Is this Chaos?

The logistic map is a classic recursive sequence defined by $x_{n+1}=rx_{n}(1-x_{n})$ and $r$ is a parameter with $0\leq r \leq 4$. It turns out, this innocent sequence is quite strange when $r$ gets closer to 4. For large enough $r$, chaos can even occur. We will investigate the fixed points of this map as well as some of its periodic orbits, and later we will look into some of the numerics with this sequence.