Here is a map of greater Washington, DC and its Metro (subway) system. The DC Metro system is one of a few that use demand pricing -- the cost of a trip depends on the pair of stations and time of day. For instance, the 13-minute direct trip from Bethesda to Rockville costs a nickel more ($2.35 regular fare) than the 27-minute, one-transfer trip from Bethesda to Foggy Bottom. (The latter route has full cars and so is more efficient.)

The travel time between stations is also not simple. Again from Bethesda, the Silver Spring station is 3.4 mi away by car but a whopping 9.7 miles by subway -- the subway route passes through downtown DC before returning. The trip to the Stadium-Armory stop, however, is 9.2 miles as the crow flies, 10.3 miles by rail, and 11-24 miles driving (the larger figure avoids downtown DC traffic).

This map lets you reimagine the geography of a region based on its travel time, distance, or price: it takes the landmarks of DC and, centered at your departure point, shifts them closer and farther to reflect the measuring stick you choose. In fact, any other structure or simple set of numbers connecting parts of the city works -- the starting point you see shows the terrain stretched to fit the wall map picture of the Metro system. Toggle between "Geography" and "Clarified map" -- you will notice that as the densely-placed downtown stops and distant suburban stops become equally-spaced for clarity, the downtown becomes "fish-eye" magnified.

If you now choose Bethesda from the list on the right (double click), and measure distance according to subway miles rather than normal miles, you will see that the direct downtown and outbound points on its line draw close in, while stops like Silver Spring (directly east of it) retreat far away. Toggling between travel time and travel distance makes transfer stations jump farther away; toggling between time and cost pushes the low-efficiency suburban routes far away, and pushes even nearby stops outside a minimum-fare bubble.

The map will let you zoom in to see more detail (top bar), and to see a topographic map or a satellite view (lower right). None of the background images are particularly good (rights-free satellite imagery is hard to find), but you can at least choose among several junky ones. Those with a mathematical bent may enjoy reading about how the map works -- if so, the grid paper and the crazy-colored triangles backgrounds can help picture what's going on.

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