Fractals are well known for the beauty of their computer-generated images, but these objects are even more intriguing when we study their properties and we explore their applications. From a mathematical viewpoint, the self–similarity structure of fractals leads to the idea of generating fractals through recursive processes. Because of the number of iterations involved, computers are indispensable; the mathematical tools that we chose for this project were two symbolic computation systems, Maple and Mathematica. Their powerful computation and graphic capabilities allowed us to examine and to generate a large number of fractals. This way we studied the perimeter-area relationship and the irregularity of fractals by computing the fractal dimension. In order to generate fractal images we wrote programs based on recursive equations. We also devoted a part of our work to applications, with special emphasis on fractals and chaos. We considered the chaos game and several examples from Biology, Physics and Economics.
|Presenter:||Sandra Lacea (Undergraduate Student)|
|Time:||9 am (Session I)|