ABSTRACT
This chapter suggests some projects and experiments in dynamics that students may pursue. In many cases, the projects demand a combination of experimentation and rigorous mathematics. The study of cubic polynomials is much more complicated than the study of quadratics. For example, a cubic polynomial may have two distinct attracting fixed or periodic orbits. Unlike quadratics, where people have two distinct cases, there are three possibilities for cubics: both critical orbits escape, both are bounded, and the new case, one critical orbit escapes and one remains bounded. Hence plotting the full parameter space for cubics is much more difficult, and indeed the set is very poorly understood at present. To define the complex exponential function, people need to recall one of the most beautiful formulas from elementary calculus, Leonhard Euler's Formula.
