\u50cf\u8ba1\u7b97\u673a\u751f\u6210\u7684\u5206\u5f62\u548c\u81ea\u7136\u5206\u5f62\u4e00\u6837\uff0c\u51cf\u5c11\u89c2\u5bdf\u8005\u7684\u8bc6\u522b\u96be\u5ea6\u3002<\/p>\n<p>\u5370\u82b1\u91c9\u6cd5 Decalcomania\u662f\u9a6c\u514b\u65af\u2022\u6069\u65af\u7279 Max Ernst\u7b49\u827a\u672f\u5bb6\u4f7f\u7528\u7684\u4e00\u79cd\u5de5\u827a\u6280\u672f\uff0c\u5b83\u53ef\u4ee5\u4ea7\u751f\u5206\u5f62\u6837\u7684\u56fe\u6848\u3002\u8be5\u6280\u672f\u5305\u62ec\u5728\u4e24\u4e2a\u8868\u9762\u4e4b\u95f4\u538b\u6f06\uff0c\u7136\u540e\u628a\u5b83\u4eec\u5206\u5f00\u7684\u6b65\u9aa4\u3002<\/p>\n<p>\u63a7\u5236\u8bba\u5b66\u8005\u3001\u6570\u5b66\u5bb6\u7f57\u6069\u00b7\u57c3\u683c\u62c9\u4ec0 Ron Eglash\u8ba4\u4e3a\u5206\u5f62\u51e0\u4f55\u548c\u6570\u5b66\u5728\u975e\u6d32\u827a\u672f\u3001\u6e38\u620f\u3001\u5360\u535c\u3001\u8d38\u6613\u548c\u5efa\u7b51\u4e2d\u5e94\u7528\u5f88\u666e\u904d\u3002\u5982\u5706\u5f62\u623f\u5c4b\u662f\u4e00\u73af\u5957\u4e00\u73af\u7684\uff0c\u77e9\u5f62\u623f\u5c4b\u662f\u4e00\u8fde\u4e32\u7684\u77e9\u5f62\u7b49\u7b49\u3002\u8fd9\u79cd\u7f29\u653e\u56fe\u6848\u4e5f\u53ef\u4ee5\u5728\u975e\u6d32\u7684\u7eba\u7ec7\u54c1\u3001\u96d5\u5851\u3001\u751a\u81f3\u53d1\u578b\u4e2d\u627e\u5230\u3002\u970d\u514b\u57fa\u00b7\u897f\u901a\u57fa\u5c14 Hokky Situngkir\u8fd8\u5efa\u8bae\u5728\u5370\u5ea6\u5c3c\u897f\u4e9a\u4f20\u7edf\u827a\u672f\u3001\u8721\u67d3\u548c\u4f20\u7edf\u623f\u5c4b\u7684\u88c5\u9970\u54c1\u4e2d\u8fd0\u7528\u5206\u5f62\u7684\u56fe\u6848\u3002<\/p>\n<p>\u63a7\u5236\u8bba\u4e13\u5bb6\u3001\u6c11\u65cf\u6570\u5b66\u5bb6 Ron Eglash \u8fd8\u8ba8\u8bba\u4e86\u904d\u5e03\u8d1d\u5b81\u7684\u57ce\u5e02\u3001\u6751\u5e84\u751a\u81f3\u623f\u95f4\u7684\u5206\u5f62\u5e03\u5c40\u3002\u4ed6\u8bc4\u8bba\u8bf4: \u201c\u5f53\u6b27\u6d32\u4eba\u7b2c\u4e00\u6b21\u6765\u5230\u975e\u6d32\u65f6\uff0c\u4ed6\u4eec\u8ba4\u4e3a\u975e\u6d32\u7684\u5efa\u7b51\u975e\u5e38\u6df7\u4e71\u4e14\u539f\u59cb\u3002\u4ed6\u4eec\u4ece\u6765\u6ca1\u6709\u60f3\u5230\u975e\u6d32\u4eba\u53ef\u80fd\u4f7f\u7528\u4e86\u4e00\u79cd\u4ed6\u4eec\u751a\u81f3\u8fd8\u6ca1\u6709\u53d1\u73b0\u7684\u6570\u5b66\u5f62\u5f0f\u6765\u8bbe\u8ba1\u5efa\u7b51\u3002\u201d<\/p>\n<p>\u57281996\u5e74\u5bf9\u8fc8\u514b\u5c14 \u00b7 \u897f\u5c14\u5f17\u5e03\u62c9\u7279 Michael Silverblatt\u7684\u91c7\u8bbf\u4e2d\uff0c\u798f\u65af\u7279\u00b7\u534e\u83b1\u58eb David Foster Wallace\u627f\u8ba4\u4ed6\u7ed9\u7f16\u8f91\u8fc8\u514b\u5c14\u00b7\u76ae\u5947 Michael Pietsch\u7684\u300a\u65e0\u5c3d\u7684\u73a9\u7b11 Infinite Jest\u300b\u7b2c\u4e00\u7a3f\u7684\u7ed3\u6784\u7075\u611f\u6765\u81ea\u4e8e\u5206\u5f62\uff0c\u7279\u522b\u662f\u8c22\u5c14\u5bbe\u65af\u57fa\u4e09\u89d2\u5f62\uff0c\u4f46\u662f\u7ecf\u8fc7\u4fee\u6539\u540e\u7684\u5c0f\u8bf4\u201c\u66f4\u50cf\u662f\u4e00\u4e2a\u4fa7\u9762\u7684\u8c22\u5c14\u5bbe\u65af\u57fa\u57ab\u7247\u201d\u3002<\/p>\n<p>\u4f5c\u54c1\u5982\u4e0b:<\/p>\n<p><img class=\"rich_pages js_insertlocalimg\" data-ratio=\"0.75\" data-s=\"300,640\"  data-type=\"jpeg\" data-w=\"420\" style=\"\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-844d8050f939bbb3b125a499d3d52e39.jpeg\"  \/><br \/>3D\u9012\u5f52\u56fe\u50cf<\/p>\n<p><img class=\"rich_pages js_insertlocalimg\" data-ratio=\"0.75\" data-s=\"300,640\"  data-type=\"jpeg\" data-w=\"420\" style=\"\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-c1ca07f1695eb78d399857ba0f5712b8.jpeg\"  \/><br \/>\u5206\u5f62\u706b\u7130<\/p>\n<p><img class=\"rich_pages js_insertlocalimg\" data-ratio=\"0.75\" data-s=\"300,640\"  data-type=\"jpeg\" data-w=\"420\" style=\"\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-353047863dae5ccaffafe781b2e58212.jpeg\"  \/><br \/>\u9012\u5f52\u5206\u5f62\u8774\u8776\u56fe\u50cf<\/p>\n<p><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/>9. \u5728\u79d1\u6280\u4e0a\u7684\u5e94\u7528<br \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br  \/>\u4e0b\u9762\u5bf9\u4e8e\u5206\u5f62\u51e0\u4f55\u5728\u7535\u5b50\u6280\u672f\u65b9\u9762\u7684\u5e94\u7528\u505a\u4e00\u4e9b\u8bf4\u660e\uff1a<\/p>\n<p>\u5206\u5f62\u5929\u7ebf<br \/>\u5206\u5f62\u5929\u7ebf\u662f\u4e00\u79cd\u65e0\u7ebf\u901a\u4fe1\u7528\u7684\u65b0\u6982\u5ff5\u5929\u7ebf\u3002\u548c\u4f20\u7edf\u5929\u7ebf\u76f8\u6bd4\uff0c\u5b83\u5728\u540c\u6837\u9762\u79ef\u6216\u4f53\u79ef\u7684\u6761\u4ef6\u4e0b\u5177\u6709\u6700\u5927\u7684\u6709\u6548\u957f\u5ea6\u6216\u5468\u957f\u3002\u8fd9\u79cd\u5929\u7ebf\u5177\u6709\u6781\u7aef\u7d27\u51d1\u548c\u591a\u5bbd\u9891\u5e26\u7b49\u7279\u6027\uff0c\u975e\u5e38\u9002\u5408\u4e8eRFID\u548c\u79fb\u52a8\u901a\u8baf\u65b9\u9762\u7684\u5e94\u7528\u3002\u7531\u4e8e\u73b0\u4ee3\u901a\u4fe1\u5de5\u5177\u79cd\u7c7b\u8d8a\u6765\u8d8a\u591a\uff0c\u4f53\u79ef\u4e5f\u8d8a\u6765\u8d8a\u5c0f\uff0c\u56e0\u800c\u9700\u8981\u628a\u5929\u7ebf\u505a\u5f97\u5f88\u5c0f\u5f88\u5c0f\uff0c\u800c\u4e14\u8d8a\u5c0f\u8d8a\u597d\u3002\u4e3a\u6b64\u76ee\u7684\uff0c\u628a\u5929\u7ebf\u7684\u5f62\u72b6\u505a\u6210\u5206\u5f62\u662f\u4e2a\u597d\u4e3b\u610f\uff0c\u56e0\u4e3a\u8fd9\u53ef\u4ee5\u5728\u540c\u6837\u9762\u79ef\u7684\u9650\u5236\u6761\u4ef6\u4e0b\u628a\u5929\u7ebf\u505a\u5f97\u5f88\u957f\uff0c\u800c\u4e14\u8fd8\u80fd\u53d6\u4ee3\u591a\u6761\u5929\u7ebf\u800c\u540c\u65f6\u5de5\u4f5c\u5728\u51e0\u4e2a\u4e0d\u540c\u9891\u7387\u533a\u95f4\u4e4b\u4e2d\u3002<\/p>\n<p>\u628a\u5929\u7ebf\u9635\u5217\u8bbe\u8ba1\u6210\u5206\u5f62\u6837\u5b50\u7684\u505a\u6cd5\u65e9\u57281957\u5e74\u5c31\u51fa\u73b0\u4e86\u3002\u5b83\u662f\u7531\u7f8e\u56fd\u4f0a\u5229\u8bfa\u4f0a\u5927\u5b66\u7535\u5b50\u5de5\u7a0b\u7cfb\u6559\u6388\u827e\u8499\u5fb7\u00b7\u675c\u54c8\u6885\u5c14 Raymond DuHamel \u548c\u5b66\u751f \u5fb7\u6000\u7279\u00b7\u4f0a\u65af\u8d1d\u5c14 Dwight Isbell\u63d0\u51fa\u7684\u5bf9\u6570\u5468\u671f\u9635\u5217 Log Periodic Array \u3002<\/p>\n<p>\u5206\u5f62\u5929\u7ebf\u9635\u5217\u4e0e\u4f20\u7edf\u5929\u7ebf\u9635\u5217\u8bbe\u8ba1\u76f8\u6bd4\uff0c\u5177\u6709\u591a\u9891\u548c\u5bbd\u9891\u7279\u6027\uff0c\u53ef\u7528\u4e8e\u5feb\u901f\u8ba1\u7b97\u65b9\u5411\u56fe\uff0c\u53ef\u6709\u6548\u5730\u5229\u7528\u72ed\u5c0f\u5730\u57df\u6765\u5e03\u7f6e\u5e9e\u5927\u7684\u5e73\u9762\u9635\u5217\uff0c\u53ef\u5b9e\u73b0\u4f4e\u526f\u74e3\u8bbe\u8ba1\u7b56\u7565\uff0c\u7b49\u7b49\u3002\u4e24\u79cd\u5178\u578b\u7684\u5206\u5f62\u9635\u5217\u5929\u7ebf\u662f\u5eb7\u6258\u96c6\u9635\u5217\u548c\u7ef4\u5c14\u65af\u7279\u62c9\u65af\u7ebf\u6027\u9635\u5217\uff0c\u76ee\u524d\u591a\u7528\u4e8e\u7535\u89c6\u5929\u7ebf\u3002<\/p>\n<p>\u57fa\u4e8e\u5206\u5f62\u7ed3\u6784\u6765\u8bbe\u8ba1\u548c\u4f18\u5316\u5355\u4e2a\u5929\u7ebf\u7684\u505a\u6cd5\u59cb\u4e8e1988\u5e74\uff0c\u7531\u6ce2\u58eb\u987f\u5927\u5b66\u6559\u6388\u5185\u68ee\u00b7\u79d1\u6069 Nathan Cohen\u9996\u5148\u63d0\u51fa\uff0c\u4f46\u76f8\u5173\u7684\u5b66\u672f\u8bba\u6587\u5230\u4e861995\u5e74\u624d\u7b2c\u4e00\u6b21\u6b63\u5f0f\u53d1\u8868\u3002\u4e0e\u4f20\u7edf\u5929\u7ebf\u76f8\u6bd4\uff0c\u5206\u5f62\u5929\u7ebf\u9664\u4e86\u5728\u7f29\u5c0f\u5c3a\u5bf8\u65b9\u9762\u72ec\u5177\u4e00\u683c\u4e4b\u5916\uff0c\u8fd8\u6709\u5176\u4ed6\u4f18\u70b9\uff0c\u4f8b\u5982\uff1a\u53ef\u4ee5\u5229\u7528\u5176\u81ea\u76f8\u4f3c\u6027\u6765\u589e\u52a0\u5de5\u4f5c\u9891\u5e26\u6570\u76ee\u548c\u5e26\u5bbd\uff0c\u5177\u6709\u81ea\u52a0\u8f7d\u7279\u6027\u800c\u4e0d\u9700\u8981\u989d\u5916\u7684\u8c03\u8c10\u7ebf\u5708\u548c\u7535\u5bb9\u7b49\u5143\u5668\u4ef6\u6216\u5339\u914d\u7535\u8def\u6765\u8f85\u52a9\u5176\u5728\u5bbd\u5e26\u5de5\u4f5c\u6761\u4ef6\u4e0b\u8fbe\u5230\u963b\u6297\u5339\u914d\uff0c\u8fd8\u53ef\u4ee5\u7b80\u5316\u7535\u8def\u8bbe\u8ba1\u548c\u964d\u4f4e\u7cfb\u7edf\u9020\u4ef7\uff0c\u7b49\u7b49\u3002<\/p>\n<p>\u636e\u62a5\u9053\uff0c\u57fa\u4e8e\u5206\u5f62\u8bbe\u8ba1\u7684\u5929\u7ebf\u53ef\u4ee5\u5728UHF\uff08862-928 MHz\uff09\u9891\u5e26\u7684\u65e0\u7ebf\u901a\u4fe1\u8bbe\u5907\u4e2dGSM+DCS\uff08900MHz\u548c1800MHz\uff09\u53cc\u9891\u79fb\u52a8\u5929\u7ebf\u7cfb\u7edf\u4e2d\u5f97\u5230\u8f83\u597d\u7684\u5e94\u7528\u3002\u76ee\u524d\u7684\u7814\u7a76\u4e3b\u8981\u96c6\u4e2d\u5728GSM\uff08900MHz\uff09\u3001PCS \uff081900MHz\uff09\u3001\u84dd\u7259\u65e0\u7ebf\u901a\u4fe1\u7cfb\u7edf\uff082.4GHz\uff09\u7b49\u65b9\u9762\u3002\u5b83\u4e0d\u4ec5\u53ef\u4ee5\u5728\u4e2a\u4eba\u624b\u63d0\uff08\u5982Cellular Phone\uff0c\u5373\u8702\u7a9d\u7535\u8bdd\uff09\u548c\u5176\u4ed6\u65e0\u7ebf\u79fb\u52a8\u8bbe\u5907 \uff08\u5982\u65e0\u7ebf\u5c40\u57df\u7f51\u4e2d\u7684laptop\uff0c\u5373\u7b14\u8bb0\u672c\u7535\u8111\u3001\u8f66\u8f7d\u5929\u7ebf\u7cfb\u7edf\uff09\u4e2d\u5f97\u5230\u5e94\u7528\uff0c\u8fd8\u53ef\u671b\u7528\u4e8e\u536b\u661f\u901a\u4fe1\u7cfb\u7edf\u548c\u76f8\u63a7\u9635\u96f7\u8fbe\u7cfb\u7edf\u3002<\/p>\n<p>\u76ee\u524d\u770b\u6765\uff0c\u5982\u679c\u76f8\u5173\u7684\u4e00\u4e9b\u6280\u672f\u969c\u788d\uff08\u5982\u591a\u9891\u9053\u4fe1\u53f7\u4e4b\u95f4\u7684\u76f8\u4e92\u5e72\u6d89\uff09\u80fd\u591f\u53d6\u5f97\u7a81\u7834\uff0c\u5219\u5206\u5f62\u5929\u7ebf\u7684\u524d\u666f\u8fd8\u662f\u9887\u4e3a\u8bf1\u4eba\u7684\u3002\u5f53\u7136\uff0c\u4ece\u6570\u5b66\u89d2\u5ea6\u4e25\u683c\u6765\u8bb2\uff0c\u8fd9\u4e9b\u4f8b\u5b50\u90fd\u53ea\u662f\u5229\u7528\u4e86\u6709\u9650\u5206\u5f62\uff08\u6216\u8005\u4f2a\u5206\u5f62\uff09\uff0c\u56e0\u800c\u5c1a\u6709\u6f5c\u529b\u53ef\u4ee5\u6316\u6398\u3002\u4e8b\u5b9e\u4e0a\uff0c\u76ee\u524d\u4e00\u5207\u8fd8\u5728\u5c1d\u8bd5\u4e4b\u4e2d\uff0c\u671f\u5f85\u65b0\u7684\u8fdb\u5c55\u3002<\/p>\n<p>\u636e\u62a5\u9053\uff0c \u65b0\u8fd1\u8fc5\u731b\u53d1\u5c55\u7684\u7eb3\u7c73\u53d8\u5f62\u6750\u6599 Metamaterials \u548c\u7528\u53d8\u5f62\u6750\u6599\u5236\u9020\u7684\u5929\u7ebf\u90fd\u5c3d\u53ef\u80fd\u6709\u6548\u5730\u5229\u7528\u5206\u5f62\u51e0\u4f55\u7ed3\u6784\u30022011\u5e74\u8fd8\u6709\u62a5\u9053\u8bf4 \uff0c\u7528\u5bc6\u5c01\u5206\u5f62\u5171\u632f\u5668\u5408\u6210\u7684\u5bbd\u5e26\u53d8\u5f62\u6750\u6599\u53ef\u4ee5\u5236\u9020\u51fa\u9690\u5f62\u5916\u5957\uff0c\u5176\u539f\u7406\u662f\u53ef\u4ee5\u8ba9\u5149\u7ed5\u8fc7\u8fd9\u4e9b\u6750\u6599\u800c\u5b9e\u73b0\u4f20\u64ad\u548c\u6298\u5c04.<\/p>\n<p>\u5206\u5f62\u7535\u5bb9<br \/>\u5206\u5f62\u7535\u5bb9\u5668\u7684\u57fa\u672c\u8bbe\u8ba1\u601d\u60f3\u548c\u5206\u5f62\u5929\u7ebf\u4e00\u6837\u3002\u7406\u8bba\u4e0a\uff0c\u524d\u8005\u662f\u5728\u6709\u9650\u7684\u9762\u79ef\u5185\u83b7\u5f97\u65e0\u9650\u957f\u7684\u66f2\u7ebf\u4ee5\u589e\u52a0\u5929\u7ebf\u7684\u6709\u6548\u957f\u5ea6\uff0c\u540e\u8005\u5219\u662f\u5728\u6709\u9650\u7684\u4f53\u79ef\u5185\u83b7\u5f97\u65e0\u9650\u5bbd\u7684\u66f2\u9762\u4ee5\u589e\u52a0\u7535\u5bb9\u5668\u7684\u50a8\u7535\u91cf\u3002<\/p>\n<p>\u7814\u7a76\u53d1\u73b0\uff0c\u5728\u4f20\u7edf\u7684\u7535\u5bb9\u5668\u4e2d\u628a\u90e8\u5206\u7eb5\u5411\u7684\u76f8\u53cd\u7535\u6781\u5206\u5e03\u6539\u4e3a\u6a2a\u5411\u53ef\u4ee5\u6709\u6548\u63d0\u9ad8\u5176\u50a8\u7535\u91cf\u3002\u5206\u5f62\u7535\u5bb9\u5668\u5e94\u7528\u7684\u4e00\u4e2a\u6210\u529f\u8bd5\u9a8c\u6027\u4f8b\u5b50\u662f\u7531\u745e\u58eb\u4fdd\u7f57\u00b7\u8c22\u4e50\u673a\u6784 Paul Scherrer Institute \u516c\u53f8\u7814\u5236\u7684\u5206\u5f62\u8d85\u7ea7\u7535\u5bb9\u5668 Supercapacitor \/Ultracapacitor\u88ab\u5b89\u88c5\u5728\u4e00\u8f86\u540d\u4e3a Hy. Power \u7684\u71c3\u6599\u9a71\u52a8\u5c0f\u6c7d\u8f66\u91cc\uff0c\u7528\u4f5c\u6c7d\u8f66\u7206\u53d1\u52a0\u901f\u65f6\u7684\u62d6\u52a8\u529f\u7387\u8865\u7ed9\u30022002\u5e741\u670816\u65e5\uff0cHy. Power \u6210\u529f\u5730\u722c\u4e0a\u4e86\u4f4d\u4e8e\u745e\u58eb\u5e03\u91cc\u683c Brig\u4e0e\u610f\u5927\u5229\u591a\u83ab\u591a\u7d22\u62c9 Domodossola \u4e4b\u95f4\u6d77\u62d4\u4e24\u5343\u591a\u7c73\u9ad8\u7684\u8f9b\u666e\u4f26 Simplon\u5c71\u53e3\u3002\u8fd9\u6bb5\u5c71\u8def\u6781\u4e3a\u9661\u5ced\uff0c\u800c\u5f53\u65f6\u5c71\u9876\u6c14\u5019\u6761\u4ef6\u6076\u52a3\uff0c\u540c\u7c7b\u578b\u7684\u5c0f\u6c7d\u8f66\u53ea\u80fd\u671b\u5c71\u5174\u53f9 \u3002\uff08\u6458\u81ea\u96c6\u667a\u4ff1\u4e50\u90e8 <a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247483995&amp;idx=1&amp;sn=b0f462c886e386bdfcacaf4cd3cb869c&amp;chksm=e89458d6dfe3d1c02b9dd1b72bca61886e2cfd3f9010c99451e62e9d9677a1841369621bde8d&amp;scene=21#wechat_redirect\" textvalue=\"\u5206\u5f62\u2014\u2014\u6545\u4e8b\u4e4b\u5916\" data-itemshowtype=\"0\" tab=\"innerlink\" data-linktype=\"2\" rel=\"noopener noreferrer\">\u5206\u5f62\u2014\u2014\u6545\u4e8b\u4e4b\u5916<\/a>\uff09<\/p>\n<p>\u79bb\u5b50\u63a8\u8fdb<br \/>\u5f53\u4e8c\u7ef4\u7a7a\u95f4\u7684\u5206\u5f62\u88ab\u591a\u6b21\u8fed\u4ee3\u65f6\uff0c\u5206\u5f62\u7684\u5468\u957f\u589e\u52a0\u5230\u65e0\u7a77\u5927\uff0c\u4f46\u9762\u79ef\u7edd\u4e0d\u4f1a\u8d85\u8fc7\u67d0\u4e00\u9608\u503c\u3002\u4e09\u7ef4\u7a7a\u95f4\u7684\u5206\u5f62\u4e0e\u6b64\u76f8\u4f3c\uff0c\u8fd9\u6837\u7684\u5206\u5f62\u53ef\u80fd\u6709\u65e0\u9650\u7684\u8868\u9762\u79ef\uff0c\u4f46\u4f53\u79ef\u7edd\u4e0d\u4f1a\u8d85\u8fc7\u67d0\u4e00\u9608\u503c\u3002\u5728\u9009\u62e9\u7535\u5b50\u53d1\u5c04\u4f53\u7684\u7ed3\u6784\u548c\u6750\u6599\u65f6\uff0c\u8fd9\u6837\u7684\u7279\u6027\u53ef\u4ee5\u7528\u6765\u6700\u5927\u9650\u5ea6\u5730\u63d0\u9ad8\u79bb\u5b50\u63a8\u8fdb\u7684\u6548\u7387\u3002\u5982\u679c\u64cd\u4f5c\u6b63\u786e\uff0c\u53ef\u4f7f\u6392\u653e\u6548\u7387\u8fbe\u5230\u6700\u9ad8\u3002<\/p>\n<p><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/>10.\u8457\u540d\u5b66\u8005\u7b80\u4ecb<br \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br  \/>\u4f2f\u52aa\u00b7\u74e6\u66fc\u5fb7\u5e03\u6d1b\u7279 Beno\u00eet B. Mandelbrot<\/p>\n<p><img class=\"rich_pages\" data-ratio=\"0.6666666666666666\" data-s=\"300,640\" data-type=\"jpeg\" data-w=\"600\"  style=\"box-sizing: border-box !important;overflow-wrap: break-word !important;width: 556px !important;visibility: visible !important;\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-b9354623ccc6e4a55e11c5c1c2d27291.jpeg\"  \/>\u4f2f\u52aa\u00b7\u74e6\u66fc\u5fb7\u5e03\u6d1b\u7279 Beno\u00eet B. Mandelbrot<br \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br \/>\u6cd5\u56fd\u3001\u7f8e\u56fd\u6570\u5b66\u5bb6\uff08\u53cc\u56fd\u7c4d\uff09\uff0c\u6700\u5927\u7684\u6210\u5c31\u662f\u521b\u7acb\u4e86\u5206\u5f62\u51e0\u4f55\u30021967\u5e74\uff0c\u66fc\u5fb7\u5e03\u6d1b\u7279\u5728\u7f8e\u56fd\u300aScience\u300b\u6742\u5fd7\u4e0a\u53d1\u8868\u9898\u76ee\u4e3a\u300a\u82f1\u56fd\u7684\u6d77\u5cb8\u7ebf\u6709\u591a\u957f\u300b\u7684\u5212\u65f6\u4ee3\u8bba\u6587\uff0c\u6807\u5fd7\u7740\u5176\u5206\u5f62\u601d\u60f3\u7684\u840c\u82bd\u3002<br \/>&nbsp;<br \/>\u6731\u5c14\u00b7\u4ea8\u5229\u00b7\u5e9e\u52a0\u83b1 Jules Henri Poincar\u00e9<\/p>\n<div class=\"post-image\"><img class=\"rich_pages\" data-ratio=\"1\" data-s=\"300,640\" data-type=\"jpeg\" data-w=\"1000\"  style=\"box-sizing: border-box !important;overflow-wrap: break-word !important;width: 408px !important;visibility: visible !important;\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-5f72dc8c5728363ab856c8d112e0071c.jpeg\"  \/><br \/>\u56fe7\uff1a\u6731\u5c14\u00b7\u4ea8\u5229\u00b7\u5e9e\u52a0\u83b1 Jules Henri Poincar\u00e9<br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><\/div>\n<p>\u6cd5\u56fd\u6700\u4f1f\u5927\u7684\u6570\u5b66\u5bb6\u4e4b\u4e00\uff0c\u7406\u8bba\u79d1\u5b66\u5bb6\u548c\u79d1\u5b66\u54f2\u5b66\u5bb6\u3002\u5e9e\u52a0\u83b1\u88ab\u516c\u8ba4\u662f19\u4e16\u7eaa\u540e\u548c20\u4e16\u7eaa\u521d\u7684\u9886\u8896\u6570\u5b66\u5bb6\uff0c\u662f\u7ee7\u9ad8\u65af\u4e4b\u540e\u5bf9\u4e8e\u6570\u5b66\u53ca\u5176\u5e94\u7528\u5177\u6709\u5168\u9762\u77e5\u8bc6\u7684\u6700\u540e\u6570\u5b66\u5bb6\u3002\u65e9\u572819\u4e16\u7eaa\u521d\uff0c\u5e9e\u52a0\u83b1\u5728\u7814\u7a76\u4e09\u4f53\u95ee\u9898\u4e2d\uff0c\u4f7f\u7528\u4e86\u65b0\u7684\u51e0\u4f55\u65b9\u6cd5\u3002<br \/>&nbsp;<br \/>\u683c\u5965\u5c14\u683c\u00b7\u5eb7\u6258\u5c14Georg Cantor<\/p>\n<div class=\"post-image\"><img class=\"rich_pages\" data-ratio=\"1.3513513513513513\" data-s=\"300,640\" data-type=\"jpeg\" data-w=\"1184\"  style=\"box-sizing: border-box !important;overflow-wrap: break-word !important;width: 339px !important;visibility: visible !important;\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-463fd616e2a6a15c2f159d2f52fee0b6.jpeg\"  \/><br \/>\u56fe8\uff1a\u683c\u5965\u5c14\u683c\u00b7\u5eb7\u6258\u5c14Georg Cantor<br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><\/div>\n<p>\u5fb7\u56fd\u6570\u5b66\u5bb6\uff0c\u521b\u7acb\u4e86\u73b0\u4ee3\u96c6\u5408\u8bba\uff0c\u662f\u5b9e\u6570\u7cfb\u4ee5\u81f3\u6574\u4e2a\u5fae\u79ef\u5206\u7406\u8bba\u4f53\u7cfb\u7684\u57fa\u7840\uff0c\u6784\u9020\u4e86\u4e09\u5206\u5eb7\u6258\u5c14\u96c6\u3002<br \/>&nbsp;<br \/>\u6d77\u91cc\u683c\u00b7\u51af\u00b7\u79d1\u8d6b Helge von Koch<\/p>\n<div class=\"post-image\"><img class=\"rich_pages\" data-ratio=\"1.3577712609970674\" data-s=\"300,640\" data-type=\"jpeg\" data-w=\"341\"  style=\"box-sizing: border-box !important;overflow-wrap: break-word !important;width: 341px !important;visibility: visible !important;\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-cc27ebc43ee7af9abb44dc656b86afd5.jpeg\"  \/><br \/>\u6d77\u91cc\u683c\u00b7\u51af\u00b7\u79d1\u8d6b Helge von Koch<br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><\/div>\n<p>\u745e\u5178\u6570\u5b66\u5bb6\uff0c\u5728\u4ed61904\u5e74\u7684\u4e00\u7bc7\u8bba\u6587\u201c\u5173\u4e8e\u4e00\u4e2a\u53ef\u7531\u57fa\u672c\u51e0\u4f55\u65b9\u6cd5\u6784\u9020\u51fa\u7684\uff0c\u65e0\u5207\u7ebf\u7684\u8fde\u7eed\u66f2\u7ebf\u201d\uff08\u539f\u6587\u7684\u6cd5\u6587\u6807\u9898\u4e3a\uff1a\u201cSur une courbe continue sans tangente, obtenue par une construction g\u00e9om\u00e9trique \u00e9l\u00e9mentaire\u201d\uff09\u4e2d\uff0c\u4ed6\u63cf\u8ff0\u4e86\u79d1\u8d6b\u66f2\u7ebf\u7684\u6784\u9020\u65b9\u6cd5\u3002<br \/>&nbsp;<br \/>\u74e6\u8328\u74e6\u592b\u00b7\u8c22\u5c14\u5bbe\u65af\u57fa Wac\u0142aw Sierpi\u0144ski<\/p>\n<p><img class=\"rich_pages\" data-ratio=\"0.75\" data-s=\"300,640\" data-type=\"jpeg\" data-w=\"960\"  style=\"box-sizing: border-box !important;overflow-wrap: break-word !important;width: 677px !important;visibility: visible !important;\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-2c91cf76372d165da1836f4597ed59c3.jpeg\"  \/><br \/>\u74e6\u8328\u74e6\u592b\u00b7\u8c22\u5c14\u5bbe\u65af\u57fa Wac\u0142aw Sierpi\u0144ski<br \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br \/>\u6ce2\u5170\u6570\u5b66\u5bb6\uff0c\u56e0\u5bf9\u96c6\u5408\u8bba\u3001\u6570\u8bba\u3001\u51fd\u6570\u7684\u7406\u8bba\u548c\u62d3\u6251\u5b66\u7684\u51fa\u8272\u8d21\u732e\u800c\u95fb\u540d\u3002\u4e24\u4e2a\u8457\u540d\u7684\u5206\u5f62\u662f\u6839\u636e\u4ed6\u7684\u540d\u5b57\u547d\u540d\uff1a\u8c22\u5c14\u5bbe\u65af\u57fa\u4e09\u89d2\u5f62\u548c\u8c22\u5c14\u5bbe\u65af\u57fa\u5730\u6bef\uff1b\u53e6\u5916\u8fd8\u6709\u8c22\u5c14\u5bbe\u65af\u57fa\u6570\u548c\u8c22\u5c14\u5bbe\u65af\u57fa\u95ee\u9898\u4e5f\u662f\u4ee5\u4ed6\u7684\u540d\u5b57\u547d\u540d\u3002<br \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br \/>\u8d39\u5229\u514b\u65af\u00b7\u8c6a\u65af\u591a\u592b&nbsp;Felix Hausdorff<\/p>\n<p><img class=\"rich_pages\" data-ratio=\"1.334\" data-s=\"300,640\" data-type=\"jpeg\" data-w=\"500\"  style=\"box-sizing: border-box !important;overflow-wrap: break-word !important;width: 386px !important;visibility: visible !important;\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-7543e6844971c58af9f849ab2cf62152.jpeg\"  \/><br \/>\u8d39\u5229\u514b\u65af\u00b7\u8c6a\u65af\u591a\u592b Felix Hausdorff<br \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br \/>\u5fb7\u56fd\u6570\u5b66\u5bb6\uff0c\u4ed6\u662f\u62d3\u6251\u5b66\u7684\u521b\u59cb\u4eba\u4e4b\u4e00\uff0c\u4ed6\u5b9a\u4e49\u548c\u7814\u7a76\u504f\u5e8f\u96c6\u3001\u8c6a\u65af\u591a\u592b\u7a7a\u95f4\u548c\u8c6a\u65af\u591a\u592b\u7ef4\uff0c\u8bc1\u660e\u8c6a\u65af\u591a\u592b\u6781\u5927\u5b9a\u7406\uff08Hausdorff maximality