death_map_2009_ajou
death_map_2009_ajou,
"The Death Map - Reading Nature's Geometry",
a talk to the Mathematics Department at Ajou University,
Suwon, Korea on 12 May 2009.
My talk was
sponsored by Professor Hyung-Chun Lee.
Despite the gruesome title, the subject was primarily
Voronoi diagrams, with a little information on their
properties and construction, and the creation of "centered"
or "centroidal" Voronoi diagrams.
A plain text abstract of the talk is available as
death_map_2009_ajou.txt.
Reference:
-
The John Snow web site
maintained by the UCLA School of Public Health at
https://www.ph.ucla.edu/epi/snow.html.
-
Eldridge Adams,
Territory Size and Shape in Fire Ants:
A Model Based on Neighborhood Interactions,
Ecology,
Volume 79, Number 4, June 1998, pages 1125-1134.
-
Franz Aurenhammer,
Voronoi diagrams -
a study of a fundamental geometric data structure,
ACM Computing Surveys,
Volume 23, Number 3, September 1991, pages 345-405.
-
George Barlow,
Hexagonal Territories,
Animal Behavior,
Volume 22, 1974, pages 876-878.
-
John Byers,
Dirichlet Tessellation of Bark Beetle Spatial Attack Points,
Journal of Animal Ecology,
Volume 61, 1992, pages 759-768.
-
John Byers,
Correct Calculation of Dirichlet Polygon Areas,
Journal of Animal Ecology,
Volume 65, 1996, pages 528-529.
-
Marc deBerg, Marc Krevald, Mark Overmars,
Otfried Schwarzkopf,
Computational Geometry,
Springer, 2000,
ISBN: 3-540-65620-0,
LC: QA448.D38.C65.
-
Qiang Du, Vance Faber, Max Gunzburger,
Centroidal Voronoi Tessellations: Applications and Algorithms,
SIAM Review,
Volume 41, Number 4, December 1999, pages 637-676.
-
Herbert Edelsbrunner,
Geometry and Topology for Mesh Generation,
Cambridge, 2001,
ISBN: 0-521-79309-2,
LC: QA377.E36.
-
Sandra Hempel,
The Strange Case of the Broad Street Pump,
University of California, 2007,
ISBN13: 978-0520250499,
LC: RA644.C3.H46.
-
Christian Icking, Rolf Klein, Peter Koellner, Lihong Ma,
A Java Applet for the Dynamic Visualization of Voronoi Diagrams,
https://www.pi6.fernuni-hagen.de/GeomLab/VoroGlide
-
Steven Johnson,
The Ghost Map,
Riverhead, 2006,
ISBN-13: 978-1594489259,
LC: RC133.G6.J64.
-
Lili Ju, Qiang Du, Max Gunzburger,
Probabilistic methods for centroidal Voronoi tessellations
and their parallel implementations,
Parallel Computing,
Volume 28, Number 10, October 2002, pages 1477-1500.
-
Atsuyuki Okabe, Barry Boots, Kokichi Sugihara, Sung Nok Chiu,
Spatial Tessellations:
Concepts and Applications of Voronoi Diagrams,
Second Edition,
Wiley, 2000,
ISBN: 0-471-98635-6,
LC: QA278.2.O36.
-
Joseph ORourke,
Computational Geometry,
Second Edition,
Cambridge, 1998,
ISBN: 0521649765,
LC: QA448.D38.
-
Robert Renka,
Algorithm 772:
STRIPACK: Delaunay Triangulation and Voronoi Diagram on the Surface
of a Sphere,
ACM Transactions on Mathematical Software,
Volume 23, Number 3, September 1997, pages 416-434.
-
Peter Vinten-Johansen, Howard Brody, Nigel Paneth,
Stephen Rachman, Michael Rip,
Cholera, Chloroform, and the Science of Medicine:
A Life of John Snow,
Oxford University Press, 2003,
ISBN: 019513544X,
LC: RA649.5.S66.S647.
