author={Waldo Tobler},
  journal={Annals of the New York Academy of Sciences},
  • W. Tobler
  • Published 1 November 1973
  • Mathematics
  • Annals of the New York Academy of Sciences
Suppose that one could stretch a geographical map so that areas containing many people would appear large, and areas containing few people would appear small. On a rubber map, for example, every person might be represented by an inked dot. We now imagine the rubber sheet to be stretched so that all the dots are at an equal distance from each other (see Ruston'). If such a map could be constructed, then all perfect political districts should be the same size, for they should contain equal… 

TEN Innovative Ways of Mapping Data About Places

Spatial information about the world and its people has always been at the forefront of visualization. Most people are used to conventional maps of their regions, countries and the world. Such

Analyzing geographic clustered response

A new DEMP algorithm is described, which avoids illegal overlapping of transformed polygons, finds the unique solution that minimizes map distortion, and can accept optional constraints such as fixed boundaries.

Fast flow-based algorithm for creating density-equalizing map projections

A flow-based algorithm whose equations of motion are numerically easier to solve compared with previous methods is introduced, allowing straightforward parallelization so that the calculation takes only a few seconds even for complex and detailed input.

From The Cover: Diffusion-based method for producing density-equalizing maps.

  • M. GastnerM. Newman
  • Physics
    Proceedings of the National Academy of Sciences of the United States of America
  • 2004
The method is conceptually simple and produces useful, elegant, and easily readable maps and is illustrated with applications to the results of the 2000 U.S. presidential election, lung cancer cases in the State of New York, and the geographical distribution of stories appearing in the news.

A New Construction Method for Circle Cartograms

An area cartogram is a transformed map on which areas of regions are proportional to statistical data values; it is considered to be a powerful tool for the visual representation of statistical data.

A New Algorithm for Continuous Area Cartogram Construction with Triangulation of Regions and Restriction on Bearing Changes of Edges

This study proposes a construction algorithm that involves triangulation of regions and regularization through restrictions on the bearing changes of the edges in order to obtain visually clear results and application to the USA population datasets reveals that the algorithm has mathematical clarity and is user friendly.

A mathematical model for political districting with compactness consideration and an application to Kentucky Senate districting

The basic redistricting problem is defined as aggregating a set of base (indivisible) units into contiguous geographical areas with almost equal voter population, called districts, and districts into

Density equalizing map projections: A new algorithm

A new DEMP algorithm is described, which avoids illegal overlapping of transformed polygons, finds the unique solution that minimizes map distortion and defines a continuous transformation over the entire map domain.

Mapping cancer: the potential of cartograms and alternative map displays

It is recommended that alternative displays are included in cancer atlases for a perceptually accurate display of the distribution of the burden of cancer over the population, in addition to the familiar choropleth map, if possible given time and budget constraints.

The Visualization of Local Urban Change across Britain

The author shows how the authors' pictures of space can be changed and argues why they should be and designs a particular solution for use in the visualization of high-resolution spatial social structure.



Geographic Area and Map Projections

BASIC truism of geography is that the incidence of phenomena differs from place to place on the surface of the earth. Theoretical treatises that assume a uniformly fertile plain or an even

The spectrum of U.S. 40

Theoretical Geography. 2nd edit

  • Geerlups Lund, Sweden
  • 1966

Map transformations of point patterns

  • Papers Regional Sci
  • 1971