MATH 178 Fractals and Chaos
Weekly Notes

  • Week 1 (May 7). Examples of fractals, self-similarity.

  • Week 2 (May 14). Constructing fractals by removing or adding pieces. Addresses of a fractal. The Cantor set.

  • Week 3 (May 21). Measuring lengths of curves. Fractal dimension.

  • Week 4 (May 28). Consistent coverings. Box counting method.

  • Week 5 (June 4). Iterated Function Systems. Affine transformations.

  • Week 6 (June 11). Encoding and Decoding an IFS. Fixed point of an IFS.

  • Week 7 (June 18). Chaos game.

  • Week 8 (June 25). Chaos game rules in "plain English". Fractal Art, fractal music.

  • Week 9 (July 2). Discrete dynamical systems. Midterm.

  • Week 10 (July 9). Experiments with the logistic function.

  • Week 11 (July 16). Period doubling bifurcations. Structure of the final state diagram of the logistic function. Symbolic dynamics.

  • Week 12 (July 23). Symbolic dynamics. Complex numbers.

  • Week 13 (July 30). Julia and Mandelbrot sets.




    Last updated: Aug 1