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第93行： − Mandelbrot created the first-ever "theory of roughness", and he saw "roughness" in the shapes of mountains, [[coastline]]s and [[river basin]]s; the structures of plants, [[blood vessel]]s and [[lung]]s; the clustering of [[galaxy|galaxies]]. His personal quest was to create some mathematical formula to measure the overall "roughness" of such objects in nature.<ref name=Mandelbrot />{{rp|xi}} He began by asking himself various kinds of questions related to nature: − 曼德布洛特创造了第一个“粗糙度理论”，他看到了山脉，海岸线和河流盆地形状的“粗糙度”。植物，血管和肺的结构的“粗糙度”；还有星系聚集的“粗糙度”。他个人的追求是创建一些数学公式来测量此类物体在自然界中的整体“粗糙度”。他首先问自己各种与自然有关的问题：+ + − Can [[geometry]] deliver what the Greek root of its name [geo-] seemed to promise—truthful measurement, not only of cultivated fields along the Nile River but also of untamed Earth?<ref name=Mandelbrot>Mandelbrot, Benoit (2012). ''The Fractalist: Memoir of a Scientific Maverick'', Pantheon Books. − 几何图形能否传达其希腊词根[geo-]所蕴含的内容，即追求真实的测量数据？不仅能测量尼罗河沿岸的耕地，还能测量未开发的土地？ + − In his paper titled [[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension]] published in [[Science (journal)|''Science'']] in 1967 Mandelbrot discusses [[self-similarity|self-similar]] curves that have [[Hausdorff dimension]] that are examples of ''fractals'', although Mandelbrot does not use this term in the paper, as he did not coin it until 1975. The paper is one of Mandelbrot's first publications on the topic of fractals.<ref>"Dr. Mandelbrot traced his work on fractals to a question he first encountered as a young researcher: how long is the coast of Britain?": Benoit Mandelbrot (1967). "[https://www.nytimes.com/2010/10/17/us/17mandelbrot.html?adxnnl=1&adxnnlx=1332064840-/vD0Sjafcl9t9BNghRf8Qw Benoît Mandelbrot, Novel Mathematician, Dies at 85] {{Webarchive|url=https://web.archive.org/web/20181231150228/https://www.nytimes.com/2010/10/17/us/17mandelbrot.html?adxnnl=1&adxnnlx=1332064840-%2FvD0Sjafcl9t9BNghRf8Qw |date=31 December 2018 }}", ''The New York Times''.</ref><ref name="Mandelbrot_Science_1967">{{cite journal | title=How long is the coast of Britain? Statistical self-similarity and fractional dimension | journal=Science | date=5 May 1967 | author=Mandelbrot, Benoit B. | pages=636–638 | volume=156 | issue=3775 | doi=10.1126/science.156.3775.636 | pmid=17837158 | url=http://users.math.yale.edu/~bbm3/web_pdfs/howLongIsTheCoastOfBritain.pdf | bibcode=1967Sci...156..636M | s2cid=15662830 | access-date=11 January 2016 | archive-date=13 July 2015 | archive-url=https://web.archive.org/web/20150713023120/http://www.sciencemag.org/content/156/3775/636 | url-status=live }}</ref>+ − − − 曼德布洛特在1967年《科学》杂志上发表的论文《英国的海岸线有多长？统计自相似性和分形维数How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension》中讨论了'''<font color="#ff8000"> 豪斯多夫维数Hausdorff dimension</font>'''的自相似曲线。这些都是分形的例子，尽管当时曼德布洛特在论文中并没有使用这个术语，因为他直到1975年才创造这个名词。该论文是曼德布洛特关于分形主题的第一批出版物之一。
→Fractals and the "theory of roughness" 分形与“粗糙度理论”
=== Fractals and the "theory of roughness" 分形与“粗糙度理论” ===
=== Fractals and the "theory of roughness" 分形与“粗糙度理论” ===
曼德布洛特创造了第一个“[[粗糙度理论]]”，他看到了山脉，[[海岸线]]和[[河流盆地形状]]的“粗糙度”。植物，血管和肺的结构的“粗糙度”；还有[[星系聚集]]的“粗糙度”。他个人的追求是创建一些数学公式来测量此类物体在自然界中的整体“粗糙度”<ref name=Mandelbrot />{{rp|xi}} 。他首先问自己各种与自然有关的问题：
[[几何图形]]能否传达其希腊词根[geo-]所蕴含的内容，即追求真实的测量数据？<ref name=Mandelbrot>不仅能测量尼罗河沿岸的耕地，还能测量未开发的土地？
In his paper titled [[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension]] published in [[Science (journal)|''Science'']] in 1967 Mandelbrot discusses [[self-similarity|self-similar]] curves that have [[Hausdorff dimension]] that are examples of ''fractals'', although Mandelbrot does not use this term in the paper, as he did not coin it until 1975. The paper is one of Mandelbrot's first publications on the topic of fractals.
曼德布洛特在1967年《科学》杂志上发表的论文《英国的海岸线有多长？统计自相似性和分形维数How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension》中讨论了'''<font color="#ff8000"> [[豪斯多夫维数]]Hausdorff dimension</font>'''的自相似曲线。这些都是分形的例子，尽管当时曼德布洛特在论文中并没有使用这个术语，因为他直到1975年才创造这个名词。该论文是曼德布洛特关于分形主题的第一批出版物之一。<ref>"Dr. Mandelbrot traced his work on fractals to a question he first encountered as a young researcher: how long is the coast of Britain?": Benoit Mandelbrot (1967). "[https://www.nytimes.com/2010/10/17/us/17mandelbrot.html?adxnnl=1&adxnnlx=1332064840-/vD0Sjafcl9t9BNghRf8Qw Benoît Mandelbrot, Novel Mathematician, Dies at 85] {{Webarchive|url=https://web.archive.org/web/20181231150228/https://www.nytimes.com/2010/10/17/us/17mandelbrot.html?adxnnl=1&adxnnlx=1332064840-%2FvD0Sjafcl9t9BNghRf8Qw |date=31 December 2018 }}", ''The New York Times''.</ref><ref name="Mandelbrot_Science_1967">{{cite journal | title=How long is the coast of Britain? Statistical self-similarity and fractional dimension | journal=Science | date=5 May 1967 | author=Mandelbrot, Benoit B. | pages=636–638 | volume=156 | issue=3775 | doi=10.1126/science.156.3775.636 | pmid=17837158 | url=http://users.math.yale.edu/~bbm3/web_pdfs/howLongIsTheCoastOfBritain.pdf | bibcode=1967Sci...156..636M | s2cid=15662830 | access-date=11 January 2016 | archive-date=13 July 2015 | archive-url=https://web.archive.org/web/20150713023120/http://www.sciencemag.org/content/156/3775/636 | url-status=live }}</ref>