Mandelbrot’s Fractals

Mandelbrot was one of the key figures responsible for the current interest in fractals, he demonstrated how Fractals occur in mathematics and in the natural world.

Mandelbrot studied a wide range of topics that seemed unrelated, from cotton commodity markets – linguistics and noise in telephone lines he came to see that all of these had mathematics in common, specifically Fractals. Mandelbrot’s work on fractals has contributed to chaos theory and to many applications in science and the world of mathematics.

Also included in his work he looked at the problem of measuring coastlines and proposed that their length depended on how you measure them. Go out into space, and they become a line or even a dot. But zoom in, and the closer you are to the detail of the coastline, the more indentations you see, even down to the raggedness of the rocks and the holes within rocks. Mandelbrot helped to coin the word ‘Fractals’ to describe ‘zooming-in’ to natural irregularities.

An interesting note he wrote on his discovery detailed his findings as such – “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. With the advent of computer technology he was able to investigate these irregularities in nature which helped him to develop the Mandelbrot’s set of fractals.

A cloud is made of billows upon billows upon billows that look like clouds. As you come closer to a cloud you don’t get something smooth, but irregularities at a smaller scale.

Benoit Mandelbrot

The studies have since allowed scientists to investigate various other avenues of Fractals including but not limited to – rock porosity, the strength of steel, the growth of lungs, the healthy heartbeat, the size – location and timing of natural disasters and, rather strangely, the irregular walking patterns of people with Parkinson’s disease. Fractals have inspired creativity in art that can be found in African art, digital art architecture and animations, composers such as Gyorgi Ligeti and Arvo Part also employ fractal techniques in their works. Fractals are also sometimes used in stock market prices.

Who was Benoit Mandelbrot?

He was born in Warsaw in 1924 to a Jewish family from Lithuania, though a little later in his life, specifically in 1936 when he was 11, the family fled from Poland to France.

Earlier it was stated that Mandelbrot was quite a strange intellectual in that he studied a range of topics that seemed unrelated, this falls apart however when one considers his turbulent upbringing which likely led to his interest in such a variety of topics.

His family was intellectual in nature, his mother was a doctor & his father a scholar who supported the family by laboring as a clothing manufacturer which makes sense as to why Mandelbrot would have had interest in the fluctuations in the cotton commodity markets.

His father worked in the clothing industry so obviously some parts of that trade would enter family discussion and spark interest in the impressionable Mandelbrot. He was taught mathematics by two of his uncles and although he went to good schools his education was interrupted during the Second World War and the subsequent German occupation through which his need for survival and fear for his life attributed to his ability for lateral thinking, he also stated that due to his unconventional education he had the time on his own to think and develop ideas. He claimed he had never learned the alphabet nor progressed beyond the five times table which is strange considering that on his retirement from the from the IBM group he became a Sterling Professor of Mathematical Science at Yale University.

Though he studies were interrupted during the Second World war he soon resumed studying in Paris and in 1945 attended the Ecole Polytechnique. From 1947 to 1949 he studied aeronautics at the California Institute of Technology afterwards returning to Paris where he would obtain a PhD in mathematical Sciences. From 1949 to 1958 Mandelbrot was a staff member of the Centre National de la Recherche Scientifique in Paris. In 1955 he married and moved to Geneva in Switzerland, later in 1958 he and his wife moved to the USA where he joined the IBM Thomas J. Watson Research Center in New York and being in an environment that encouraged explorations Mandelbrot remained there for 32 years, during this time becoming an ‘IBM Fellow’.

He was also made visiting professor of Mathematics and Economics at Harvard University and has also been awarded many prizes including the Legion of Honor in France and an asteroid – the 27500 Mandelbrot – was named after him.

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