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第48行： − Because of his access to IBM's computers, Mandelbrot was one of the first to use computer graphics to create and display fractal geometric images, leading to his discovery of the Mandelbrot set in 1980. He showed how visual complexity can be created from simple rules. He said that things typically considered to be "rough", a "mess", or "chaotic", such as clouds or shorelines, actually had a "degree of order".[10] His math and geometry-centered research career included contributions to such fields as statistical physics, meteorology, hydrology, geomorphology, anatomy, taxonomy, neurology, linguistics, information technology, computer graphics, economics, geology, medicine, physical cosmology, engineering, chaos theory, econophysics, metallurgy, and the social sciences.+ − − 由于曼德布罗特可以使用IBM的计算机，因此他是最早使用计算机图形来创建和显示分形几何图像的人之一。他于1980年发现了曼德布洛特集合。他展示了如何从简单的规则图形创建出视觉复杂的图形。他认为那些通常被认为是“粗糙”，“杂乱”或“混乱”的事物，例如云层或海岸线，实际上都具有“'''<font color="#ff8000"> 有序度Degree of order </font>'''”。他以数学和几何学为中心的延申研究领域包括了统计物理学，气象学，水文学，地貌学，解剖学，分类学，神经学，语言学，信息技术，计算机图形学，经济学，地质学，医学，物理宇宙学，工程学，混沌理论等领域的贡献 ，经济物理学，冶金学和社会科学。 − + − Toward the end of his career, he was Sterling Professor of Mathematical Sciences at Yale University, where he was the oldest professor in Yale's history to receive tenure.[12] Mandelbrot also held positions at the Pacific Northwest National Laboratory, Université Lille Nord de France, Institute for Advanced Study and Centre National de la Recherche Scientifique. During his career, he received over 15 honorary doctorates and served on many science journals, along with winning numerous awards. His autobiography, The Fractalist: Memoir of a Scientific Maverick, was published posthumously in 2012. − − 在他职业生涯后期，他是耶鲁大学数学科学系的斯特林教授，在那里他被授予了耶鲁历史上最年长的终身教授职位。曼德布罗特还在西北太平洋国家实验室，里尔-北法兰西院校联盟，普林斯顿高等研究院和法国国家科学研究中心担任过职务。他的自传《分形主义者:一个科学特立独行者的回忆录The Fractalist: Memoir of a Scientific Maveric》于2012年死后出版。 第67行：
第62行： − − Mandelbrot was born in a Lithuanian Jewish family, in Warsaw during the Second Polish Republic.[14] His father made his living trading clothing; his mother was a dental surgeon. During his first two school years, he was tutored privately by an uncle who despised rote learning: "Most of my time was spent playing chess, reading maps and learning how to open my eyes to everything around me."[15] In 1936, when he was 11, the family emigrated from Poland to France. The move, the war, and his acquaintance with his father's brother, the mathematician Szolem Mandelbrojt (who had moved to Paris around 1920), further prevented a standard education. "The fact that my parents, as economic and political refugees, joined Szolem in France saved our lives," he writes. −
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Because of his access to IBM's computers, Mandelbrot was one of the first to use computer graphics to create and display fractal geometric images, leading to his discovery of the [[Mandelbrot set]] in 1980. He showed how visual complexity can be created from simple rules. He said that things typically considered to be "rough", a "mess", or "chaotic", such as clouds or shorelines, actually had a "degree of order".<ref name="Wolfram" /> His math and geometry-centered research career included contributions to such fields as [[statistical physics]], [[meteorology]], [[hydrology]], [[geomorphology]], [[anatomy]], [[taxonomy (biology)|taxonomy]], [[neurology]], [[linguistics]], [[information technology]], [[computer graphics]], [[economics]], [[geology]], [[medicine]], [[physical cosmology]], [[engineering]], [[chaos theory]], [[econophysics]], [[metallurgy]], and the [[social science]]s.<ref>list includes specific sciences mentioned in [[#Hudson|Hudson & Mandelbrot]], the Prelude, p. xvi, and p. 26</ref>
