Number Theory


On a Strange Class of Algebraic Numbers

Authors: Simon Plouffe

The iteration formula Z_(n+1)=Z_n^2+c of Mandelbrot will give an algebraic number of degree 4 when it converges most of the time. If we take a good look at some of these algebraic numbers: some of them have a very persistent pattern in their binary expansion. La formule d’itération de Mandelbrot Z_(n+1)=Z_n^2+c converge vers un nombre algébrique de degré 4 si c est un rationnel simple. Mais en regardant de près certains nombres algébriques en binaire on voit apparaître un motif assez évident et très persistant.

Comments: 9 Pages. The abstract in english and the main text in french

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Submission history

[v1] 2014-08-26 22:22:43

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