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(1936). Rectangular Statistical Cartograms of the World. Journal of Geography: Vol. 35, No. 1, pp. 8-10.

Beyond the sheer hexagon, an image deeply rooted in mental representations of the French, publicity plays with more or less reinterpreted shapes., Au-delà du simple hexagone, largement ancré dans les cartes mentales des Français, la publicité joue sur la forme, plus ou moins réinterprétée., Más alia del simple hexágono, ampliamente aferrado en los mapas mentales de los franceses, la publicidad juega de la forma mas o menos reinterpretada., Mappemonde. Jeux de cartes. In: Mappemonde, 1986/4. p. 48.

An approach is presented to display and analyze epidemiologic data using population density equalized maps (cartograms). The algorithm for generating these maps is discussed. A specific method for statistically analyzing plotted data is given, followed by an application of maps and analysis to 73 sets of age-, race-, sex-, and site-specific cancer incidence data. The data were obtained from the Surveillance, Epidemiology and End Results project for San Francisco City/County (1978–1981) and combined with 1980 U.S. Census data.

The authors use 1981 census data to create a cartogram showing the counties of New Zealand in proportion to their population. (ANNOTATION)

The territorial or geographical series are used to present the geographical distribution of events. Such a presentation is possible only on a map of territorial division. Facts relating to each territorial unit or the sum of values corresponding to these facts are given; sometimes the intensity of a given phenomenon in each territory may be given instead. It may be the number of farms or the total area of arable land in each county, the number of traffic accidents in different precincts of a city, or the population density in different parts of a country. Each phenomenon may require its own type of territorial unit, the one that is most natural from its point of view. Each unit should be as uniform internally as possible, and the contrasts between one and another should appear between particular units. Cartogram is a map on which the geographical distribution of statistical phenomena is marked. As a base, a schematic map is commonly used. All the details that might obscure the statistical picture are usually removed. Very often only the administrative boundaries are marked.

The purpose of this article is to offer a develop ment of the demographic map as an alternative to the geographical base-map for the presentation of areal data in epidemiology. The results of geographical investigations into disease morbidity or mortality are often presented cartographically and invariably the base-map used is the normal geographical one, showing the relevant administrative areas. The relating of disease rates to area is useful, in that the recognition of areas characterized by high or low rates may lead to clues of aetiological significance. When considering areal patterns of disease, however, the epidemiologist requires information about the size of the population at risk in the areas concerned. Sutherland (1962) drew attention to the principal deficiency of the geographical base-map in this respect. Referring to Scotland, he showed that on the normal map correct weighting could not be given to the large urban populations which occupy small areas, whilst small rural populations, often sparsely distributed over large areas, could appear to be over-represented. Thus, base-maps which would relate disease rates to the local populations at risk as well as to geographical position might prove useful epidemiological tools. Development of the demographic map, in which the area of each administrative unit is made proportional to its population whilst contiguity of geographical boun daries and the relative geographical positions of the units are maintained as far as is possible (Hollings worth, 1966) offers interesting possibilities in this direction. The use of such maps in epidemiology is not new, Levison and Haddon (1965), for example, having used the technique for plotting cases of Wilm's tumour in New York State. To date, however, these maps have not been used to present data at the national level. Sutherland (1962) developed a form of demo graphic diagram, using the same principle of area proportional to population, called an isodemic representation. As a basis he split Scotland into its five hospital regions and showed them separated. He thus lost geographical contiguity between the administrative units, a condition it would seem desirable to preserve. An attempt has been made in developing the age sex specific cartograms illustrated below (Figs 1, 3, and 4) to relate disease rates to both the popula tion at risk and to geographical position in the 57 public health districts of Scotland.* A basic aim was also to try to produce cartograms similar to each other in local outline as well as in overall shape to make them readily comparable and hence of greater potential utility. Efforts to simplify their construc tion and final shape have also been made. To date demographic maps have presented complicated construction problems and their final appearance has often been of considerable complexity. These factors may well have obscured their advantages and contributed to their limited application so far.

