A mathematician who transformed our understanding of "complex systems" - from the shape of clouds to the performance of the stock market - has died.
Benoît Mandelbrot was born into a Jewish family in Warsaw on 20 November 1924. His uncle Szolem Mandelbrojt, also a mathematician, moved to Paris around 1920, and Benoît's father followed him as an economic migrant. This decision, his son later wrote, had "the unanticipated eventual merit of saving our lives".
After spending much of the war in virtual hiding, Professor Mandelbrot completed his education at the Lycée Louis-le-Grand in Paris and the elite École Polytechnique.
He then secured a scholarship at the California Institute of Technology, returned to Paris, spent a year at Princeton's Institute for Advanced Study and a further period in France and Switzerland. In 1958, however, he joined IBM's research division.
Although he always stressed the influence of his uncle, Professor Mandelbrot's career turned out to be very different. While Szolem Mandelbrojt rapidly reached the pinnacle of the French academic establishment, his nephew claimed to have "fled from teachers and mentors, and even existing disciplines". IBM put few restraints on his wide-ranging interests, with his appointment as an IBM Fellow in 1974 explicitly granting him "freedom to choose and carry out work in areas related to (his) specialization in order to promote creative achievements".
Despite a number of visiting professorships, it was only after leaving IBM that he returned fully to the academy. He eventually became tenured as Yale University's Sterling professor of mathematical sciences at the age of 75.
In 1967, Professor Mandelbrot posed his celebrated question: "How long is the coast of Britain?" The answer, he suggested, was "It all depends" - on whether we include every bay, every bay within a bay, every tiny indentation, every stone or grain of sand.
Fractals offer a way of describing such phenomena, with their patterns of extraordinary complexity generated, he once explained, by "a simple iterative formula...that most children can program their home computers to produce".
Some of the core applications are explored in Professor Mandelbrot's best-selling 1982 work The Fractal Geometry of Nature, which includes some of the most beautiful images ever found in a maths book.
The implications for economics were spelled out in The (Mis)behavior of Markets: A Fractal View of Risk, Ruin and Reward (co-written with Richard L. Hudson, 2004). Its conclusions, Professor Mandelbrot believed, were largely vindicated by the banking crisis of 2008.
He died of pancreatic cancer on 14 October and is survived by his wife Aliette and two sons.