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refreshments by Mari at 3:30 in Mudd 412A
Chaos and Fractals: A Taste of Nonlinear Dynamics
This talk provides a trip into the world of nonlinear dynamics to view chaos and fractals in both continuous and discrete systems. The talk starts along a path of simple definitions and concepts that will provide the necessary background to understand chaos and fractals in a general sense. The talk then comes to a fork, a bifurcation perhaps, as it splits from a general overview into two specific examinations of chaos and fractals in two different types of systems: continuous and discrete. For continuous systems, the focus will be on the Lorenz equations and the notion of a strange attractor, looking at the butterfly effect in three dimensional space. For discrete systems, the goal is to comprehend the magnificent Mandelbrot set and its index of Julia sets through a series of interactive applets and pictures. In short, this talk will trace the mathematical path that leads to some of the most beautiful geometric shapes in mathematics.