Publisher Summary This chapter discusses the graphic presentation of various functions. An equation is represented by a curve if the equation is satisfied by the coordinates of every point on the curve and, mutatis mutandis, every pair of values satisfying the equation is represented by a point on the curve. In the graphic presentation of a time-series, primary interest attaches to the general trend of chronological variations in the values of the data and to fluctuations about the trend. Another type of ogive—the Lorenz curve—is particularly useful for the representation of income distributions. For the representation of simple classifications, bar charts are frequently used with a horizontal or vertical base line. For the representation of systems of three variables, stereograms are used, which show the aggregate of the points corresponding to the three variables in three-dimensional space. The cartogram is an ordinary geographical map on which the distribution in space of the characteristic considered is displayed by means of shading, coloring, images, and others.

Introduction Disease prevalence can be spatially analysed to provide support for service implementation and health care planning, these analyses often display geographic variation. A key challenge is to communicate these results to decision makers, with variable levels of Geographic Information Systems (GIS) knowledge, in a way that represents the data and allows for comprehension. The present research describes the combination of established GIS methods and software tools to produce a novel technique of visualising disease admissions and to help prevent misinterpretation of data and less optimal decision making. The aim of this paper is to provide a tool that supports the ability of decision makers and service teams within health care settings to develop services more efficiently and better cater to the population; this tool has the advantage of information on the position of populations, the size of populations and the severity of disease. Methods A standard choropleth of the study region, London, is used to visualise total emergency admission values for Chronic Obstructive Pulmonary Disease and bronchiectasis using ESRI’s ArcGIS software. Population estimates of the Lower Super Output Areas (LSOAs) are then used with the ScapeToad cartogram software tool, with the aim of visualising geography at uniform population density. An interpolation surface, in this case ArcGIS’ spline tool, allows the creation of a smooth surface over the LSOA centroids for admission values on both standard and cartogram geographies. The final product of this research is the novel Cartogram Interpolation Surface (CartIS). Results The method provides a series of outputs culminating in the CartIS, applying an interpolation surface to a uniform population density. The cartogram effectively equalises the population density to remove visual bias from areas with a smaller population, while maintaining contiguous borders. CartIS decreases the number of extreme positive values not present in the underlying data as can be found in interpolation surfaces. Discussion This methodology provides a technique for combining simple GIS tools to create a novel output, CartIS, in a health service context with the key aim of improving visualisation communication techniques which highlight variation in small scale geographies across large regions. CartIS more faithfully represents the data than interpolation, and visually highlights areas of extreme value more than cartograms, when either is used in isolation.

Typhetum laxmannii (Ubrizsy 1961) Nedelcu 1968 is a plant association new to Poland, built by an expansive kenophyte - Typha laxmannii Lepech. This paper presents the general distribution of both, the species and the association, paying particular attention to the area of Europe and Poland where, in recent years, many new locations as well as an increasing participation in vegetation cover have been observed. The habitat preferences of Typhetum laxmannii, the floristic composition of the association and its geographical differentiation within the occupied area are described. The current distribution of the association in Poland is presented on the cartogram map 10x10 km and possible expansion routes are suggested.

This paper presents a simple way to compensate the magnification effect of Self-Organizing Maps (SOM) when creating cartograms using Carto-SOM. It starts with a brief explanation of what a cartogram is, how it can be used, and what sort of metrics can be used to assess its quality. The methodology for creating a cartogram with a SOM is then presented together with an explanation of how the magnification effect can be compensated in this case by pre-processing the data. Examples of cartograms produced with this method are given, concluding that Self-Organizing Maps can be used to produce high quality cartograms, even using only standard software implemen-tations of SOM.

An experimental model animates contiguous computer cartograms by distorting the topological lengths of their edges. Using traffic information for the city of Lisbon, the authors distort a road map to depict traffic velocities. Areas of the city distend when velocities are low and compress when velocities are high. This model is applied to two visualizations: a trajectory visualization of vehicles, creating a temperature map for traffic velocities, and a figurative visualization that portrays Lisbon as a system of pulsing blood vessels. The proposed model can efficiently generate and animate edge-based cartograms with low representation errors.

