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:
-
cholera.png,
an image of the cholera bacteria.
-
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.
-
cvd_01.png
step 1 in a CVT calculation.
-
cvd_02.png
step 2 in a CVT calculation.
-
cvd_03.png
step 3 in a CVT calculation.
-
cvd_04.png
step 4 in a CVT calculation.
-
cvd_05.png
step 5 in a CVT calculation.
-
cvd_10.png
step 10 in a CVT calculation.
-
cvd_15.png
step 15 in a CVT calculation.
-
cvd_20.png
step 20 in a CVT calculation.
-
cvt_circle_nonuniform_step50.png,
an image of a CVT calculation on a circle with a nonuniform density.
-
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.
-
different_maps.png,
shows that, without the correct organizing principle, the
explanation for the cholera death data can be invisible.
-
fsu_logo.pdf,
a logo.
-
ghostmap_cover.png,
the cover of Steven Johnson's "The Ghost Map".
-
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
http://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
http://www.epi.msu.edu/johnsnow/index.html.
-
john_snow.png,
an image of Dr John Snow.
-
p36.txt,
the coordinates of 36 points.
-
p36_points.png,
an image of 36 points.
-
p36_voronoi.png,
an image of the Voronoi diagram of 36 points.
-
p9.txt,
the coordinates of 9 points.
-
p9_points.png,
an image of 9 points.
-
p9_voronoi.png,
an image of the Voronoi diagram of 9 points.
-
pixel_10.png
the output of the command pixel_plot(10,10).
-
pixel_100.png
the output of the command pixel_plot(100,100).
-
pixel_1000.png
the output of the command pixel_plot(1000,1000).
-
pixel_plot.m
a command to make a pixel plot of the Voronoi diagram of the 9 points.
-
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.
-
sphere.png,
an exact Voronoi diagram on a sphere.
-
sphere_generators.png,
Voronoi centers on a sphere.
-
sphere_voronoi.png,
an approximate Voronoi diagram on a sphere.
-
strange_case_cover.png,
the cover of Sandra Hempel's "The Strange Case of the Broad Street Pump".
-
usa_voronoi.png,
the USA after the state capitals were moved to the state centroids,
and then states were replaced by Voronoi cells.
-
voronoi_torus.png,
a Voronoi diagram on a torus.
Last revised on 13 February 2024.