Fig. 2 — enlarged from sheet 01
A map of Seattle where the distance between two places is how long it takes to get there. Three versions: driving at the speed limits, driving in Friday evening traffic, and transit on a weekday morning, with a slider that morphs the city between its geography and each one.
Have you heard of sensory and motor homunculi? They’re those distorted drawings of a person where a body part is bigger if it has more nerves in it. Giant hands, giant lips.
The last time I was in Seattle I got the thought to do the same thing for a map of travel times: make the map visually match how long it actually takes to get somewhere. I was staying on Capitol Hill. Visiting friends in Ballard took far longer than the distance on the map suggested, while Phinney Ridge to downtown, which looks farther, went by quickly. Drive times there depend on direction and on which body of water you have to get around, and a geographic map can’t show that even though it shows the water.
A hex grid of 883 anchor points covers the city, skipping the water. The drivable street network comes from OpenStreetMap through Overpass, with speed limits and one-way rules. Every pair of anchors gets routed over that network with Dijkstra, which gives one travel time matrix per scenario. The traffic scenario multiplies each road’s time by a slowdown read from TomTom’s flow API near every anchor. The transit scenario runs RAPTOR over the published GTFS timetables, walking included, so waiting for the bus is part of the shape.
Then a layout step (classical MDS, then SMACOF refinement) places the anchors so that drawn distance matches timed distance as well as a flat plane allows, and the viewer warps the streets and shoreline through that displacement field. There’s an X-ray toggle that shows the grid itself, and an illustrated math page with the details.
At posted speed limits, north-south freeway trips draw at about two-thirds of their geographic length (Green Lake to Georgetown comes out at 0.61x), while east-west water crossings stretch to half again as far (Magnolia to Capitol Hill, 1.53x). Friday evening traffic lengthens the average trip by roughly a fifth and cuts into the freeway advantage. No flat map can satisfy every travel time at once, so the fit has some error left in it (stress of 0.12 free-flow, 0.11 with traffic).
Next I want more slices, for other times of day and days of the week: midday, late night, transit at other hours. A bike version needs elevation and is its own project.