The shriveling map construction principle

Unlike all previous time-space relief representations (1997, 2009) where the surface is based on the edges of a graph,  in the representations developed in 2016, we introduce conic shapes to represent time-space. The cone is the basic structure of this representation. Cones are characterized by a slope that follows the ratio between the speed of basic terrestrial networks, i.e. the road system, and the maximum available speed, which is attained, on the period we consider, through the air transport system.

Cones for time-space representation
Cones and edges in three dimensions as a basic structure for time-space representation CC-BY L’Hostis

On the figure we have two cities joined by a fast non-stop transport system, and also by a slower terrestrial transport mode. The fast transport link is represented through a red straight line, while the cones represent the surface on which slower terrestrial transport mode are drawn.  Assuming that travel speed are similar in all the geographic space considered, the slope of the cones centered on the two cities is a coherent representation of time-space. The two cones intersect midway between the two cities. The slope of the cones implies that the length of  the straight red line, and of the line drawn on the cone and joining the two cities, are proportional to the respective transport time. This forms a time space representation with different transport speed, and a time-space scale can be added, as in the USA map (p. 8).

 

A shriveling world

Time space relief cartography was invented in 1993 to map the time-space contraction assuming the coexistence of fast and slow transport modes. Initially applied locally to terrestrial modes (1993 p. 41), the principle has been applied to urban spaces (1997 p. 209 and 235) continental scales (1994 p. 253) and to the air mode (2009). The next major step, an ongoing work, is to create a cartographic representation of the earth, the global time-space.