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1878 - 1929
Pierre Fatou began his studies
on mathematics in 1898 at the Ecole Normale Supérieure in Paris. After
the exams in 1901 he applied for a job at the observatory in Paris; he thought,
that it would be useless to wait for a position as mathematician. He got the
job, but nevertheless he continued on his thesis about integration and complex
function theory. This having finished 1906, he got his doctorate in 1907.
In 1915 the Académie des Sciences published the topic of her "Grand
Prix" for 1918. It should be a study regarding Iterations. The Académie
des Sciences hoped for a continuation on Montel’s concept about "normale
(Abbildungs-)Familien". So Fatou wrote an extensive paper covering a fundamental
theory about Iterations. One assumes his intention to take part at this "Grand
prix". Nobody was astonished, that other mathematicians took part, since
the question had been published. So Gaston Julia developed the same theory on
a very similar base.
Later it was obvious that these two mathematicians worked on the very same problem going a different way. When submitting the two papers some strange things happened, it is difficult to see there the light. Seemingly Fatou did not participate at the contest, but anyway, later he was honored.
It seems that Fatou did not really treat fractals, but he prepared basics for the researches of Julia and Mandelbrot. Nevertheless, Julia sets from outside the Mandelbrot set are called "Fatou Dust". My Julia-programm allows to draw such structures, but since it dyes values between maximum and minimum, these "dusts" do not appear as lots of separated spots.
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1893 - 1978
Gaston M. Julia was born february 3 1893 at Sidi Abbès in Algeria. When going to the elementary school he already attracted attention due to his intelligence. However, he started studying until at August 4 of 1914 he got his call-up orders. And our soldier Julia became corporal and then lieutenant, and in this charge he led his troops to an action that should become a really fierce fighting. Then suddenly he was hit by a bullet that injured his face and teared him off the nose. Back at the barracks he was not able to speak, so he wrote to a scrap that he would not like to be exempted from military service and so he went to the military hospital where doctors tried to cobble him together again.
It should become a time of horrible pains. And to leave them behind, he buried himself into a mathematical problem: it was the behavioral pattern of the formula behind the so called Julia fractal. After his discharge from the hospital - the war was over then - he published a booklet of some 200 pages: "Mémoire sur l'iteration des fonctions rationelles". This book made him to receive the Grand Prix from the Académie des Sciences and brought him great respect from recommended mathematicians. Later he became lecturer at the Ecole Polytechnique. 1925 seminars were held in Berlin to study his discoveries more thoroughly. However, since there were no computers yet, Julia and his work fell into oblivion.
It was Prof. Benoît B. Mandelbrot to rediscover Julia. Shortly before his death (March 19. 1978) Mandelbrot picked up Julia’s discoveries and continued on it.
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1924 -
Benoît B. Mandelbrot was born november 20. 1924 in Poland. His father was a trader on clothing, his mother was a medical doctor. Benoît was introduced already as a youngster into mathematics by two uncles.
The family Mandelbrot emigrated to France in 1936. Szolem Mandelbrojt, an uncle of Benoît and professor of mathematics at the Collège de France took care of its education. The influence of Szolem was positive as well as negative, since he was a great admirer of Hardy and his mathematical philosophy. That is the reason for the aversion Mandelbrot developed to theoretical mathematics; however, he was able to understand Hardy’s aversion to applied mathematics. As a fanatic pacifist he was of the opinion that this science during war times might become a really dangerous tool.
Now Mandelbrot went to
the Lycée Rolin at Paris till the second world war broke out. Then his
family moved to Tulle in central France. Due to war he was not able to attend
school regularly, so he learned much as an adjudicate. This strange education
turned out to be an advantage: His noteworthy intuition on geometry and his
powers of imagination enabled many understandings of mathematical problems.
He begun his studies at the Ecole Polytechnique (Palaiseau/Paris) in 1944, where
he was educated among others by Gaston Julia and Paul Lévi, the latter
having much influenced him. Later he first went to the California Institute
or Technology, then to the Institute of Advanced Study at Princetown, where
he was supported by John von Neumann. He obtained his doctorate 1952 at the
University of Paris.
In the year 1958 he went for good to the USA. He started working for IBM at
the famous laboratories in Yorktown Heights, New York State.
At IBM Mandelbrot had the possibility to follow many interesting ideas. Later he said that no university could have given him that freedom to select among research topics.
It was 1945 that his uncle showed him the paper of Gaston Julia published 1918 and pretended this might be a source of interesting problems. But Mandelbrot was not interested yet.
But in the year 1970 came back to Julia’s paper. He worked then at the Watson Research Center of IBM where as first he displayed graphically a Julia set. To do so he not only had to find new mathematical principles but also to write one of the first computer programs displaying graphics.
He published this in the book "Les objets fractales: Forme, hasard et dimension" (1975), and more in-depth in "The fractal geometry of nature" (1982).
Mandelbrot treated many different fields. This was a firm decision he took in early years having the intention to contribute to the most different fields of science. It is noteworthy that he really succeeded. So his versatility gave him the chance to find fractales everywhere: in physics, in economics, in physiologics, in biologics.
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my notes
To tell the truth, Mr. Mandelbrot first got his muzzle too. Time was not ready yet and other mathematicians or physicist disliked chaos theories. They were chasing after a so called World Formula that would lead to understand and precalculate everything.
But slowly scientists now
begin to see that it is chaos that rules the world and that predictable events
are the exceptions.