This approach is still incorrect, and the bias toward the set of 4 points S = {(1,0),(-1,0),(0,1),(0,-1)} can be seen in the diagram. There is no way to break out of this bias by flipping or reordering coordinates because those two operations preserve the symmetries of S:
- if you flip the x-coord of a point near S, e.g. (-.9,0), you still get a point near S, e.g. (.9,0)
- if you swap the x-coord and y-coord of a point near S you still get a point near S.
- if you flip the x-coord of a point near S, e.g. (-.9,0), you still get a point near S, e.g. (.9,0)
- if you swap the x-coord and y-coord of a point near S you still get a point near S.
- etc.