Mitchell Feigenbaum
Mitchell Jay Feigenbaum (born December 19 1944; Philadelphia, USA) is a mathematical physicist whose pioneering studies in chaos theory led to the discovery of the Feigenbaum constant.
The son of a Polish and a Ukrainian immigrant, Feigenbaum's education was not a happy one. Despite excelling in examinations, his schooling at Tilden High School, Brooklyn and the City College of New York seemed unable to stimulate his appetite to learn, and in 1964 he began graduate studies at the Massachusetts Institute of Technology. Enrolling to study electrical engineering, he changed to physics and was awarded a doctorate in 1970 for a thesis on dispersion relations under Francis Low.
After short positions at Cornell University and Virginia Polytechnic Institute, he was offered a longer-term post at Los Alamos National Laboratory to study turbulence. Although the group was ultimately unable to unravel the intractable theory of turbulent fluids, his research led him to study chaotic mappings.
Many mathematical mappings involving a single linear parameter exhibit apparently random behaviour known as chaos when the parameter lies in a certain range. As the parameter is increased towards this region, the mapping undergoes bifurcations at precise values of the parameter. At first there is one stable point, then bifurcating to oscillate between two points, then bifurcating again to oscillate between four points and so on. In 1975 Feigenbaum, using the HP-65 computer he was given, discovered that the ratio of the difference between the values at which such successive period-doubling bifurcations occur tends to a constant of around 4.6692. He was then able to provide a mathematical proof of the fact, and showed that the same behaviour and the same constant would occur in a wide class of mathematical functions prior to the onset of chaos. For the first time this universal result enabled mathematicians to take their first huge step to unravelling the apparently intractable "random" behaviour of chaotic systems. This "ratio of convergence" is now known as the Feigenbaum constant.
The Logistic map is a well known example of the mappings that Feigenbaum studied in his famous 1978 article: Quantitative Universality for a Class of Nonlinear Transfomations.
Feigenbaum's other contributions include important new fractal methods in cartography when he was hired by Hammond to develop techniques to allow computers to assist in drawing maps. The introduction to the Hammond Atlas (1992) states:
"Using fractal geometry to describe natural forms such as coastlines, mathematical physicist Mitchell Feigenbaum developed software capable reconfiguring coastlines, borders, and mountain ranges to fit a multitude of map scales and projections. Dr Feigenbaum also created a new computerised type placement program which places thousands of map labels in minutes, a task which previously required days of tedious labour."
In 1983 he was given a MacArthur Fellowship, and 1986 was awarded the Wolf Prize in Physics. He has been Toyota Professor at Rockefeller University since 1986.