Fractal Geometry








Mandelbrot helped open our eyes to these shapes and he has changed our entire outlook on mathematics by doing so.


Benoit Mandelbrot was born on November 20, 1924 in Warsaw, Poland. His family believed strongly in education. His mother did not send him to school however so the. The beginning of his life he spent working and being taught by his family. His two uncles introduced him to the world mathematics and geometry.


In 1936 he moved to Paris where he was taught at a secondary school. At the start of World War II, Mandelbrot and his family moved to Tulle, France to avoid the Nazi regime. There he attended another secondary school. In 1944, after the war was over, he went to Paris.

Mandelbrot went to many colleges in the United States and France. He studied at Caltech, the University of Paris, Ecole Normale Supérieure, Ecole Polytechnique. He also learned at the Institute for Advanced Study in Princeton, the University of Geneva, and the University of Lille. He obtained many degrees and titles, such as a Ph.D, Professional Engineer in Aeronautics, and Master of Science. He joined the French Air Force, and visited the Massachusetts Institution of Technology where he was a research associate, then lecturer in electrical engineering, and then Institute Lecturer.

In 1958 Mandelbrot and his wife, Alitette, moved to the United States. Mandelbrot joined the research staff at the IBM Thomas J. Watson Research Center in Yorktown Heights, New York.


While working for IBM an error occurred in the system. Files were deleted, data was lost, and people could not communicate. IBM was using phone lines to send emails, and this was causing problems. Mandelbrot observed these errors on a graph and found the errors were coming in a pattern. If you viewed the errors over an hour, it would look the same as you viewed it in a minute, and for a second, and millisecond, and so on.


This reminded Mandelbrot about something that interested him as a child. His uncle had talked to him about papers written by a man named Gaston Julia. Mandelbrot studied these papers and started to think up the basics of fractal geometry.


Mandelbrot started to graph all the Julia Sets using a computer. He found the images to create strange patterns. In 1975 Mandelbrot coined the word “fractal.” Then in 1980 Mandelbrot came up with a formula, z1=z^2+c. This formula combined all of the Julia Sets. Mandelbrot put this formula into a computer, and iterated it over and over until he created an image. The fractal he made is now known as the Mandelbrot Set, the M Set for short.


Mandelbrot introduced his new geometry to mathematicians, who did not embrace the idea. To them fractals were just pictures. In response of being ridiculed for his idea he started to write a book, The Fractal Geometry of Nature. In this he explained what fractal geometry was and how it worked.





Mandelbrot created the Mandelbrot Set









Click to listen to "Mandelbrot Set by Jonathan Coulton"









The Mandelbrot Set formula is: