Manhattan Metric

Urbica is a design firm specializing in urban data analysis. They have developed a program called Galton that graphs, for a few select cities, how far you could walk in 10 minutes (in dark blue) or 20 minutes (in lighter blue). The map of Manhattan above shows those regions for a walk originating at Broadway and 42st Street. As you walk NYC you are, for the most part, constrained to travel the grid of avenues and streets. Of course, you cannot travel as the crow flies. If you could, these regions would be concentric circles with a perimeter an equal (Euclidean) distance from your start. But walking the streets, your distance is measured by the city block metric (also known as the taxicab metric or more appropriate here the Manhattan metric). This measures distances constrained along perpendicular avenues and streets. Plotting points of equal distance with this metric from would result in the roughly rectangular (or diamond-shaped) regions shown above. Since the streets and avenues are not equally spaced and obstacles can block our travel, we don't see perfect square or rectangular regions. By the Manhattan metric, circles become squares.
Via Maps Mania.

Next week, we will see directly the results of minimizing the distance traveled in such constrained walking.