digraph {
    "start: (0, 0)" -> "N: (0, 1)"
        "N: (0, 1)" -> "N N: (0, 2)"
            "N N: (0, 2)" -> "N N N: (0, 3)"
            "N N: (0, 2)" -> "N N E: (1, 2)"
"N N E: (1, 2)" [color=blue fontcolor=red]
            "N N: (0, 2)" -> "N N NE: (1, 3)"
        "N: (0, 1)" -> "N E: (1, 1)"
            "N E: (1, 1)" -> "N E N: (1, 2)"
"N E N: (1, 2)" [color=blue fontcolor=red]
            "N E: (1, 1)" -> "N E E: (2, 1)"
            "N E: (1, 1)" -> "N E NE: (2, 2)"
        "N: (0, 1)" -> "N NE: (1, 2)"
"N NE: (1, 2)" [color=blue fontcolor=red]
    "start: (0, 0)" -> "E: (1, 0)"
        "E: (1, 0)" -> "E N: (1, 1)"
            "E N: (1, 1)" -> "E N N: (1, 2)"
"E N N: (1, 2)" [color=blue fontcolor=red]
            "E N: (1, 1)" -> "E N E: (2, 1)"
            "E N: (1, 1)" -> "E N NE: (2, 2)"
        "E: (1, 0)" -> "E E: (2, 0)"
            "E E: (2, 0)" -> "E E N: (2, 1)"
            "E E: (2, 0)" -> "E E E: (3, 0)"
            "E E: (2, 0)" -> "E E NE: (3, 1)"
        "E: (1, 0)" -> "E NE: (2, 1)"
            "E NE: (2, 1)" -> "E NE N: (2, 2)"
            "E NE: (2, 1)" -> "E NE E: (3, 1)"
            "E NE: (2, 1)" -> "E NE NE: (3, 2)"
    "start: (0, 0)" -> "NE: (1, 1)"
        "NE: (1, 1)" -> "NE N: (1, 2)"
"NE N: (1, 2)" [color=blue fontcolor=red]
        "NE: (1, 1)" -> "NE E: (2, 1)"
            "NE E: (2, 1)" -> "NE E N: (2, 2)"
            "NE E: (2, 1)" -> "NE E E: (3, 1)"
            "NE E: (2, 1)" -> "NE E NE: (3, 2)"
        "NE: (1, 1)" -> "NE NE: (2, 2)"
            "NE NE: (2, 2)" -> "NE NE N: (2, 3)"
            "NE NE: (2, 2)" -> "NE NE E: (3, 2)"
            "NE NE: (2, 2)" -> "NE NE NE: (3, 3)"
}