Comparing the quarter-turn metric and the "standard" metric is very interesting.
I'm fascinated that for both, the number of positions above a certain distance starts to reduce again (which is much more pronounced in the quarter-turn table). Intuitively, it isn't obvious to me why this would be so, but it's nerd sniped me into thinking about how combinations work in general and the geometry of the Rubik's cube particularly.
I'm fascinated that for both, the number of positions above a certain distance starts to reduce again (which is much more pronounced in the quarter-turn table). Intuitively, it isn't obvious to me why this would be so, but it's nerd sniped me into thinking about how combinations work in general and the geometry of the Rubik's cube particularly.
Off to Wikipedia!