Abstract
The color of a complex number is defined as the number of vertices of the convex hull of powers of that number. This induces a coloring of the unit disk. The structure of the set Λ of points where the color changes is investigated here. It is observed that there is a connection between this fractal set Λ and some family of trinomial equations. Three algorithms for coloring the unit disk are described, the last one (related to the Farey sequence) arising out of a conjecture. This conjecture is formulated and proved in this presentation.
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Communicated by C.A. Micchelli
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Dubuc, S., Malik, A. Convex hull of powers of a complex number, trinomial equations and the Farey sequence. Numer Algor 2, 1–32 (1992). https://doi.org/10.1007/BF02142203
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DOI: https://doi.org/10.1007/BF02142203