Lyapunov Fractal - Algorithm For Generating Lyapunov Fractals

Algorithm For Generating Lyapunov Fractals

An algorithm, for computing the fractal is summarized as follows.

1. Choose a string of As and Bs of any nontrivial length (e.g., AABAB).
2. Construct the sequence formed by successive terms in the string, repeated as many times as necessary.
3. Choose a point .
4. Define the function if, and if .
5. Let, and compute the iterates .
6. Compute the Lyapunov exponent:
   
   In practice, is approximated by choosing a suitably large .
7. Color the point according to the value of obtained.
8. Repeat steps (3–7) for each point in the image plane.