Are there any condition that hexagon grids will work better than square grids? Intuitively, hexagon also has some properties that square has.
In square pixels two pixels can touch each other just by a corner. In the hexagon grid this is not possible. I think this allows smoother color gradients since a hexagon is completely surrounded by neighbors.
They also have the least perimeter to area ratio for any regular tiling. That might help.
We discussed how some display hardware actually encodes the hexagon representation, but is there any imaging hardware to capture images in this way? Otherwise, display of real images would always require a transform between square and hexagonal representations.
Apparently some hexagonal hexagonal photo-sensors exist. One I found is called Hawksbill. It would be interesting to see if this eventually takes off some day.