Waldo R. Tobler

Waldo R. Tobler (1930–2018) was an American-Swiss geographer and cartographer who developed the first law of geography and advanced analytical cartography.

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First law of geography: The principle that nearby things tend to be more related than distant things. Tobler formulated this concise statement of spatial dependence.
Cartogram: A map that distorts geographic area or distance to represent a variable or spatial relationship. Tobler developed computational methods for constructing cartograms.
Arthur H. Robinson: An American cartographer and geographer who shaped modern map design and cartographic education. Robinson’s cartographic scholarship provides a contemporaneous point of comparison for Tobler’s work.
Diffusion cartogram: A cartogram that transforms geographic space to represent modeled diffusion or movement. Tobler’s diffusion-based transformations linked spatial modeling directly to map construction.
A Computer Movie Simulating Urban Growth in the Detroit Region: A 1970 study by Waldo Tobler that simulated urban growth in the Detroit region using a computer model. This work exemplifies Tobler’s use of computation to model geographic change.
Spatial autocorrelation: The correlation of a variable with itself across locations, reflecting spatial patterns. It gives a statistical framework for the geographic dependence Tobler described.
Diffusion model: A mathematical representation of how a substance, influence, or process spreads through space or time. Tobler used spatial models to study how phenomena spread geographically.
Brian Berry: An American geographer known for advancing quantitative methods and spatial analysis. Berry was another leading figure in the quantitative transformation of geography.
Map projection: A mathematical transformation that represents Earth’s curved surface on a flat plane. Tobler analyzed projections as transformations with measurable geometric properties.
Map Transformations of Geographic Space: A 1979 article by Waldo Tobler examining mathematical transformations of geographic space. It presents his influential treatment of maps as spatial transformations.