[gugagore]

It could be worth mentioning that, for thinning points, ideally you'd use a circle, so that points are thinned equally in all directions. When you use a square, diagonal lines are thinned more (by a factor of sqrt(2)) than horizontal/vertical lines. However, checking inclusion within a axis-aligned square requires only comparisons/subtractions, but checking inclusion within a circle requires square roots and squares... certainly a big deal back then.

[jackschaedler]

This is a great point. When I first implemented the visualization, I actually used a circle until someone pointed out to me that the formula describes a square region around the datapoint and not a circle. I think you are very right in saying that this decision was made by Groner solely for efficiencies' sake in 1966. I'll probably add a side-note to explain this a bit.