The Death Map: Reading Nature's Geometry

A talk presented to the SIAM Student Chapter,
Auburn University, 05 February 2009.

John Burkardt
Interdisciplinary Center for Applied Mathematics
Virginia Tech


  In the 1830's and 1840's, Victorian England was afflicted with
localized outbreaks of cholera.  The standard explanation was 
an invisible cloud of "bad air".  But a London doctor named 
John Snow blamed dirty water.  No one believed him, until he 
visited the sites of the outbreaks and drew the right kind of map.
When he showed it to the town council, they put a lock on the 
poisoned pump.

  Dr Snow had stumbled across an example of something we now
call a Voronoi diagram.  These mathematical objects can display
natural and social phenomena in which a large region or group
spontaneously organizes itself into smaller cells.  In some cases,
these cells will have a common shape and size.

  Voronoi diagrams have been used to classify the behavior of
competing ant colonies, the shape of patches on a giraffe's skin,
the structure of cells in human tissue.  Along the way, we will
encounter the related concepts of the Delaunay triangulation 
and a version of the Voronoi diagram that corresponds more
closely to the hexagonal patterns of nature.