theorem\uff09\u3002\u63d0\u51fa\u4e86\u8c6a\u65af\u591a\u592b\u7ef4\u6570\u6765\u8ba1\u7b97\u5206\u5f62\u7ef4\u6570\u3002<\/p>\n<p><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/>11. \u76f8\u5173\u8d44\u6e90\u63a8\u8350<br \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><\/p>\n<p>\u4e66\u7c4d\u63a8\u8350<br \/>\u5206\u5f62\u5bf9\u8c61\uff1a\u5f62\u3001\u673a\u9047\u548c\u7ef4\u6570 Fractals:From,Chance,and Dimension<br \/>\u672c\u4e66\u8003\u5bdf\u548c\u7814\u7a76\u51fa\u73b0\u5728\u81ea\u7136\u754c\u4e2d\u7684\u82e5\u5e72\u5178\u578b\u5206\u5f62\u5bf9\u8c61\uff0c\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5173\u4e8e\u5206\u5f62\u7684\u5185\u5bb9\uff0c\u610f\u4e49\u53ca\u65b9\u6cd5\u7684\u627c\u8981\u4ecb\u7ecd\u3002\u5c3d\u7ba1\u81ea\u8be5\u4e66\u7b2c\u4e00\u7248\uff08\u6cd5\u6587\u7248\uff09\u95ee\u4e16\u4ee5\u6765\uff0c\u5206\u5f62\u7684\u7406\u8bba\u53ca\u5176\u5e94\u7528\u53d1\u5c55\u6781\u4e3a\u8fc5\u901f\uff0c\u5e76\u51fa\u73b0\u4e86\u5927\u91cf\u7684\u6709\u5173\u8457\u4f5c\uff0c\u4f46\u6b64\u4e66\u4ecd\u4e0d\u5931\u4e3a\u5206\u5f62\u7406\u8bba\u6700\u597d\u7684\u5165\u95e8\u4e66\u4e4b\u4e00<\/p>\n<p>\u5927\u81ea\u7136\u7684\u5206\u5f62\u51e0\u4f55 The Fractal Geometry of Nature&nbsp;<br \/>\u8fd9\u672c\u4e66\u4ecb\u7ecd\u4e86\u81ea\u7136\u754c\u4e2d\u5404\u79cd\u5404\u6837\u7684\u5206\u5f62\u7406\u8bba\uff0c\u4ece\u6d77\u5cb8\u7ebf\u3001\u96ea\u82b1\uff0c\u5230\u6cb3\u6d41\u3001\u661f\u7cfb\u7b49\u81ea\u7136\u73b0\u8c61\uff0c\u53bb\u9610\u8ff0\u5206\u5f62\u8fd9\u4e00\u6982\u5ff5\u3002\u4f5c\u4e3a\u591a\u4e2a\u5b66\u79d1\u7684\u4ea4\u53c9\uff0c\u5206\u5f62\u51e0\u4f55\u5bf9\u4ee5\u5f80\u6b27\u6c0f\u51e0\u4f55\u4e0d\u5c51\u4e00\u987e\uff08\u6216\u8bf4\u65e0\u80fd\u4e3a\u529b\uff09\u7684\u201c\u75c5\u6001\u201d\u66f2\u7ebf\uff08\u5982\u79d1\u8d6b\u96ea\u82b1\u66f2\u7ebf\u7b49\uff09\u7684\u5168\u65b0\u89e3\u91ca\uff0c\u662f\u4eba\u7c7b\u8ba4\u8bc6\u5ba2\u89c2\u4e16\u754c\u4e0d\u65ad\u5f00\u62d3\u7684\u5fc5\u7136\u7ed3\u679c\u3002\u8fd9\u8bf4\u660e\u6b27\u6c0f\u51e0\u4f55\u53ea\u662f\u5bf9\u5ba2\u89c2\u4e16\u754c\u7684\u8fd1\u4f3c\u53cd\u6620\uff0c\u800c\u5206\u5f62\u51e0\u4f55\u5219\u6df1\u5316\u4e86\u8fd9\u79cd\u8ba4\u8bc6\uff0c\u56e0\u6b64\u5206\u5f62\u51e0\u4f55\u5b66\u662f\u63cf\u8ff0\u5404\u79cd\u590d\u6742\u81ea\u7136\u66f2\u7ebf\u7684\u5927\u81ea\u7136\u7684\u51e0\u4f55\u5b66\u3002<\/p>\n<p>\u5e02\u573a\u7684\uff08\u9519\u8bef\uff09\u884c\u4e3a\uff1a\u98ce\u9669\u3001\u7834\u4ea7\u4e0e\u6536\u76ca\u7684\u5206\u5f62\u89c2\u70b9&nbsp;<br \/>The Misbehavior of Markets: A Fractal View of Financial Turbulence<br \/>\u300a\u5e02\u573a\u7684\uff08\u9519\u8bef\uff09\u884c\u4e3a\u300b\u4ee5\u5206\u5f62\u89c6\u89d2\u89c2\u5bdf\u91d1\u878d\u5e02\u573a\u7684\u884c\u4e3a\uff0c\u63a8\u7ffb\u4e86\u4f5c\u4e3a\u5f53\u4ee3\u91d1\u878d\u5206\u6790\u57fa\u7840\u7684\u201c\u968f\u673a\u6e38\u8d70\u201d\u7406\u8bba\u3002\u901a\u8fc7\u5206\u5f62\u6a21\u578b\uff0c\u5e02\u573a\u8868\u73b0\u88ab\u91cd\u65b0\u9610\u91ca\u3002\u672c\u4e66\u662f\u73b0\u4ee3\u91d1\u878d\u7406\u8bba\u6807\u51c6\u5de5\u5177\u548c\u6a21\u578b\u7684\u4e00\u6b21\u9769\u547d\u6027\u91cd\u4f30\uff0c\u4e66\u4e2d\u7684\u89c2\u70b9\u98a0\u8986\u4e86\u6210\u5343\u4e0a\u4e07\u6295\u8d44\u8005\u7684\u65e2\u6709\u89c2\u5ff5\u3002<\/p>\n<p>\u7f51\u7ad9\u8d44\u6e90<\/p>\n<p>\u5206\u5f62\u827a\u672f\u7f51<br \/>\u5206\u5f62\u827a\u672f\u7f51\u662f\u4e00\u4e2a\u5c55\u793a\u5206\u5f62\u827a\u672f\u4e4b\u7f8e\uff0c\u5b66\u4e60\u4ea4\u6d41\u5206\u5f62\u827a\u672f\u521b\u4f5c\u7684\u5e73\u53f0\uff0c\u5176\u4e2d\u5305\u542b\u4e86\u5f88\u591a\u5206\u5f62\u827a\u672f\u4f5c\u54c1\u53ca\u5206\u5f62\u8d44\u6e90\u63a8\u8350\u3002<\/p>\n<p>\u89c6\u9891\u8d44\u6e90<br \/>TED\u5206\u4eab\u89c6\u9891\uff1a\u4f2f\u52aa\u00b7\u74e6\u66fc\u5fb7\u5e03\u6d1b\u7279: \u5206\u5f62\u548c\u7c97\u7cd9\u7684\u827a\u672f Benoit Mandelbrot: Fractals and the Art of Roughness<br \/>Benoit