The algorithm for computing the fractal is summarized as follows:
1. Choose a string of A’s and B’s 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
, and compute the iterates
6. Compute the Lyapunov exponent:
. In practice,
is approximated by choosing a suitably large
(in the Manipulate code, the variable “iterations” corresponds to
7. Color the point
according to the value of
8. Repeat steps 3–7 for each point in the image plane.
THINGS TO TRY
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