2006/04/02 by Petrus H. Potgieter, Potgieter, Petrus H.
Computer Science · Mathematics · #Artificial intelligence #Cellular Automata and Applications #Computability #Computability, Logic, AI Algorithms #Computational Complexity (cs.CC) #Computer science #Decidability #Discrete mathematics #F.1.1 #FOS: Computer and information sciences #Fractal #Mandelbrot set #Mathematics #Object (grammar) #Programming language #Rational number #Set (abstract data type) #Simple (philosophy) #cs.CC #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.cs/0604003
published in arXiv (Cornell University) (Cornell University) · 11 pages, 2 figures
arxiv created 2006/04/02 · openalex publication_date 2006/04/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Mandelbrot set is an extremely well-known mathematical object that can be described in a quite simple way but has very interesting and non-trivial properties. This paper surveys some results that are known concerning the (non-)computability of the set. It considers two models of decidability over the reals (which have been treated much more thoroughly and technically by Hertling (2005), Blum, Shub and Smale, Brattka (2003) and Weihrauch (1999 and 2003) among others), two over the computable reals (the Russian school and hypercomputation) and a model over the rationals.