The following files were used:
-
causeway1.png,
an image of the Giant's Causeway, showing how the hexagonal
pillars seem to form a staircase into the ocean;
-
causeway2.png,
an image of the Giant's Causeway from above, emphasizing the
roughly equal size and hexagonal shape of the "tiles", and
the irregularity of the pattern;
-
cholera_art.png,
an imaginative piece of artwork showing the spread of cholera,
which also illustrates the belief that it was spread through
"bad air";
-
cholera_spread.png,
a map of the world, showing the spread of cholera during the
seventh pandemic.
-
cube.png,
an image of a 3D cube, to illustrate Euler's Formula for
bounded polyhedrons.
-
cvt_movie2_0001.png,
frame 1 of an animation of a CVT computation in the square.
For the whole movie, refer to
CVT_MOVIE2.
-
cvt_movie2_0002.png,
frame 2 of an animation of a CVT computation in the square.
-
cvt_movie2_0010.png,
frame 10 of an animation of a CVT computation in the square.
-
cvt_movie2_0020.png,
frame 20 of an animation of a CVT computation in the square.
-
cvt_movie2_0040.png,
frame 40 of an animation of a CVT computation in the square.
-
cvt_movie2_0080.png,
frame 80 of an animation of a CVT computation in the square.
-
diamond_mountains.png,
a "mountain" plot of the diamond points shows the generators
as peaks, and the diagram lines as straight valleys, generated
by
VORONOI_MOUNTAINS.
-
diamond_pixel_plot_l1.png,
a pixel plot of the Delaunay triangulation of the diamond points,
generated by
VORONOI_PLOT, using the L1 distance. Some "mistakes" in the
plot are actually caused by the fact that for the L1 distance,
the boundary can consist of an area, rather than a line, that
is, for certain generators, a relatively huge (and area filling)
number of points can be equidistant from two generators. The plotting
routine doesn't spot this, but its results suggest what is happening.
-
diamond_pixel_plot_l2.png,
a pixel plot of the Delaunay triangulation of the diamond points,
generated by
VORONOI_PLOT, using the L2 distance.
-
diamond_points.png,
a set of 9 points, whose Voronoi diagram includes a "diamond",
generated using MATLAB.
-
diamond_voronoi.png,
the Voronoi diagram of the diamond points,
generated using MATLAB.
-
different_maps.png,
shows that, without the correct organizing principle, the
explanation for the cholera death data can be invisible.
-
drying_mud.png,
a photograph of drying mud shows a pattern of cracks which
suggests a Voronoi pattern, except that the mud drying is a
slow process, and the initial patterns seem to divide further
as the process proceeds.
-
fsu_logo.pdf,
a logo.
-
giraffe.png,
a photograph of a giraffe shows the distinctive pattern
of patches that have some features of a Voronoi diagram.
-
golden_square.png,
a map of the Golden Square area, where a highly localized
outbreak of cholera occurred in 1854, from the John Snow
archive and research companion site at
https://www.epi.msu.edu/johnsnow/index.html.
-
golden_square_detail.png,
a detail of the Golden Square map, showing the suspected
pump, and a dotted line around its "neighborhood", from
the John Snow archive and research companion site at
https://www.epi.msu.edu/johnsnow/index.html.
-
hundred_points.png,
a hundred points chosen randomly in the unit square,
generated using MATLAB.
-
hundred_voronoi.png,
a plot of the Voronoi diagram of the hundred points,
generated using MATLAB.
-
john_snow.png,
an image of Dr John Snow.
-
pump_memorial.png,
a photograph of the John Snow memorial in Broad Street,
which is a replica of the pump he identified as the source
of the epidemic.
-
pumps_map.png,
a map of the locations of pumps and deaths in the Golden Square
cholera epidemic.
-
pumpwomen.png,
a drawing of the Broad Street Pump, suggesting how local women
collected water in pumps for use at home.
-
random_mountains.png,
a "mountain" plot of a set of random points, tilted a bit, and
with a banded color map to emphasize contours, generated
by
VORONOI_MOUNTAINS.
-
star.png,
the figure of a star, used to illustrate Euler's formula.
-
tilapia_birth.png,
a photograph of tilapia "giving birth", showing why they
are called "mouthbreeders";
-
tilapia_nest.png,
a photograph of tilapia nests in a sandy bottom, from the paper
by Barlow.
Last revised on 10 February 2024.