Because of his access to IBM's computers, Mandelbrot was one of the first to use computer graphics to create and display fractal geometric images, leading to his discovery of the [[Mandelbrot set]] in 1980. He showed how visual complexity can be created from simple rules. He said that things typically considered to be "rough", a "mess", or "chaotic", such as clouds or shorelines, actually had a "degree of order".<ref name="Wolfram" /> His math and geometry-centered research career included contributions to such fields as [[statistical physics]], [[meteorology]], [[hydrology]], [[geomorphology]], [[anatomy]], [[taxonomy (biology)|taxonomy]], [[neurology]], [[linguistics]], [[information technology]], [[computer graphics]], [[economics]], [[geology]], [[medicine]], [[physical cosmology]], [[engineering]], [[chaos theory]], [[econophysics]], [[metallurgy]], and the [[social science]]s.<ref>list includes specific sciences mentioned in [[#Hudson|Hudson & Mandelbrot]], the Prelude, p. xvi, and p. 26</ref>
由于曼德布罗特可以使用IBM的计算机，他是最早使用计算机图形来创建和显示分形几何图像的人之一。他于1980年发现了曼德布洛特集合，展示了如何从简单的规则图形创建出视觉复杂的图形。他认为那些通常被认为是“粗糙”，“杂乱”或“混乱”的事物，例如云层或海岸线，实际上都具有“'''<font color="#ff8000"> 有序度Degree of order </font>'''”的性质。他以数学和几何学为中心的延申研究领域包括了统计物理学，气象学，水文学，地貌学，解剖学，分类学，神经学，语言学，信息技术，计算机图形学，经济学，地质学，医学，物理宇宙学，工程学，混沌理论等领域的贡献 ，经济物理学，冶金学和社会科学。
Toward the end of his career, he was [[Sterling Professor]] of Mathematical Sciences at [[Yale University]], where he was the oldest professor in Yale's history to receive tenure.<ref>{{cite web |author=Steve Olson |url=http://archives.yalealumnimagazine.com/issues/2004_11/mandelbrot.html |title=The Genius of the Unpredictable |publisher=Yale Alumni Magazine |date=November–December 2004 |access-date=22 July 2014 |author-link=Steve Olson (writer) |archive-date=22 October 2014 |archive-url=https://web.archive.org/web/20141022092605/http://archives.yalealumnimagazine.com/issues/2004_11/mandelbrot.html |url-status=live }}</ref> Mandelbrot also held positions at the [[Pacific Northwest National Laboratory]], [[Université Lille Nord de France]], [[Institute for Advanced Study]] and [[Centre National de la Recherche Scientifique]]. During his career, he received over 15 honorary doctorates and served on many science journals, along with winning numerous awards. His autobiography, ''The Fractalist: Memoir of a Scientific Maverick'', was published posthumously in 2012.
Toward the end of his career, he was [[Sterling Professor]] of Mathematical Sciences at [[Yale University]], where he was the oldest professor in Yale's history to receive tenure.<ref>{{cite web |author=Steve Olson |url=http://archives.yalealumnimagazine.com/issues/2004_11/mandelbrot.html |title=The Genius of the Unpredictable |publisher=Yale Alumni Magazine |date=November–December 2004 |access-date=22 July 2014 |author-link=Steve Olson (writer) |archive-date=22 October 2014 |archive-url=https://web.archive.org/web/20141022092605/http://archives.yalealumnimagazine.com/issues/2004_11/mandelbrot.html |url-status=live }}</ref> Mandelbrot also held positions at the [[Pacific Northwest National Laboratory]], [[Université Lille Nord de France]], [[Institute for Advanced Study]] and [[Centre National de la Recherche Scientifique]]. During his career, he received over 15 honorary doctorates and served on many science journals, along with winning numerous awards. His autobiography, ''The Fractalist: Memoir of a Scientific Maverick'', was published posthumously in 2012.
在他职业生涯后期，他担任耶鲁大学数学科学系的斯特林教授，并且被授予了耶鲁历史上最年长的终身教授职位。曼德布罗特还在西北太平洋国家实验室，里尔-北法兰西院校联盟，普林斯顿高等研究院和法国国家科学研究中心担任过职务。他的自传《分形主义者:一个科学特立独行者的回忆录The Fractalist: Memoir of a Scientific Maveric》于2012年死后出版。
Mandelbrot was born in a [[Lithuanian Jews|Lithuanian Jewish]] family, in [[Warsaw]] during the [[Second Polish Republic]].<ref>{{Cite news|last=Hoffman|first=Jascha|date=2010-10-16|title=Benoît Mandelbrot, Novel Mathematician, Dies at 85 (Published 2010)|language=en-US|work=The New York Times|url=https://www.nytimes.com/2010/10/17/us/17mandelbrot.html|access-date=2020-11-20|issn=0362-4331|archive-date=21 January 2017|archive-url=https://web.archive.org/web/20170121082521/http://www.nytimes.com/2010/10/17/us/17mandelbrot.html|url-status=live}}</ref> His father made his living trading clothing; his mother was a dental surgeon. During his first two school years, he was tutored privately by an uncle who despised [[rote learning]]: "Most of my time was spent playing chess, reading maps and learning how to open my eyes to everything around me."