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→Research career 科研生涯
作为哈佛大学的客座教授，曼德布洛特开始研究名为'''<font color="#ff8000"> 朱莉娅集合Julia sets</font>'''的分形，这些分形在复杂平面的变换下依旧保持不变。在加斯顿·朱莉娅Gaston Julia和皮埃尔·法图Pierre Fatou先前工作的基础上，曼德尔布洛特使用计算机绘制出了朱莉娅集合的图像。在他研究这些朱莉娅集的拓扑时，他研究了他于1979年提出的曼德布洛特集。1982年，他在《大自然的分形几何学》一书中扩展并更新了他的思想。这项颇具影响力的著作将分形技术引入到专业数学和大众数学中，同时也进入到了那些将分形技术仅视为“程序工件”的批评者眼中。
作为哈佛大学的客座教授，曼德布洛特开始研究名为'''<font color="#ff8000"> 朱莉娅集合Julia sets</font>'''的分形，这些分形在复杂平面的变换下依旧保持不变。在加斯顿·朱莉娅Gaston Julia和皮埃尔·法图Pierre Fatou先前工作的基础上，曼德尔布洛特使用计算机绘制出了朱莉娅集合的图像。在他研究这些朱莉娅集的拓扑时，他研究了他于1979年提出的曼德布洛特集。1982年，他在《大自然的分形几何学》一书中扩展并更新了他的思想。这项颇具影响力的著作将分形技术引入到专业数学和大众数学中，同时也进入到了那些将分形技术仅视为“程序工件”的批评者眼中。
[[文件:Mandelbrot p1130876.jpg|缩略图|右|曼德布洛特在2006年法国荣誉军团勋章的提名演讲，当时他提到了曼德布洛特集合]]
[[文件:Mandelbrot p1130876.jpg|缩略图|右|曼德布洛特在2006年法国荣誉军团勋章的提名演讲，当时他提到了曼德布洛特集合]]
In 1975, Mandelbrot coined the term ''[[fractal]]'' to describe these structures and first published his ideas, and later translated, ''Fractals: Form, Chance and Dimension''.<ref>''Fractals: Form, Chance and Dimension'', by Benoît Mandelbrot; W H Freeman and Co, 1977; {{isbn|0-7167-0473-0}}</ref> According to computer scientist and physicist [[Stephen Wolfram]], the book was a "breakthrough" for Mandelbrot, who until then would typically "apply fairly straightforward mathematics ... to areas that had barely seen the light of serious mathematics before".<ref name=Wolfram>Wolfram, Stephen. [https://www.wsj.com/articles/SB10001424127887324439804578107271772910506 "The Father of Fractals"] {{Webarchive|url=https://web.archive.org/web/20170825102714/https://www.wsj.com/articles/SB10001424127887324439804578107271772910506 |date=25 August 2017 }}, ''Wall Street Journal'', 22 November 2012</ref> Wolfram adds that as a result of this new research, he was no longer a "wandering scientist", and later called him "the father of fractals":
In 1975, Mandelbrot coined the term fractal to describe these structures and first published his ideas, and later translated, Fractals: Form, Chance and Dimension.[22] According to computer scientist and physicist Stephen Wolfram, the book was a "breakthrough" for Mandelbrot, who until then would typically "apply fairly straightforward mathematics ... to areas that had barely seen the light of serious mathematics before".[10] Wolfram adds that as a result of this new research, he was no longer a "wandering scientist", and later called him "the father of fractals":
1975年，曼德布洛特创造了“分形”一词来描述这些结构，并首先发表了他的想法，其翻译为《分形：形式，机会和维度》。根据计算机科学家和物理学家斯蒂芬·沃尔夫拉姆Stephen Wolfram的说法，这本书对曼德尔布洛特来说是一个“突破”，他在那之前通常会“将相当简单的数学应用于……以前几乎没有看到过的严肃数学领域”。沃尔夫拉姆补充说，由于这项新研究，他不再是“流浪的科学家”，后来称他为“分形之父”：
Mandelbrot ended up doing a great piece of science and identifying a much stronger and more fundamental idea—put simply, that there are some geometric shapes, which he called "fractals", that are equally "rough" at all scales. No matter how close you look, they never get simpler, much as the section of a rocky coastline you can see at your feet looks just as jagged as the stretch you can see from space.
