Valuing Voronoi Visualization: Beauty and Scale Independence in Biological Spatial Point Tessellations
November 11, 2003
Nearest-neighbor diagrams, including Voronoi polygons and polyhedra, are
associated with biological phenomena such as growth, diffusion, division, packing, docking of ligands, strength of materials,
molecular folding, foraging behavior, predator avoidance,and crowding.
Nearest-neighbor diagrams were known in art and
science for centuries, but serious applications stemmed from the pioneering work of two mathematicians from the Ukraine,
Geogii Voronoi (1868--1908) and Boris Nikolaevich Delone ("Delaunay") (1890--1980).
We will illustrate the five-fold
approach of curricular reform in mathematics: (1) analytical (theorem/proof), (2) numerical, (3) symbolic, (4)
visual/graphical, and (5) applied to relevant scientific and social problems.
We will apply multiple methods for
constructing Voronoi polygons/polyhedra, Delaunay triangulations, and minimal spanning trees to epithelial cell boundaries,
fish boundaries on sandy lake bottoms, dragonfly wing venation, cross-sections of leaves, fiddler crab flocking behavior,
drug design, packing of side chains in polypeptides, bird territories, and forest canopies. Finally, we will compare
statistical analyses of Voronoi polygons and L-mosaics to determine whether nearest-neighbor or long-range interactions better
apply to a given set of biological data.
BioQUEST Staff Attending:
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