You are correct about the first part (I actually came back here to add a comment to mine saying that I'd goofed and the exponent should be 20, not 10). Also, I

You are correct about the first part (I actually came back here to add a comment to mine saying that I'd goofed and the exponent should be 20, not 10). Also, I suspect that the width (your N) should be large enough in most of the cases where we'd be wondering about peaks vs. ridge lines that the large-N limit of (2N-2)/N could safely be taken (that is, 2). [The whole motivation for peaks vs. ridges is the question of whether there is a connected path that passes "near" all the points in the space, which is generally taken to mean within a ball of radius r, with 1 < r << N; since the grid is discrete, this implies N is >> 1.]