[Animats]

There's a lot to be said for a hexagonal grid. I looked at this once for a collision detection system. It's convenient to get rid of the special cases needed where four cells meet. You have to invent some new bookkeeping, but it can be worth it.

[jacobolus]

The aliasing / moiré artifacts are also dramatically less objectionable with hexagonal grids.

Now that image sensors and e.g. smartphone displays are very high resolution, and most content ends up going through multiple resampling routines on its way from capture -> storage/processing -> display, I would love to see people start to experiment with hexagon-grid cameras and displays. The slightly more complicated resampling wouldn’t really be a big deal for modern DSP hardware, and the visual output could be significantly better for the same pixel count.