Taxicab Spheres

This is a visualization of day 23 of Advent of Code 2018, Experimental Emergency Teleportation. In this puzzle you are asked to find the closest point to the origin which is within the signal range of the most possible nanobots.

Because the distance between points is measured in Manhattan distance, the three-dimensional space in the puzzle has a taxicab geometry. This means that the "spheres" defined by the radius around each nanobot are really octahedrons.

The nanobots are colored according to their radius. The largest ranges are shown in dark purple, while smaller ones are lighter. The origin point is bright green.