I don't think any of these solutions are taking into account a visually pleasing layout where the amount of white space between each icon is roughly similar. in 'circular_layou t.jpg' above where the icons are regularly spaced, you can see where the icons at 45 degrees almost touch but the vertically or horizontally adjacent ones have a gap. A smarter algorithm that takes the shortest distance between the nearest points of adjacent icons into account...

(elegantly...) string a in words the reversing is problem interesting more much A