Open Access Senior Thesis
Bachelor of Science
2021 Eleanor Devin Byrnes
Inspired by the fractals generated by the discretizations of the Continuous Newton Method and the notion of a fractional derivative, we ask what it would mean if such a fractional derivative were to replace the derivatives in Newton's Method. This work, largely experimental in nature, examines these new iterative methods by generating their Julia sets, computing their fractal dimension, and in certain tractable cases examining the behaviors using tools from dynamical systems.
Byrnes, Eleanor, "Fractals, Fractional Derivatives, and Newton-Like Methods" (2021). HMC Senior Theses. 244.