MAT335: Term Project
Here is a list of suggestions for term projects. Students can choose to
do a term project instead of writing the final exam.
Students are also encouraged to find project topics on their own. In any
case, students should discuss project topics with me before embarking
on their research. The projects are due at the end of the examination
period.
Some project topics (this list is updated occasionally);
- Applications of the box counting method to fractal-like objects
(PJS Chapters 4 and 12 and other references - see me)
- Adaptive cut methods for drawing fractals (PJS Section 6.5)
- Computing optimal probabilities for the chaos game (PJS pp 328-
329 and Section 6.5; FFAS pp 183-224)
- Fractal image compression (Appendix A of PJS)
- Fractal modelling of real-world images (PJS Section 5.8; SFI
Chapter 5)
- Random fractals (PJS Chapter 9; F Chapter 15)
- Fractal landscapes (PJS Chapter 9; SFI Chapter 1)
- Percolation (PJS Chapter 9)
- Brownian motion (PJS Chapter 9; SFI Chapter 2; F Chapter 16)
- Cellular automata (PJS Chapter 8)
- L-systems (PJS Chapter 7)
- Symbolic dynamics (PJS Section 10.5; D Chapter 9; H Chapter 11)
- The structure of the final state diagram for the logistic
equation (Section 11.4 PJS)
- Universality and renormalization (PJS Section 11.2 and other
references - see me)
- Charkovsky's Theorem. Is there an 'intuitive', geometric proof?
(PJS pages 638,639 for the theorem, and the section in Chapter 11
explaining the structure of the final state diagram of the logistic function
for ideas on how to approach it geometrically.)
- Reconstructing strange attractors (PJS Section 12.7)
- The evolution of the notion of 'chaos' in the sciences (G; S)
References:
- D; A First Course in Chaotic Dynamical Systems,
Robert Devaney
- F; Fractal Geometry, Kenneth Falconer.
- FFAS; Fractals in the Fundamental and Applied
Sciences, H.-O. Peitgen, J.M. Henriques, L.F. Penedo,
editors.
- G; Chaos, James Gleick.
- H; A First Course in Discrete Dynamical Systems, Richard
Holmgren.
- PJS; Chaos and Fractals, New Frontiers of Science,
H.-O. Peitgen, H. Jurgens, and D. Saupe.
- S; Does God Play Dice?, by Ian Stewart.
- SFI; The Science of Fractal Images, M.F. Barnsley,
R.L. Devaney, B.B. Mandelbrot, H.-O. Peitgen, D. Saupe, and
R.F. Voss.