<ref name="wolf">{{cite web |last=Mandelbrot |first=Benoît |title=The Wolf Prizes for Physics, ''A Maverick's Apprenticeship'' |publisher=Imperial College Press |year=2002 |url=http://users.math.yale.edu/~bbm3/web_pdfs/mavericksApprenticeship.pdf |access-date=23 April 2012 |archive-date=3 December 2013 |archive-url=https://web.archive.org/web/20131203024639/http://users.math.yale.edu/~bbm3/web_pdfs/mavericksApprenticeship.pdf |url-status=live }}</ref> In 1936, when he was 11, the family emigrated from Poland to France. The move, the [[World War II|war]], and his acquaintance with his father's brother, the mathematician [[Szolem Mandelbrojt]] (who had moved to Paris around 1920), further prevented a standard education. "The fact that my parents, as economic and political refugees, joined Szolem in France saved our lives," he writes.<ref name=Mandelbrot />{{rp|17}}<ref name="bbc_obit">{{cite news|url=https://www.bbc.co.uk/news/world-europe-11560101|title=BBC News – 'Fractal' mathematician Benoît Mandelbrot dies aged 85|date=17 October 2010|work=[[BBC Online]]|access-date=17 October 2010|archive-date=18 October 2010|archive-url=https://web.archive.org/web/20101018045143/http://www.bbc.co.uk/news/world-europe-11560101|url-status=live}}</ref>
Mandelbrot was born in a [[Lithuanian Jews|Lithuanian Jewish]] family, in [[Warsaw]] during the [[Second Polish Republic]].<ref>{{Cite news|last=Hoffman|first=Jascha|date=2010-10-16|title=Benoît Mandelbrot, Novel Mathematician, Dies at 85 (Published 2010)|language=en-US|work=The New York Times|url=https://www.nytimes.com/2010/10/17/us/17mandelbrot.html|access-date=2020-11-20|issn=0362-4331|archive-date=21 January 2017|archive-url=https://web.archive.org/web/20170121082521/http://www.nytimes.com/2010/10/17/us/17mandelbrot.html|url-status=live}}</ref> His father made his living trading clothing; his mother was a dental surgeon. During his first two school years, he was tutored privately by an uncle who despised [[rote learning]]: "Most of my time was spent playing chess, reading maps and learning how to open my eyes to everything around me."<ref name="wolf">{{cite web |last=Mandelbrot |first=Benoît |title=The Wolf Prizes for Physics, ''A Maverick's Apprenticeship'' |publisher=Imperial College Press |year=2002 |url=http://users.math.yale.edu/~bbm3/web_pdfs/mavericksApprenticeship.pdf |access-date=23 April 2012 |archive-date=3 December 2013 |archive-url=https://web.archive.org/web/20131203024639/http://users.math.yale.edu/~bbm3/web_pdfs/mavericksApprenticeship.pdf |url-status=live }}</ref> In 1936, when he was 11, the family emigrated from Poland to France. The move, the [[World War II|war]], and his acquaintance with his father's brother, the mathematician [[Szolem Mandelbrojt]] (who had moved to Paris around 1920), further prevented a standard education. "The fact that my parents, as economic and political refugees, joined Szolem in France saved our lives," he writes.<ref name=Mandelbrot />{{rp|17}}<ref name="bbc_obit">{{cite news|url=https://www.bbc.co.uk/news/world-europe-11560101|title=BBC News – 'Fractal' mathematician Benoît Mandelbrot dies aged 85|date=17 October 2010|work=[[BBC Online]]|access-date=17 October 2010|archive-date=18 October 2010|archive-url=https://web.archive.org/web/20101018045143/http://www.bbc.co.uk/news/world-europe-11560101|url-status=live}}</ref>
曼德布洛特出生于波兰第二共和国时期，华沙的一个立陶宛犹太家庭。父亲以服装贸易为生，母亲是一名牙科医生。他入学后的前两年，一直由他叔叔私下辅导，这位叔叔尤其鄙视死记硬背的学习方法：“我的大部分时间都花在下棋，阅读地图和学习如何打开我的视角观察周围的一切。”后来1936年，他11岁时，一家人从波兰移民到了法国。这次移民，战争，和他父亲兄弟Szolem Mandelbrojt（数学家斯佐勒姆·曼德尔贝罗亚特，1920年左右移居巴黎）的接触，更进一步阻碍了他受到规范的教育。他曾写道：“我的父母作为经济和政治难民，在法国投靠了佐勒姆，因此而挽救了我们的生命。”
曼德布洛特出生于波兰第二共和国时期，华沙的一个立陶宛犹太家庭。父亲以服装贸易为生，母亲是一名牙科医生。他入学后的前两年，一直由他叔叔私下辅导，这位叔叔尤其鄙视死记硬背的学习方法：“我的大部分时间都花在下棋，阅读地图和学习如何打开我的视角观察周围的一切。”后来1936年，他11岁时，一家人从波兰移民到了法国。这次移民，战争，和他父亲兄弟Szolem Mandelbrojt（数学家斯佐勒姆·曼德尔贝罗亚特，1920年左右移居巴黎）的接触，更进一步阻碍了他受到规范的教育。他曾写道：“我的父母作为经济和政治难民，在法国投靠了佐勒姆，因此而挽救了我们的生命。”