death_map_2009_auburn
death_map_2009_auburn,
"The Death Map - Reading Nature's Geometry",
a talk to the SIAM Student Chapter at Auburn University
on 05 February 2009. My talk was
sponsored by Professor Yanzhao Cao.
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_auburn.txt.
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.
-
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 27 January 2009.