NOTICES:

• Rossler.java
• LV.java
• Orbit.java
• IFS.java
• Plotter.java
• WorkBook.pdf

• Eigen.java
• Wolfram.java

• office : 3-185 CST
• office phone : 443-3565
• e-mail: blair@ecs.syr.edu

The course will give students a working knowledge of how to model diverse kinds of interesting natural phenomena on a computer. Modeling natural phenomena necessarily draws on knowledge of certain common mathematical techniques, which will be covered in the course in a self-contained manner. The four topics listed in the course title illustrate the diversity of topics covered. A series of exercises involving brief programming tasks will be given that will lead students to see the mathematical models that are constructed as if they were computer programs in detail. The course objective is to give students an appreciation for the power of such computational models and the fundamentals of the skills to build them.

The course may be taken for credit by students who previously took CIS 400/600 Dynamical Systems

• The construction of fractals via escape time algorithms and randomized algorithms. Mandelbrott, Julia, Cantor and Sierpinski sets. Fractal dimension.
• Bifurcation and the route to chaos. Definition of chaos. Feigenbaum's constant.
• The stability of flows as characterized by Lyapunov exponents and spectra. Locating self-organizing behavior in rule space. Continuous deformations of rule-based systems.
• Cellular automata: Game of Life, CA-based cryptography.
• Emergence of robust dynamical structures. Artificial life.
• Genetic and evolutionary processes.
• Self-organized criticality. Autocatalytic systems.
• A computational perspective on calculus: computing with differential equations. Orbits of planets and spacecraft.
• Lorenz, Roessler, and Sprott attractors. Poincare sections and return maps.

• Peitgen, Heinz-Otto, Hartmut Juergens, and Dietmar Saupe, Chaos and Fractals. Springer-Verlag, 1992. (Required Text)
• Barnesley, Michael F.   SuperFractals   Cambridge University Press, 2006.
• Casti, John L. Reality Rules: I and II Wiley Interscience, 1992.
• Barnesley, Michael F. Fractals Everywhere Academic Press, 1993.
• Devaney, Robert L. and Linda Keen (eds.), Chaos and Fractals Proceedings of Symposia in Applied Mathematics, vol. 39. American Mathmematical Society, 1989. (Articles giving an essential and basic mathematical foundation for fractals including a condensed version of Barnsley's book.)
• Bak, Per. How Nature Works. Springer-Verlag, 1996.
• http://sprott.physics.wisc.edu/sprott.htm Contains a large amount of material on dynamical systems, chaos and fractals. I highly recommend visiting Clint Sprott's website.