Computability in Europe 2006
Logical Approaches to Computational Barriers

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Regular Talk:
Hypercomputing the Mandelbrot Set?

Speaker: Petrus Hendrik Potgieter
Presentation: PHP_MandelbrotCiE2006Swansea_Jul2006.pdf
Slot: Tue, 11:10-11:30, Faraday C (col. 3)

Abstract

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 are treated much more thoroughly and technically elsewhere), two over the
computable reals (the Russian school and hypercomputation) and one model over
the rationals. 


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