March 15, 2019 - 1:30pm

**Title: **Julia Sets

**Abstract:** In numerical analysis, Newton’s Method (NM) is an iterative method used to approximate the roots of a function. We would like to understand how this method is related to the Julia Set of a function, which is the set of points that do not converge to any given solution. Thus, we implement NM for several functions of complex variables. Depending on the initial guess, the iteration will converge to one of the roots. Using the results acquired for a number of different initial guesses, we then generate a Julia Set for the corresponding function in question.

### Location

COB-1 276