Lyapunov Exponent Shader

The Lyapunov exponent is a measure of the stability of a dynamical system. It describes how much a small error of the input will affect the system. The calculation of the graph in the range -1 to 0 for a subset of the complex plane can produce very aesthetic pictuers. The implemantation as a pixel shader 3.0 code is very easy because its just an iteration for every point on the screen. The code for each pixel is as simpe as that:

// Compute single Lyapunov lambda value
float lyapunovExponent (const float2 ab)
{

double r;
double sum = 0;
double x = xStart;
int k;

for(k = 0; k < MaxIter+WarmUp; k++){

r = sequence(k) ? ab.x : ab.y;

x = r * x * ( 1-x );

if (k >= WarmUp) sum += log( r - 2*r*x );

}

return sum/MaxIter;

}

Where ab is a 2D point in the complex plane, which is related to the pixel position on the screen and sequence(k) is a simple function, which chooses the x or y coordinate for each iteration.
Here is the download and here a picture:

Fractal Shader

Joreg found a demo scene link with an easy to implement fractal shader for Mandelbrot and Julia fractals. Download here.

HD Video Rendering With Realtime FFT Data

For this little project the FFT data of a 3 minute song was recorded with 60 fps into more than 10000 text files, where each text file got a timestamp in its file name. During the rendering the text file with closest timestamp to the current rendering time was read and processed into parameters of a 3D-object which is based on Johan Gielis superformula.
A small video is here, and here some frames in full 3840x2400 resolution (which obviously where resized by blogger on upload).