List Tutorial Exercise 14
-------------------------

We want to use `H V U' to nest a function which adds a random step to
an `(x,y)' coordinate.  The function is a bit long, but otherwise the
problem is quite straightforward.

     2:  [0, 0]     1:  [ [    0,       0    ]
     1:  50               [  0.4288, -0.1695 ]
         .                [ -0.4787, -0.9027 ]
                          ...

         [0,0] 50       H V U ' <# + [random(2.0)-1, random(2.0)-1]> RET

Just as the text recommended, we used `< >' nameless function notation
to keep the two `random' calls from being evaluated before nesting
even begins.

We now have a vector of `[x, y]' sub-vectors, which by Calc's rules
acts like a matrix.  We can transpose this matrix and unpack to get a
pair of vectors, `x' and `y', suitable for graphing.

     2:  [ 0, 0.4288, -0.4787, ... ]
     1:  [ 0, -0.1696, -0.9027, ... ]
         .

         v t  v u  g f

Incidentally, because the `x' and `y' are completely independent in
this case, we could have done two separate commands to create our `x'
and `y' vectors of numbers directly.

To make a random walk of unit steps, we note that `sincos' of a random
direction exactly gives us an `[x, y]' step of unit length; in fact,
the new nesting function is even briefer, though we might want to
lower the precision a bit for it.

     2:  [0, 0]     1:  [ [    0,      0    ]
     1:  50               [  0.1318, 0.9912 ]
         .                [ -0.5965, 0.3061 ]
                          ...

         [0,0] 50   m d  p 6 RET   H V U ' <# + sincos(random(360.0))> RET

Another `v t v u g f' sequence will graph this new random walk.

An interesting twist on these random walk functions would be to use
complex numbers instead of 2-vectors to represent points on the plane.
In the first example, we'd use something like `random + random*(0,1)',
and in the second we could use polar complex numbers with random phase
angles.  (This exercise was first suggested in this form by Randal
Schwartz.)