N THE course of dealing with certain morphological questions' the writer encountered the problem of relief classification and mapping and cartographic expression of the extent to which relief is dissected. The commonly used method of giving absolute heights does not meet the need for clear-cut morphological expression, since altitude in itself fails to express sharpness of relief. This shortcoming has already been noted by other authors.2 The problem cartographers must solve, namely how to express three-dimensional relief with a two-dimensional medium, remains, though much progress has been made by the use of several methods in conjunction. One method of expressing relief morphologically is the "relief energy" cartogram; this seems to have been originated by Partsch in 1911 and adopted by Krebs, Schrepfer and Kallner, Smith, Waldbaur, and Thauer.3 To express "relief energy," all these authors employed the difference in altitude between the highest and lowest points within a defined area-that is, the relative altitude. The points (or pairs of points, used by Krebs) were measured by different authors in squares of different sizes (o.s-1o kilometers on a side) and on maps of different scales. Critics of this method objected to the lack of uniformity in the size of the squares and in the scale.4 Smith and Krebs used isopleths instead of squares. Thauer also opposed the use of the square as a unit area and suggested a circle instead. The method proposed in the present paper differs from previous ones in that, instead of the relative altitude within a defined area, it employs the ratio between the maximum relative altitude and the maximum absolute altitude within a defined area. An attempt is also made to analyze orographical data statistically, with a view to classification of the area and comparison with other areas. The Mt. Carmel region has been selected to demonstrate the method because of its mountainous character and its relative isolation from other landscape features.

T HE cartogram showing distribution of population by political divisions has obvious limitations: seldom is distribution uniform even for small areas. A method of approaching nearer the actual facts is attempted in the accompanying population map of Japan. The symbols used are circles and dots. The former represent the larger cities, 69 of which are distinguished.1 The area of the circles is proportional to the size of the cities, which range from 28,685 to 2,050,126. The population of these 69 cities subtracted from the total for the provinces2 leaves a remainder distributed in smaller cities, towns, and rural districts and here shown by dots. Each dot represents o,o000 persons, the scale being one-fourth that for the circles. In connection with the placing of the dots there were used (I) a hachured relief map on a scale of I:I,200,000 which showed, in addition to topography, the location of cities and towns; (2) the topographic map of the Imperial Geological Survey of Japan on a scale of I:I,ooo,ooo, showing, in addition to topography, the location of "cities, towns, small towns, villages, and hamlets"; (3) 280 topographic maps of the Imperial Geological Survey of Japan on scales varying from I:20,000 to 1:200,000, showing, in addition to topography, the use of the land in great detail; and (4) a sketch map for the province of Hokkaido, showing the distribution of cultivated land on the island in I9I4.3 These maps, together with numerous photographs and the relevant literature available, afforded helpful clues as to the detailed distribution of population. The map reflects the relation of the distribution and density of population to relief. The thickly populated plains stand out in sharp contrast to the sparsely peopled mountains. The Kwanto Plain, on the island of Honshiu, with about six million people, is

T HE idea of the statistical cartogram occurred to the author when he had occasion to prepare maps of the United States showing the distribution of various economic units, such as steel factories, textile mills, power plants, banks, etc. These maps were far too crowded in the northeast to be useful, while elsewhere, for the most part, they were relatively empty. If a way could be found to increase the scale of the northeastern region and reduce that of the west, distribution could be shown more clearly. Simple distortion of the map would be misleading, but, if we go a step farther, discard altogether the outlines of the country, and give each region a rectangular form of size proportional to the value represented, we arrive at the rectangular statistical cartogram. For purposes of comparison it is essential that a definite system of construction should be followed and identical arrangement should be used whatever values are represented. The system here used starts always with the larger divisions and by "proportionate halving" arrives at the smaller ones. It should be emphasized that the statistical cartogram is not a map. Although it has roughly the proportions of the country and retains as far as possible the relative locations of the various regions, the cartogram is purely a geometrical design to visualize certain statistical facts and to work out certain problems of distribution. Examples of these cartograms are given in the accompanying figures. The division into regions follows the usage of the United States Census Bureau, because only from this source are data available. If natural geographic regions could be used instead, the cartograms would be still more instructive.