Certain things in the game occur when you have taken x steps. Happiness, egg production/hatching, etc are all determined by the number of steps you have taken.
In previous Pokemon games, it is immediately obvious when you take a step. You press up, your character moves one step. There are only four directions to move in, and each step is locked to a grid.
In X/Y, however, movement is more fluid. I can take what seems to be a "partial step" by bumping the analog stick quickly, or move at an angle that wasn't possible before. In addition, there's no built-in step counter (like the Poketch app for DPPT), so it seems I have no way of knowing at all what a step is.
Is there a specific distance that counts as one step? If so, what is it? When moving at an angle, is the distance Euclidean (e.g. ~√2 steps if I'm moving at 45 degrees for one unit in both x/y directions)?