Date of Submission

Spring 2018

Academic Programs and Concentrations


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.

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Open Access

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Mathematics Commons