Mandelbrot ended up doing a great piece of science and identifying a much stronger and more fundamental idea—put simply, that there are some geometric shapes, which he called "fractals", that are equally "rough" at all scales. No matter how close you look, they never get simpler, much as the section of a rocky coastline you can see at your feet looks just as jagged as the stretch you can see from space.
曼德布洛特最终完成了一部伟大的科学著作。他找到了更强大，更根本的概念，简单地说，就是有些几何形状（他称之为“分形”）在各个尺度上都同样“粗糙”。不管您凑多近去看，它们都永远不会变得简单，就像您在脚下看到的多岩石的海岸线与从太空中看到的伸展部分一样参差不齐。
Wolfram briefly describes fractals as a form of geometric repetition, "in which smaller and smaller copies of a pattern are successively nested inside each other, so that the same intricate shapes appear no matter how much you zoom in to the whole. [[Fern|Fern leaves]] and [[Romanesco broccoli|Romanesque broccoli]] are two examples from nature."<ref name=Wolfram /> He points out an unexpected conclusion:
Wolfram briefly describes fractals as a form of geometric repetition, "in which smaller and smaller copies of a pattern are successively nested inside each other, so that the same intricate shapes appear no matter how much you zoom in to the whole. Fern leaves and Romanesque broccoli are two examples from nature."[10] He points out an unexpected conclusion:
沃尔夫拉姆简要地将分形描述为几何重复的一种形式，“在其中，越来越少的相同复制图案相继被嵌套在彼此内部，因此无论您放大多少，同样的复杂形状都会展现出来。蕨叶和罗马式西兰花是自然界的两个例子。“他指出了一个出乎意料的结论：
One might have thought that such a simple and fundamental form of regularity would have been studied for hundreds, if not thousands, of years. But it was not. In fact, it rose to prominence only over the past 30 or so years—almost entirely through the efforts of one man, the mathematician Benoit Mandelbrot.
One might have thought that such a simple and fundamental form of regularity would have been studied for hundreds, if not thousands, of years. But it was not. In fact, it rose to prominence only over the past 30 or so years—almost entirely through the efforts of one man, the mathematician Benoit Mandelbrot.
可能有人以为，这种简单而基本的规律性将被研究数百年甚至数千年，但事实并非如此。实际上，它仅在过去30多年中才受到关注，而且几乎完全是通过一个人的努力，即数学家伯努瓦 曼德布洛特。
Mandelbrot used the term "fractal" as it derived from the Latin word "fractus", defined as broken or shattered glass. Using the newly developed IBM computers at his disposal, Mandelbrot was able to create fractal images using graphics computer code, images that an interviewer described as looking like "the delirious exuberance of the 1960s [[psychedelic art]] with forms hauntingly reminiscent of nature and the human body". He also saw himself as a "would-be Kepler", after the 17th-century scientist [[Johannes Kepler]], who calculated and described the orbits of the planets.<ref>Ivry, Benjamin. [http://forward.com/articles/166094/benoit-mandelbrot-influenced-art-and-mathematics/?p=all "Benoit Mandelbrot Influenced Art and Mathematics"] {{Webarchive|url=https://web.archive.org/web/20130602171300/http://forward.com/articles/166094/benoit-mandelbrot-influenced-art-and-mathematics/?p=all |date=2 June 2013 }}, ''Forward'', 17 November 2012</ref>
Mandelbrot used the term "fractal" as it derived from the Latin word "fractus", defined as broken or shattered glass. Using the newly developed IBM computers at his disposal, Mandelbrot was able to create fractal images using graphics computer code, images that an interviewer described as looking like "the delirious exuberance of the 1960s psychedelic art with forms hauntingly reminiscent of nature and the human body". He also saw himself as a "would-be Kepler", after the 17th-century scientist Johannes Kepler, who calculated and described the orbits of the planets.
曼德布洛特使用了“分形”一词，因为它源自拉丁语 fractus”，意为碎玻璃。通过使用新开发的IBM计算机和图形计算机代码，曼德布洛特创建了分形图像，这些图像被采访者描述为“1960年代迷幻艺术的疯狂，其形式令人不禁联想到自然和人体”。他还将自己视为“未来的开普勒”（在17世纪，科学家约翰尼斯·开普勒Johannes Kepler计算并描述了行星的轨道）。
==Awards and honors==
==Awards and honors==