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

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

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Mathematics Commons

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