Seminar 12/02/16: Ways of Seeing Julia Sets: Visualizing the forces that shape fractal Julia sets

Ways of Seeing Julia Sets: Visualizing the forces that shape fractal Julia sets
Ted Burke
School of Electrical and Electronic Engineering, DIT
Friday 12 February 2016
1pm, Blue Room, DIT Kevin Street

Abstract:

Early in the 20th century, work by mathematicians such as Pierre Fatou and Gaston Julia on complex dynamics led to the definition of so-called Julia sets. When a rational complex polynomial function is applied iteratively to a complex number, z, it produces a sequence of complex values called the orbit of z. Depending on the particular function and on the value of z, that orbit may or may not remain bounded. For a given function, the Julia set forms the boundary between those regions of the complex plane where the orbits remain bounded and those where they do not.

Intriguingly, even for quite simple iterative complex functions, Julia sets often take on very striking fractal shapes. With the aid of a computer, it is easy to visualize the Julia set of a function but, for most people, understanding why it takes on a fractal shape is difficult. In my own ongoing struggle to gain a more intuitive understanding of fractals, I have written many short computer programs to visualize them in different ways. In this presentation, I will explore some ways of visualizing Julia sets which I found helpful in understanding why they are fractal.