Date of Submission
Spring 2018
Academic Programs and Concentrations
Mathematics
Project Advisor 1
Jim Belk
Abstract/Artist's Statement
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.
Open Access Agreement
Open Access
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Recommended Citation
Liu, Yuan Jessica, "Graph Replacement Systems for Julia Sets of Quadratic Polynomials" (2018). Senior Projects Spring 2018. 139.
https://digitalcommons.bard.edu/senproj_s2018/139
This work is protected by a Creative Commons license. Any use not permitted under that license is prohibited.