death_map_2009_vt


death_map_2009_vt, "The Death Map", a talk to the students of Patricia Hammer from Hollins University, at Virginia Tech on 10 November 2009.

The subject was primarily Voronoi diagrams, with a little information on their properties and construction, and the creation of "centered" or "centroidal" Voronoi diagrams.

Abstract:

The markings on giraffes are an example of a peculiar kind of irregular pattern that recurs in many other situations, including cracks in drying mud, the territories of competing "tribes" of fire ants, and the network of discrete churning "cells" in boiling liquid. A mathematical structure can be abstracted from these different cases, and used to classify and understand new problems as well. The Voronoi diagram is one tool of the field of computational geometry, a subject you didn't study in high school! We will suggest some areas where the Voronoi diagram can provide insight, we will suggest some of its mathematical properties, talk about its extensions to other geometries, distances and dimensions. We will show a special kind of Voronoi diagram that arises when the defining center points are allowed to adjust themselves, and we will show how random numbers can be used to approximate this shape.

The following files were used:


Last revised on 13 February 2024.