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
For more information, see the Wikipedia entry for
the Wolfram Demonstrations Project
Embed Interactive Demonstration
More details »
Download Demonstration as CDF »
Download Author Code »
More by Author
Chaos Game Fractals
IFS: Rotation, Translation, and Scaling
Step-by-Step Julia Sets
The Rossler Attractor
Daniel de Souza Carvalho
Classic Logistic Map
Robert M Lurie
Chaotic Itinerary but Regular Pattern
Rob Morris and Rickey Bowers Jr. (bitRAKE)
Plotting Julia Sets
Binary Coding Functions for Generalized Logistic Maps with z-Unimodality
Version 8 Features
Browse all topics
The #1 tool for creating Demonstrations
and anything technical.
Explore anything with the first
computational knowledge engine.
The web's most extensive
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
STEM Initiative »
Programs & resources for
educators, schools & students.
Join the initiative for modernizing
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
© 2016 Wolfram Demonstrations Project & Contributors |
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have