Author: Capri Granville

This chart communicates the same insights as a contour plot. What is interesting is the choice of hexagonal buckets (rather than squares) to aggregate data. In fact, any tessellation would work, in particular Voronoi tessellations.

*3-D Voronoi tessellation *

The reason for using hexagons is that it is still pretty simple, and when you rotate the chart by 60 degrees (or a multiple of 60 degrees) you still get the same visualization. For squares, rotations of 60 degrees don’t work, only multiples of 90 degrees work. Is it possible to find a tessellation such that smaller rotations, say 45 or 30 degrees, leave the chart unchanged? The answer is no. Octogonal tessellations don’t really exist, so the hexagon is an optimum.

*Hexagonal binning plots (source: here)*

**Implementation in R**

The three plots described here (Voronoi diagram, hexagonal binning and contour plots) are available in the ggplot2 package.

- Hexagonal binning: ggplot function with the parameter stat_binhex, see here
- Contour plot: ggplot function with the parameters geom_density2 or stat_contour, see here (also works with contour)
- Voronoi diagram: ggplot with the parameter geom_segment, see here

**Applications**

Voronoi diagrams can be used for nearest neighbor clustering or density estimation, the density estimate attached to a point being proportional to the inverse of the area of the Voronoi polygon containing it.

*Example of contour map (source: here)*