My brother pointed out this series of maps over at New Scientist. Combining a Buckminster Fuller-like interest in the most efficient way to map a sphere in two dimensions with a deployment of new algorithms, the maps show alternative ways of representing the earth’s surface.
“Making truly accurate maps of the world is difficult,” New Scientist points out, “because it is mathematically impossible to flatten a sphere’s surface without distorting or cracking it. The new technique developed by computer scientist Jack van Wijk at the Eindhoven University of Technology in the Netherlands uses algorithms to ‘unfold’ and cut into the Earth’s surface in a way that minimises distortion, and keeps the distracting effect of cutting into the map to a minimum.”
In van Wijk’s own abstract, published by The Cartographic Journal, we read that these “myriahedral projections,” as they’re called, “are a new class of methods for mapping the earth”:
The globe is projected on a myriahedron, a polyhedron with a very large number of faces. Next, this polyhedron is cut open and unfolded. The resulting maps have a large number of interrupts, but are (almost) conformal and conserve areas. A general approach is presented to decide where to cut the globe, followed by three different types of solution. These follow from the use of meshes based on the standard graticule, the use of recursively subdivided polyhedra and meshes derived from the geography of the earth.
It would be amazing to see what effect this technique might have on a much smaller scale—if, for instance, you could run one of these cuts through a populated area like London, say, and watch as parts of the city fractal off to opposite sides of the planet, the city’s roads opened up into algorithmic fissures.