Mandelbrot\u7684\u7814\u7a76\u4f7f\u4e16\u754c\u5bf9\u5206\u5f62\u6709\u4e86\u66f4\u6df1\u523b\u7684\u7406\u89e3\uff0c\u5206\u5f62\u662f\u7814\u7a76\u7c97\u7cd9\u7684\u5e7f\u6cdb\u800c\u6709\u529b\u7684\u5de5\u5177\uff0c\u5728\u81ea\u7136\u754c\u548c\u4eba\u7c7b\u7684\u4f5c\u54c1\u4e2d\u90fd\u662f\u5982\u6b64\u3002\u8be5\u89c6\u9891\u6982\u8ff0\u4e86\u5206\u5f62\u7684\u7814\u7a76\uff0c\u4ee5\u53ca\u5b83\u4eec\u4e3a\u8bb8\u591a\u9886\u57df\u5e26\u6765\u7684\u98a0\u8986\u6027\u89c1\u89e3\u3002<\/p>\n<p>TED\u5206\u4eab\u89c6\u9891\uff1aBenoit Mandelbrot: Fractals and the Art of Roughness \u4f2f\u52aa\u00b7\u74e6\u66fc\u5fb7\u5e03\u6d1b\u7279: \u5206\u5f62\u548c\u7c97\u7cd9\u7684\u827a\u672f\uff1a<br \/>http:\/\/www.ted.com\/talks\/benoit_mandelbrot_fractals_the_art_of_roughness.html<br \/>\u5bfb\u627e\u9690\u85cf\u7684\u7ef4 Hunting the Hidden Dimension<br \/>\u4ec0\u4e48\u662f\u7535\u5f71\u7279\u6548\uff0c\u80a1\u7968\u5e02\u573a\uff0c\u548c\u5fc3\u810f\u75c5\u7684\u5171\u540c\u70b9\uff1f\u5b83\u4eec\u8fde\u63a5\u4e86\u4e00\u4e2a\u9769\u547d\u6027\u7684\u65b0\u7684\u6570\u5b66\u5206\u652f\uff0c\u6539\u53d8\u4e86\u6211\u4eec\u770b\u4e16\u754c\uff0c\u5f00\u8f9f\u4e86\u5e7f\u9614\u7684\u65b0\u9886\u57df\uff0c\u4ee5\u79d1\u5b66\u7684\u5206\u6790\u548c\u7406\u89e3\u3002\u6570\u5b66\u5bb6\u4eec\u5f00\u53d1\u4e0d\u89c4\u5219\u788e\u7247\u5f62\u662f\u4ece\u5355\u7eaf\u7684\u597d\u5947\u5fc3\u5230\u63a5\u89e6\u51e0\u4e4e\u6bcf\u4e00\u4e2a\u5206\u79d1\u7684\u7406\u89e3\uff0c\u5305\u62ec\u6211\u4eec\u5b87\u5b99\u7684\u547d\u8fd0\u3002<br \/>\u7eaa\u5f55\u7247\uff1a<br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br \/>Hunting the Hidden Dimension \u5bfb\u627e\u9690\u85cf\u7684\u7ef4<br \/>https:\/\/www.bilibili.com\/video\/av13766486\/?p=2<\/p>\n<p>\u8bfe\u7a0b\u63a8\u8350<br \/>\u5206\u5f62\u7684\u4e16\u754c<br \/>\u5728\u6b64\u5802\u8bfe\u7a0b\uff0c\u4e3b\u8981\u4ecb\u7ecd\u4e86\u5173\u4e8e\u5206\u5f62\u7684\u601d\u60f3\u4e0e\u8109\u7edc\uff0c\u5206\u5f62\u73b0\u8c61\u3001\u5206\u5f62\u7ef4\u6570\u3001\u5229\u7528\u5206\u5f62\u89c4\u5f8b\u7684\u8ba1\u7b97\u65b9\u6cd5\u4ee5\u53ca\u6df7\u6c8c\u3002\u4e3b\u8bb2\u4eba\u4e3a\u5317\u4eac\u5e08\u8303\u5927\u5b66\u7cfb\u7edf\u5b66\u9662\u72c4\u589e\u5982\u6559\u6388\u3002\u72c4\u589e\u5982\u6559\u6388\u4e3b\u8981\u4ece\u4e8b\u590d\u6742\u7f51\u7edc\u548c\u7ecf\u6d4e\uff08\u91d1\u878d\uff09\u7269\u7406\u5b66\u7b49\u65b9\u9762\u7684\u7814\u7a76\uff0c\u662f\u56fd\u5185\u6700\u65e9\u4ece\u4e8b\u7ecf\u6d4e\u7269\u7406\u5b66\u7814\u7a76\u7684\u5b66\u8005\u4e4b\u4e00\u3002<\/p>\n<div class=\"post-image\"><img class=\"rich_pages\" data-ratio=\"0.38203125\" data-s=\"300,640\"  data-type=\"png\" data-w=\"1280\" style=\"\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-e45d0ad454af6bd7c092b2dd0578084f.png\"  \/><\/div>\n<p>\u5206\u5f62\u7684\u4e16\u754c\uff1a<br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br \/>https:\/\/campus.swarma.org\/course\/760<\/p>\n<p><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/>12. \u767e\u79d1\u9879\u76ee\u5fd7\u613f\u8005\u62db\u52df<br \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><\/p>\n<p>\u4f5c\u4e3a\u96c6\u667a\u767e\u79d1\u9879\u76ee\u56e2\u961f\u7684\u6210\u5458\uff0c\u672c\u6587\u5185\u5bb9\u7531\u8da3\u6728\u6728\u3001\u8584\u8377\u53c2\u4e0e\u8d21\u732e\u3002\u6211\u4eec\u4e5f\u4e3a\u6bcf\u4f4d\u4f5c\u8005\u548c\u5fd7\u613f\u8005\u51c6\u5907\u4e86\u4e13\u5c5e\u7b80\u4ecb\u548c\u4e2a\u4eba\u96c6\u667a\u767e\u79d1\u4e3b\u9875\uff0c\u66f4\u591a\u4fe1\u606f\u53ef\u4ee5\u8bbf\u95ee\u5176\u96c6\u667a\u767e\u79d1\u4e2a\u4eba\u4e3b\u9875\u3002<br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><\/p>\n<p><img class=\"rich_pages js_insertlocalimg\" data-ratio=\"0.5555555555555556\" data-s=\"300,640\"  data-type=\"jpeg\" data-w=\"900\" style=\"width: 463px;height: 257px;\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-56a0e2de574474b0433fa48809d90ba9.jpeg\"  \/><img class=\"rich_pages\" data-ratio=\"0.5555555555555556\" data-s=\"300,640\" data-type=\"png\" data-w=\"900\"  style=\"box-sizing: border-box !important;overflow-wrap: break-word !important;width: 459px !important;visibility: visible !important;\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-d7af1216c585ebe937c77a639358a993.png\"  \/><br  \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br \/>\u4ee5\u4e0a\u5185\u5bb9\u90fd\u662f\u6211\u4eec\u505a\u8fd9\u9879\u76ee\u7684\u8d77\u70b9\uff0c\u4f5c\u4e3a\u6765\u81ea\u4e0d\u540c\u5b66\u79d1\u548c\u9886\u57df\u7684\u5fd7\u613f\u8005\uff0c\u6211\u4eec\u5efa\u7acb\u8d77\u4e00\u4e2a\u6709\u6548\u7684\u767e\u79d1\u56e2\u961f\uff0c\u5206\u914d\u6709\u5ba1\u6821\u3001\u7ffb\u8bd1\u3001\u7f16\u8f91\u3001\u5ba3\u4f20\u7b49\u5de5\u4f5c\u3002\u6211\u4eec\u79c9\u6301\uff1a\u77e5\u8bc6\u4ece\u6211\u800c\u6765\uff0c\u95ee\u9898\u5230\u6211\u4e3a\u6b62\u7684\u4fe1\u5ff5\uff0c\u8ba4\u771f\u8d1f\u8d23\u7f16\u64b0\u6bcf\u4e00\u4e2a\u8bcd\u6761\u3002<br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br \/><img class=\"rich_pages\" data-ratio=\"0.5555555555555556\" data-s=\"300,640\" data-type=\"png\" data-w=\"900\"  style=\"box-sizing: border-box !important;overflow-wrap: break-word !important;visibility: visible !important;width: 677px !important;\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-96a62292ad1641ec07d2bdfec113a955.png\"  \/><br \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br \/>\u5728\u8fd9\u91cc\u4ece\u590d\u6742\u6027\u77e5\u8bc6\u51fa\u53d1\u4e0e\u4f19\u4f34\u540c\u884c\uff0c\u540c\u65f6\u6211\u4eec\u5e0c\u671b\u6709\u66f4\u591a\u5fd7\u613f\u8005\u52a0\u5165\u8fd9\u4e2a\u56e2\u961f\uff0c\u4f7f\u767e\u79d1\u8bcd\u6761\u5185\u5bb9\u5f97\u5230\u6269\u5145\uff0c\u5e76\u4e3a\u6bcf\u4f4d\u5fd7\u613f\u8005\u63d0\u4f9b\u76f8\u5e94\u5956\u52b1\u4e0e\u8d44\u6e90\uff0c\u5efa\u7acb\u4e2a\u4eba\u4e3b\u9875\u4e0e\u8d21\u732e\u8bb0\u5f55\uff0c\u4f7f\u5176\u80fd\u591f\u7ee7\u7eed\u63a2\u7d22\u590d\u6742\u4e16\u754c\u3002<br \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br \/>\u5982\u679c\u4f60\u6709\u610f\u53c2\u4e0e\u66f4\u52a0\u7cfb\u7edf\u7cbe\u7ec6\u7684\u5206\u5de5\uff0c\u626b\u63cf\u4e8c\u7ef4\u7801\u586b\u5199\u62a5\u540d\u8868\uff0c\u6211\u4eec\u671f\u5f85\u4f60\u7684\u52a0\u5165\uff01<br \/><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br \/><img class=\"rich_pages\" data-cropselx1=\"0\" data-cropselx2=\"562\" data-cropsely1=\"0\" data-cropsely2=\"312\" data-ratio=\"1\" data-s=\"300,640\" data-type=\"png\" data-w=\"500\"  style=\"box-sizing: border-box !important;overflow-wrap: break-word !important;visibility: visible !important;width: 188px !important;\" src=\"\/wp-content\/uploads\/2020\/12\/wxsync-2020-12-2362e8c744727da7bd820ef764b6029b.png\"  \/>\u96c6\u667a\u767e\u79d1\u62a5\u540d\u8868<br  \/>\u6765\u6e90\uff1a\u96c6\u667a\u767e\u79d1\u5ba1\u6821\uff1aLUX\u7f16\u8f91\uff1a\u66fe\u7965\u8f69<br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br  \/>\u63a8\u8350\u9605\u8bfb<a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247500519&amp;idx=1&amp;sn=0c45a8679b45286a9eeeeacab923fc50&amp;chksm=e897986adfe0117c0670e37efc6cdaf7091390625b9968bf201ddad75cb63b623cb42773ed68&amp;scene=21#wechat_redirect\" data-itemshowtype=\"0\" tab=\"innerlink\" style=\"text-decoration: underline;font-size: 14px;\" data-linktype=\"2\" rel=\"noopener noreferrer\">\u8c01\u662f\u6700\u201c\u590d\u6742\u201d\u7684\u5c0f\u8bf4\uff1a\u6587\u5b66\u53d9\u4e8b\u4e2d\u7684\u957f\u7a0b\u5173\u8054\u4e0e\u591a\u91cd\u5206\u5f62<\/a><br style=\"max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;\"  \/><br \/><a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247526490&amp;idx=3&amp;sn=cfc69afd00e6cff9a0dd17c5c1a16101&amp;chksm=e89732d7dfe0bbc12f1826c76d7c5a4ebd07b65c0644979a220d03221eef65194a860d9e889a&amp;scene=21#wechat_redirect\" textvalue=\"\u4ec0\u4e48\u662f\u5143\u80de\u81ea\u52a8\u673a\uff1f| \u96c6\u667a\u767e\u79d1\" data-itemshowtype=\"0\" tab=\"innerlink\" data-linktype=\"2\" hasload=\"1\" style=\"text-decoration: underline;-webkit-tap-highlight-color: rgba(0, 0, 0, 0);cursor: pointer;max-width: 100%;font-size: 14px;box-sizing: 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