Sine-based Tiled Procedural Bump

Question

I am trying to implement this formula to generate bump but I am facing some issue. The result doesn't look the same it's much darker.

Here is my result (without same parameters) but it is much darker and I don't get why.

And here is the associated code.

// randx, randy and frequencies are array with some random values for each sin wave.
for (int x = 0; x < _width; ++x)
{
    for (int y = 0; y < _height; ++y)
    {
        float color = 0.0f;
        for (int i = 0; i < _iterations; ++i)
        {
            val += Mathf.Sin(Mathf.Sqrt(Mathf.Pow(x - randx[i], 2.0f) + Mathf.Pow(y - randy[i], 2.0f)) * 1.0f / (2.08f + 5.0f * frequencies[i]));
        }
        color /= (float)_iterations;
    }
}

Any idea why I am getting this result ?
Thanks a lot !

EDIT: Thanks to @trichoplax it works by doing this.

float tmp = Mathf.Sin(Mathf.Sqrt(Mathf.Pow(x - randx[i], 2.0f) + Mathf.Pow(y - randy[i], 2.0f)) * 1.0f / (2.08f + 5.0f * frequencies[i]));
tmp = tmp * 0.5f + 0.5f;
val += tmp;

Answer 1

As you are taking the mean of a number of sine waves, your colour values will range from -1 to 1. From your example image, it looks like only the top half of this range of values (from 0 to 1) is resulting in colour, with everywhere else remaining black.

If whatever you are using to display the result can only handle positive values, then you will need to convert the result to the correct range of values. For example, to convert from the range [-1 to 1] into the range [0 to 1], you would add 1 and divide by 2.

In the context of your example code, this could be by following the line

color /= (float)_iterations;

with

color += 1;
color /= 2;