更改

{{short description|French-American mathematician}}

{{short description|French-American mathematician}}

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.

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》于2012年死后出版。

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。

As a visiting professor at Harvard University, Mandelbrot began to study fractals called Julia sets that were invariant under certain transformations of the complex plane. Building on previous work by Gaston Julia and Pierre Fatou, Mandelbrot used a computer to plot images of the Julia sets. While investigating the topology of these Julia sets, he studied the Mandelbrot set which was introduced by him in 1979. In 1982, Mandelbrot expanded and updated his ideas in The Fractal Geometry of Nature.[21] This influential work brought fractals into the mainstream of professional and popular mathematics, as well as silencing critics, who had dismissed fractals as "program artifacts".

As a visiting professor at Harvard University, Mandelbrot began to study fractals called Julia sets that were invariant under certain transformations of the complex plane. Building on previous work by Gaston Julia and Pierre Fatou, Mandelbrot used a computer to plot images of the Julia sets. While investigating the topology of these Julia sets, he studied the Mandelbrot set which was introduced by him in 1979. In 1982, Mandelbrot expanded and updated his ideas in The Fractal Geometry of Nature.[21] This influential work brought fractals into the mainstream of professional and popular mathematics, as well as silencing critics, who had dismissed fractals as "program artifacts".

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，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，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The Fractal Geometry of Nature》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。

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":

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”，他被称为“分形之父”：

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Fractals: Form, Chance and Dimension》。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”，他被称为“分形之父”：

In his paper titled How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension published in Science in 1967 Mandelbrot discusses 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.

In his paper titled How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension published in Science in 1967 Mandelbrot discusses 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》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。

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。

*{{Annotated link|Zipf–Mandelbrot law}}

*{{Annotated link|Zipf–Mandelbrot law}}

* 1 / f噪声1/f noise –幅度与频率成反比的信号类型

* '''<font color="#ff8000"> 1 / f噪声1/f noise</font>''' –幅度与频率成反比的信号类型

* 分形维数Fractal dimension –一个比率，表示复杂度随比例变化的统计指标

* '''<font color="#ff8000"> 分形维数Fractal dimension</font>''' –一个比率，表示复杂度随比例变化的统计指标

* 分数布朗运动Fractional Brownian motion

* '''<font color="#ff8000"> 分数布朗运动Fractional Brownian motion</font>'''

* 英国海岸线有多长？– 伯努瓦 曼德布洛特的论文讨论了分形的性质（但内容未使用该术语）

* 英国海岸线有多长？– 伯努瓦 曼德布洛特的论文讨论了分形的性质（但内容未使用该术语）

* 赫斯特指数Hurst exponent – 衡量时间序列的长期依赖性

* '''<font color="#ff8000"> 赫斯特指数Hurst exponent</font>''' – 衡量时间序列的长期依赖性

* 峰度风险Kurtosis risk – 决策理论术语

* '''<font color="#ff8000"> 峰度风险Kurtosis risk</font>''' – 决策理论术语

* 间隙度Lacunarity – 几何和分形分析术语

* '''<font color="#ff8000"> 间隙度Lacunarity </font>'''– 几何和分形分析术语

* 劳伦斯·巴施里耶Louis Bachelier – 法国数学经济学先驱

* 劳伦斯·巴施里耶Louis Bachelier – 法国数学经济学先驱

* 曼德布洛特竞赛 – 高中数学竞赛

* 曼德布洛特竞赛 – 高中数学竞赛

* 多重分形系统Multifractal system – 具有多重分形维数的系统

* '''<font color="#ff8000"> 多重分形系统Multifractal system</font>''' – 具有多重分形维数的系统

* 自相似性Self-similarity – 对象的整体在数学上与其自身相似

* '''<font color="#ff8000"> 自相似性Self-similarity </font>'''– 对象的整体在数学上与其自身相似

* 七种随机状态Seven states of randomness – 随机性思想的概括

* '''<font color="#ff8000"> 七种随机状态Seven states of randomness</font>''' – 随机性思想的概括

* 偏度风险Skewness risk – 财务建模术语

* '''<font color="#ff8000"> 偏度风险Skewness risk</font>''' – 财务建模术语

* Zipf–曼德布洛特定律 – 离散概率分布

* Zipf–曼德布洛特定律 – 离散概率分布

*

*