Benoit Mandelbrot, who discovered
mathematical shapes known as fractals, has died of cancer at the age of 85.
Mandelbrot, who had joint French and US
nationality, developed fractals as a mathematical way of understanding the
infinite complexity of nature.
The concept has been used to measure
coastlines, clouds and other natural phenomena and had far-reaching effects in
physics, biology and astronomy.
Mandelbrot’s family said he had died in
a hospice in Cambridge, Massachusetts.
The visionary mathematician was born
into a Jewish family in Poland but moved to Paris at the age of 11 to escape
He spent most of his life in the US,
working for IBM computers and eventually became a professor of mathematical
science at Yale University.
His seminal works, Fractals: Form,
Chance and Dimension and The Fractal Geometry of Nature, were published in 1977
and 1982. In these, he argued that seemingly random mathematical shapes in fact
followed a pattern if broken down into a single repeating shape.
The concept enabled scientists to
measure previously immeasurable objects, including the coastline of the British
Isles, the geometry of a lung or a cauliflower.
“If you cut one of the florets of a
cauliflower, you see the whole cauliflower but smaller,” he explained at
the influential Technology Entertainment and Design (TED) conference earlier
“Then you cut again, again, again,
and you still get small cauliflowers. So there are some shapes which have this
peculiar property, where each part is like the whole, but smaller.”
Fractal mathematics also led to
technological developments in the fields of digital music and image
It has also been influential in pop
culture, with the patterns being used to create beautiful and intricate pieces
of art. One such design is named in his honour.
Mandelbrot was also highly critical of
the world banking system, arguing the economic model it used was unable to cope
with its own complexity.
In a statement, French President Nicolas
Sarkozy praised Mandelbrot for his “powerful, original mind that never
shied away from innovation and battering preconceived ideas”.
“His work, which was entirely
developed outside the main research channels, led to a modern information
theory,” he said.