Perhaps someone can shed a little light on the POV-Ray noise function. 
Looking at the code, towards the bottom of the function Noise(...),
there is:

  sum = sum + 0.5; /* range at this point -0.5 - 0.5... */
  
  if (sum < 0.0)
    sum = 0.0;
  if (sum > 1.0)
    sum = 1.0;

However, in attempts to get a distribution of values that come close to
the POV-Ray noise function out of a standard Perlin noise function, I
found that there is a problem.

I took several million samples of the noise function in a box with sides
of length 1000. These are the basic statistics for POV-Ray's Noise(),
before adding the 0.5 and clamping to the range [0,1]:

Min, max: -1.05242, 0.988997
Mean: -0.0191481, Median: -0.535493, Std Dev: 0.256828

Clearly, the range of values for sum is not -0.5 to 0.5 as suggested in
the code.  In fact, since the median value is less than -0.5, the actual
Noise() returns 0.0 more than half of the time (after adding 0.5 and
clamping).  Doesn't make sense.

Compare the above to a traditional Perlin solid noise function, which
for the same set of sample points yields:

Min, max: -0.6746, 0.672579
Mean: -0.000140859, Median: 0.0487365, Std Dev: 0.180682

As would be expected, the values are centered around 0.  Another
interesting point is that the standard deviation for the POV-Ray noise
function is not even close to the Perlin noise.

I'll have to go digging around and see if I can find the way POV-Ray
used to compute the solid noise function (using a CRC table, giving a
machine dependent result) and see if it had similar characteristics.  In
any case, this really looks abnormal.

Xander

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