Date of Submission
Academic Programs and Concentrations
Project Advisor 1
Belk and Forrest construct a specific class of graph replacement systems that give sequences of graphs that converge to fractals. Given a polynomial, we have an algorithm that gives a replacement system that leads to a graph sequence which we conjecture converges to the Julia set. We prove the conjecture for the quadratic polynomial $z^2+c$ where $c$ is a real number and the critical point is in a three cycle. We present some additional results and observations on replacement systems obtained from certain polynomials.
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Liu, Yuan Jessica, "Graph Replacement Systems for Julia Sets of Quadratic Polynomials" (2018). Senior Projects Spring 2018. 139.