Algorithms for classifying points in a 2-adic Mandelbrot set

Abstract

In her Ph.D. thesis, Jacqueline Anderson identified a nonarchimedean set similar in spirit to the Mandelbrot set which appears to exhibit a fractal-like boundary. We continue this research by presenting algorithms for determining when rational points lie in this set. We then prove that certain infinite families of points lie in (or out) of this set, giving greater resolution to the self-similarity present in this set.