Pierre Fatou was the first to define the Mandelbrot set.

Pierre Joseph Louis Fatou (28 February 1878, Lorient - 10 August 1929, Pornichet) was a French mathematician working in the field of complex analytic dynamics. He entered the École Normale Supérieure in Paris in 1898 to study mathematics and graduated in 1901 when he was appointed an astronomy post in the Paris Observatory. Fatou continued his mathematical explorations and studied iterative and recursive processes like Download high resolution version (1024x768, 207 KB)Another Mandelbrot set pic. ... Download high resolution version (1024x768, 207 KB)Another Mandelbrot set pic. ... A rendering of the Mandelbrot set: black points represent the stable points under the iterative map In mathematics, the Mandelbrot set is a fractal that is defined as the set of points c in the complex plane for which the iteratively defined sequence does not tend to infinity. ... February 28 is the 59th day of the year in the Gregorian calendar. ... 1878 (MDCCCLXXVIII) was a common year starting on Tuesday (see link for calendar). ... Lorient is a commune and a seaport of Brittany, France, in the Morbihan département, of which it is a sous-préfecture. ... August 10 is the 222nd day of the year (223rd in leap years) in the Gregorian Calendar. ... 1929 (MCMXXIX) was a common year starting on Tuesday (link will take you to calendar). ... This article is in need of attention from an expert on the subject. ... Complex dynamics is the study of dynamical systems for which the phase space is a complex manifold. ... The quadrangle at the main ENS building on rue dUlm is known as the Cour aux Ernests – the Ernests being the goldfish in the pond. ... The Eiffel Tower has become a symbol of Paris throughout the world. ... 1898 (MDCCCXCVIII) was a common year starting on Saturday (see link for calendar) of the Gregorian calendar (or a common year starting on Monday of the 12-day-slower Julian calendar). ... 1901 (MCMI) was a common year starting on Tuesday (see link for calendar) of the Gregorian calendar (or a common year starting on Wednesday of the 13-day-slower Julian calendar). ... Lunar astronomy: the large crater is Daedalus, photographed by the crew of Apollo 11 as they circled the Moon in 1969. ... gros pd]], enfoire at Nançay. ... Iteration is the repetition of a process, typically within a computer program. ... See: Recursion Recursively enumerable language Recursively enumerable set Recursive filter Recursive function Recursive set Primitive recursive function This is a disambiguation page — a list of pages that otherwise might share the same title. ...

, where Z is a number in the complex plane of the form , resulting in a series

Fatou was particularly interested in the case where Z₀ = 0, which was later analysed with computers by Benoit Mandelbrot to generate graphical representations of the behaviour of this series for each point, c, in the complex plane - now popularly called the Mandelbrot set. Beno t Mandelbrot was the first to use a computer to plot the Mandelbrot set. ... A rendering of the Mandelbrot set: black points represent the stable points under the iterative map In mathematics, the Mandelbrot set is a fractal that is defined as the set of points c in the complex plane for which the iteratively defined sequence does not tend to infinity. ...

Fatou wrote many papers developing a Fundamental theory of iteration in 1917, which he published in the December 1917 part of Comptes Rendus. His findings were very similar to those of Gaston Maurice Julia, who submitted a paper to the Académie des Sciences in Paris for their 1918 Grand Prix on the subject of iteration from a global point of view. Their work is now commonly referred to as the Generalised Fatou Julia theorem. Gaston Maurice Julia (February 3, 1893 – March 19, 1978) was a French mathematician who devised the formula for the Julia set. ...

See also

Fatou's lemma, Fatou set Fatous lemma establishes an inequality relating the integral (in the sense of Lebesgue) of the limit inferior of a sequence of functions to the limit inferior of the sequence of integrals of the functions. ... In mathematics, a Fatou set is defined informally as the largest open set of points on which iterations of a given map (or collection of maps) have relatively tame long-term behaviour, in the sense that points that start close together stay close together. ...

External link

• MacTutor biography