1. Simple, deterministic systems can produce random behavior. Example: logistic equation.

2. Complicated, large systems can have relatively simple dynamics. Example: Random boolean networks with K=2 have only sqrt(N) attractors.

3. Fractals can be produced by deterministic and stochastic systems. Examples: making snowflakes via a deterministic rule; flipping coins to build a Sierpinsky triangle.

4. Mathematical models are sometimes not used for prediction, but instead to gain a qualitative feel for a system.

5. Universality. Some features of dynamical systems are universal. These features as quantitatively the same for lots of different dynamical systems and can (and have) been measured experimentally.

6. The mathematics of dynamical systems comes in many different forms, flavors, and styles.

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