Vol. 12, No. 6, 2019

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Algorithms for classifying points in a 2-adic Mandelbrot set

Brandon Bate, Kyle Craft and Jonathon Yuly

Vol. 12 (2019), No. 6, 969–994
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.

Keywords
$p$-adic Mandelbrot set, nonarchimedean dynamical systems
Mathematical Subject Classification 2010
Primary: 37P05, 11S82
Secondary: 11Y99
Milestones
Received: 27 July 2018
Revised: 8 January 2019
Accepted: 18 February 2019
Published: 3 August 2019

Communicated by Kenneth S. Berenhaut
Authors
Brandon Bate
Department of Mathematics
Houghton College
Houghton, NY
United States
Kyle Craft
Houghton College
Houghton, NY
United States
Jonathon Yuly
Houghton College
Houghton, NY
United States