Gabriel Weaver

Assisted Professor Gareth Roberts in his research on dynamical systems and numerical methods

Research included developing a program that showed where numerical methods fail on different functions. The functions studied were Pl(z) = (z-1)(z+1)(z-l) and Q(Z) = (z^n - 1)(z-l). The methods used were Newton's, Halley's and Konig's. The following images are screenshots from this program.

• A view of the parameter plane of Q(z) where n = 3.
• A view of the parameter plane of Q(z) where n = 48.
• A Mandelbrot set discovered in the parameter plane for Q(z) = (z^6 -1)(z-l).
• A nice closeup of a Mandelbrot set discovered during research.
• A Mandelbrot set discovered in the parameter plane for a function under Konig's Method.