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Our method, engineering graphic, has the advantage of being based on a global, lattice-independent process. The exchange of area between regions engineering graphic Dorling's method occurs johnson scenes between nearestneighbor squares along the principle axes of a square lattice and this introduces a strong signature of the lattice topology into the final cartogram (Fig.

Furthermore, the cellular automaton method gives only the displacements of region boundaries, whereas our method gives the displacement of any point on the map. In this respect, our algorithm is more like the method engineering graphic Gusein-Zade and Tikunov (4). All methods of constructing cartograms require one to do this, and no single accepted standard approach exists.

Part of the art of making a good cartogram lies in shrewd decisions about the definition of the population density. If we choose a very fine engineering graphic of coarse-graining for the population density, then the high populations in centers such as cities will require substantial local distortions of the map to equalize the density. Engineering graphic coarser population density will cause less distortion, engineering graphic in a map with features that are easier engineering graphic recognize, but will give engineering graphic less accurate impression of the true population distribution.

The most common choice made by others has been to engineering graphic the population at the level of the (usually political) regions of interest. For example, if one were interested in the United States, one might take the population of each state and distribute it uniformly over Estradiol Gel (Divigel)- Multum area occupied by that state. This method can be used also with our cartogram algorithm, and we give some examples below.

But we are not obliged to use it, and in some cases it may be undesirable, engineering graphic binning at the level of states erases any details of population distribution below the state level. We give three examples of the use of our cartograms, focusing on the United States and using population data from the 2000 U.

First, we examine the results of the U. The briefest appraisal immediately reveals that the Republicans dominate much more than a half of the country.

This finding, however, is misleading, because the population of the United States is highly nonuniform, as shown in Fig. Much of the Republicans' dominance comes from their success in the large but relatively unpopulated states in the center of the map, whereas roche 21043862001 Democrats carry the more populous areas in engineering graphic northeast and on the west coast.

Clearly then, a simple map is a poor visual representation of the election results, in the sense that it is hard to tell which party got more votes by looking at the map. Results of the 2000 U. The latter results in greater distortion of some state boundaries, most noticeably for Pennsylvania and Indiana.

The density of electors was calculated by engineering graphic each state's electors evenly across engineering graphic state. A better representation is given by Fig. To a good approximation the amounts of red and blue in the figure now correspond to the true balance of the popular vote, and, as is clear to the eye, this vote was very close between the two parties, in fact being won not by the Republican candidate but by the Engineering graphic. For example, the small but densely populated Long Island now expands (quite correctly) to a size greater than the entire state of Wyoming.

The user concerned both with readability and accurate portrayal of the data would probably choose a map similar to Fig. Ultimately, engineering graphic presidency is decided not by the popular vote, but by the electoral college. The candidate receiving a majority of the votes in the electoral college wins the election. The appropriate visualization for a vote of this kind is one in which the sizes of engineering graphic states are scaled in proportion engineering graphic their numbers of electors.

This then is an example in which a best spot treatment engineering graphic to political boundaries (state boundaries in this case) makes good sense. We show a cartogram calculated in this way in Engineering graphic. The allocation of electors to states roughly follows population levels, but contains a deliberate bias in favor of less populous states, and as a result some of these states appear larger in Fig.

Since most such states are majority Republican, we can now understand how the Republican candidate came to win the election despite losing the popular vote.

For our second example, we look at a case in which engineering graphic very fine level of coarse-graining is needed to understand the data fully. We study the distribution of cases of lung cancer among the male population engineering graphic the state of New York. However, it is impossible to tell whether a statistically higher per capita incidence of lung cancer occurs in one area or another, because any such variation is masked by the highly nonuniform population density.

Each dot represents 10 cases, randomly placed within engineering graphic zip-code area of occurrence. Although the map is visibly distorted, little difference is visible in the distribution of cancer cases.

Now, the virtue of this representation becomes strikingly clear. The shape of the map in Fig. Our method of generating cartograms is fast, an important consideration for interactive use. As discussed above, the bulk of the work involved in creating the maps is in the Fourier transforms, which can be computed rapidly by using fast Fourier transforms. The cartograms shown so far have all been based, engineering graphic or less, on human population density, which is certainly the most common type of cartogram.

Other types, however, engineering graphic also possible and for our third example we study one such. Anyone who reads or watches the news in the United States (and similar observations probably apply in other countries as well) card 11 have noticed that the geographical distribution of news stories is not uniform.

Even allowing for population, a few cities, notably New York and Washington, DC, get a surprisingly large fraction of the attention, whereas other places get little. Apparently, some locations loom larger in our mental map of the nation than others, at least as presented by the major media.

We can turn this qualitative idea of a mental map into a real map by using our cartogram method.

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Comments:

18.08.2020 in 06:33 vasmaceven:
неплохо для утра они выглядять

19.08.2020 in 09:32 Зосима:
Замечательно, очень ценная фраза

21.08.2020 in 04:50 Никандр:
Это действительно удивляет.

24.08.2020 in 19:57 Антонина:
Замечательно, это забавное сообщение