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I have nothing substantive to say, but I thought it might be helpful to include an example of random diagonals, which I have drawn from an earlier MO question, "Shortest grid-graph paths with random diagonal shortcuts":
   

I have nothing substantive to say, but I thought it might be helpful to include an example of random diagonals, which I have drawn from an earlier MO question, "Shortest grid-graph paths with random diagonal shortcuts":
   

I have nothing substantive to say, but I thought it might be helpful to include an example of random diagonals, which I have drawn from an earlier MO question, "Shortest grid-graph paths with random diagonal shortcuts":
    Random Diagonals 50x50 http://cs.smith.edu/%7Eorourke/MathOverflow/RandomDiagonals50.jpg

I have nothing substantive to say, but I thought it might be helpful to include an example of random diagonals, which I have drawn from an earlier MO question, "Shortest grid-graph paths with random diagonal shortcuts":
   

I have nothing substantive to say, but I thought others might enjoy an example random diagonals, which is drawn from an earlier MO question, "Shortest grid-graph paths with random diagonal shortcuts":
    Random Diagonals 50x50 http://cs.smith.edu/%7Eorourke/MathOverflow/RandomDiagonals50.jpg

I have nothing substantive to say, but I thought it might be helpful to include an example of random diagonals, which I have drawn from an earlier MO question, "Shortest grid-graph paths with random diagonal shortcuts":
    Random Diagonals 50x50 http://cs.smith.edu/%7Eorourke/MathOverflow/RandomDiagonals50.jpg