ALPHABET SHMALPHABET:

OBIT: Benoit Mandelbrot: Benoit Mandelbrot, who died on October 14 aged 85, was largely responsible for developing the discipline of fractal geometry – the study of rough or fragmented geometric shapes or processes that have similar properties at all levels of magnification or across all times. (Daily Telegraph, 10/17/10)

Examining coastlines, he found that while the lines on maps featured bays, they did not feature the small bays that are within the bays, or the small structures within the small bays, and so on.

In a seminal essay entitled How Long Is the Coast of Britain? (1967), Mandelbrot showed that the answer to that question depends on the scale at which one measures it: the coastline grows longer as one takes into account first every bay or inlet, then every stone, then every grain of sand.

These patterns could not be explained by existing statistical methods, so Mandelbrot set about devising a system that would. Through the years that followed, he developed the concept of fractal geometry, codifying the "self-similarity" characteristics of many fractal shapes. (He coined the word "fractal" – from the Latin verb frangere, "to break" – in 1975). Mandelbrot's eclectic research ultimately led to a great breakthrough summarised by a simple mathematical formula: z = z² + c. This formula is now named after its inventor and is called the Mandelbrot set. Computer images of fractal shapes became popular on T-shirts and album covers.

First in isolated papers and lectures, then in The Fractal Geometry of Nature (1982), which has sold more copies than any other book of advanced mathematics, Mandelbrot argued that most traditional mathematical and classical geometric models were ill-suited to natural forms and processes. "Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line," he wrote.

Instead these phenomena and others, including variations in stock market prices, the fluctuations in turbulent fluids, geologic activity, planetary orbits, animal group behaviour, socioeconomic patterns and even music, can be modelled using fractals. The difference between the flower heads of broccoli and cauliflower, for example, can be exactly characterised in fractal theory.

The discipline of fractals came into its own in the computer age. It is now possible to create "fractal forgeries" of mountains, coastlines, trees, clouds, cell growth and other processes which bear an uncanny resemblance to the real thing. Applications range from digital compression in computers to finding the best mix of tyre ingredients, and from modelling turbulence on aircraft wing designs to texturing medical images.

Benoit B Mandelbrot (he awarded himself a middle initial, although it stood for nothing) was born on November 20 1924 in Warsaw, Poland, into a family of Lithuanian Jewish extraction. His father made his living selling clothes while his mother was a doctor, but the family had a strong academic tradition and, as a boy, Mandelbrot was introduced to mathematics by two uncles.

In 1936 Mandelbrot's family emigrated to France where one uncle, Szolem Mandelbrot, a Professor of Mathematics at the Collège de France, took responsibility for the boy's education. Mandelbrot attended the Lycée Rolin in Paris, but was not a good student; it was said that he never learned the alphabet (he could never use a telephone directory, for example), nor his multiplication tables past five.

At the outbreak of war, his family moved to Tulle, a small town to the south of Paris. There, the war, the constant threat of poverty and the need to survive kept him away from school and, in consequence, he was largely self taught.

At this time, French mathematical training and thinking was strongly analytic and abstract, dominated by an influential group of young formalist mathematicians who wrote under the pseudonym of Nicolas Bourbaki; Mandelbrot's uncle Szolem was a member of the "Bourbaki" set. In contrast to their approach, Mandelbrot visualised problems whenever possible, preferring geometry to abstract formalism.

Despite his poor performance at school, he found that he had a quite extraordinary ability to "visualise" mathematical questions and solve problems with leaps of geometric intuition rather than the "proper" established techniques of strict logical analysis.