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A Dynamical System Using the Voronoï Tessellation
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A Dynamical System Using the Voronoï Tessellation
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Journal Article
A Dynamical System Using the Voronoï Tessellation
2010
Overview
There are many good reasons to make a tiling around some discrete set of points. For example, maybe you need to know what regions are served by some set of post offices or cell phone satellites. Once you have a tiling, there are many reasons to define a point set with it. For instance, you might want to decorate each tile with a few points to create or destroy symmetry, or to obtain combinatorial information. Since you can go from point sets to tilings and back again, you might come across some interesting ways to associate one set of points to another. Once you have a map from a class of objects back to itself, you can take a dynamical systems viewpoint to analyze the situation. This paper does exactly that, with a new dynamical system based on the vertices of Voronoï tessellations.
