An Oscar Algorithm - Silverlight Real-time 3D Perlin Noise

Perlin Noise is a computer graphics algorithm, which is widely used in computer games and movies as a visual effect. It was developed by Ken Perlin in the early 1980's and was used in the movie TRON. In 1997 Perlin received a Technical Achievement Award from the Academy of Motion Picture Arts for his work. So Perlin Noise is an Oscar-winning algorithm and I'm pretty sure almost everyone has seen it before.

Perlin Noise could produce pseudo-random semi-natural textures with fractal characteristics and is mostly used for procedural image generation. The algorithm can be controlled with various parameters and is able to produce good looking cloud / sky, fire, smoke, wood or marble textures and height maps, just to name a few.

In short, the Perlin Noise algorithm generates random noise functions with various frequencies and amplitudes, sums them up and smoothes the result. I don't want to bore you with more mathematical details, which were already explained several times on the web. If you are interested, I refer you to the Wikipedia article and the link section, Ken Perlin's site and to this excellent explanation. 

Live

My Silverlight implementation is the three dimensional improved Perlin Noise algorithm.

The initial Frequency and the Amplitude of the noise function can be changed. The Octaves parameter defines how many iterations of the noise function are summed up. Like in music the frequency is doubled in every subsequent octave. The Persistence controls how much the amplitude changes after each iteration. Press the Randomize button to reinitialize the noise function with new pseudo-random seeds.

How it works

The Perlin Noise computing loop:

for (int i = 0; i < this.Octaves; i++)
{
   noise += Noise(x * freq, y * freq, z * freq) * amp;
   freq  *= 2;
   amp   *= Persistence;
}

Each frame the Perlin Noise for every pixel of the 2D destination image is computed in real-time and is used as the alpha value for blending the noise color over the base color, then the z-value is increased. The noise's third dimension, the z-value, is actually used as time for the animation. So each frame the next slice of the 3D noise cube is computed and shown, thus resulting in a smooth animation.

For the source of the destination image the great RawPngBufferStream from the open source GameEngine Balder is used.

int off = 0;
for (int y = 0; y < bufferStream.Height; y++)
{
   for (int x = 0; x < bufferStream.Width; x++)
   {
      float a = perlinNoise.Compute(x, y, perlinZ);
      float ai = 1 - a;
      bufferStream[off + aOff] = (byte)(a * noiseColor.A + ai * baseColor.A); 
      bufferStream[off + rOff] = (byte)(a * noiseColor.R + ai * baseColor.R);
      bufferStream[off + gOff] = (byte)(a * noiseColor.G + ai * baseColor.G);
      bufferStream[off + bOFF] = (byte)(a * noiseColor.B + ai * baseColor.B);
      off += 4;
   }
   off++;
}
if (Chk3D.IsChecked.Value)
{
   perlinZ++;
}
imgSource.SetSource(bufferStream);

Source code

You can download the Silverlight 2 version here. Feel free to use or modify it as you like. If you do so please drop me a line, because I'm curious to know where (you want to) use it. Have fun!

Update 07-26-2009
I updated the project to Silverlight 3. Now it uses the WriteableBitmap instead of Balder's RawPngBufferStream. You can download the updated Visual Studio 2008 solution from here.