哔咔漫画

1997 First Nagle Lecture

Robert Devaney
Chaos, Fractals, and Dynamics
February 13, 1997

 

Professor Devany is a Professor of Mathematics at Boston University.  He is a leading expert on dynamic systems, and a co-director of the NSF's Dynamical Systems and Technology Project, which shows teachers how to bring ideas from modern mathematics into the high school classroom.

Summary

In his talk, he led us through the maze of the Mandelbrot set, the most famous figure arising from the mathematical theory of chaos.  Carefully explaining the recursion that defines the picture, Devaney showed us how to recognize the various shapes and figures appearing on successively smaller and smaller scales.  The set gradually becomes less chaotic as we learned to count features to see where we were: there is actually regularity hiding there.  The audience enjoyed learning to identify the mathematics underlying each part of the picture, but our favorite part of the lecture no doubt was seeing an actual application of the way we always wanted to add fractions, for example, 1/2+1/3=2/5.  From the geometry, this addition tells us that in between the first periodic orbit of the period 2 and the first periodic orbit of period 3 lies the second periodic orbit of period 5.