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.

• death_map_2009_auburn.tex
• death_map_2009_auburn.pdf

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.