Benoit B. Mandelbrot, the Yale professor who gave the world mathematical tools to describe such complex phenomena as clouds and the patterns of leaves on trees, died last week at the age of 85.

The “father of fractal geometry,” Mandelbrot worked at Yale from 1987 until his retirement in 2004 as Sterling Professor Emeritus of Mathematical Sciences. He was living in Cambridge, Massachusetts, at the time of his death.

Until Mandelbrot, most mathematicians believed the irregular shapes found in nature were too fragmented or amorphous to be described mathematically. However in the 1960s and 1970s, Mandelbrot developed his concept of fractal geometry, which helped bring order to complex problems in physics, biology, and even financial markets.

“He contributed to mathematics and the sciences in an important but quite unusual way. He focused more on observations that pointed toward new directions, rather than on the more standard theorem-proving activity of mathematicians,” said Yair N. Minsky, professor and chair of mathematics at Yale. “His geometric observations showed that certain types of mathematical objects, which he termed fractals, rather than comprising a marginal class of monsters, were in fact quite naturally occurring in both mathematics and the sciences.”

Mandelbrot once observed that under magnification the coastline of Britain appears to be infinite: that now matter how close the observation the same irregular patterns keep appearing. The best way to describe the coastline mathematically is what he eventually called a fractal dimension.

His work led to a simple mathematic formula called the Mandelbrot set, which described the self-similarity of shapes found in irregular objects in nature and even galaxies.

Mandelbrot's earlier work combined linguistics and statistical thermodynamics, as well as mathematics and finance. In the 1960s he demonstrated that price fluctuations in markets are not smooth, as economists believed, but are often discontinuous and are always concentrated in time.

The mathematician's publications include the books "Les objets fractals" and "The Fractal Geometry of Nature," which have been translated into several languages.

Born in Poland, Mandelbrot moved with his family to France and studied at the Ecole Polytechnique in Paris. He held M.S. and Ae.E. degrees in aeronautics from the California Institute of Technology and a doctorate in mathematics from the University of Paris. In 1958, he began a long association with IBM's research laboratories in New York, where he is IBM Fellow Emeritus of the T.J. Watson Research Center.

Prior to his appointment as Sterling Professor in 2000, Mandelbrot was the Abraham Robinson Professor of Mathematics at Yale. He has held visiting professorships at Harvard University, the Albert Einstein College of Medicine and the University of Paris-Sud, among others.

A member of the National Academy of Sciences, Mandelbrot received many awards including the Wolf Prize in Physics and the Japan Prize.