html('<h1>A Random Walk</h1>')

vv = []

nn = 0

@interact

def foo(pts=checkbox(True, "Show points"), 

        refresh=checkbox(False, "New random walk every time"),

        steps=slider([10..500],default=50)):

    # We cache the walk in the global variable vv, so that

    # checking or unchecking the points checkbox does not change

    # the random walk.

    html("<h2>%s steps</h2>"%steps)

    global vv

    if refresh or not vv:

        s = 0

        v = [(0, 0)]

        for i in range(steps): 

             s += random() - 0.5

             v.append((i, s)) 

        vv = v

    elif len(vv) != steps:

        # Add or subtract some points

        s = vv[-1][1]

        j = len(vv)

        for i in range(steps - len(vv)):

            s += random() - 0.5

            vv.append((i + j, s))

        v = vv[:steps]

    else:

        v = vv

    L = line(v, rgbcolor='#4a8de2')

    if pts:

        L += points(v, pointsize=10, rgbcolor='red')

    show(L, xmin=0, figsize=[8, 3])