1. The quadratic family: $f_c(x)=x^2+c$
2. The logistic family: $f_{\lambda}(x)=\lambda x(1-x)$
The cobweb plots shown back in Figure 2.2.1 are all chosen from the logistic family with $\lambda=2.8\text{,}$ $\lambda=3.2\text{,}$ and $\lambda=4\text{.}$ Even in those three pictures with graphs that look so very similar, we see three different types of behavior: an attractive fixed point, an attractive orbit of period two, and chaos (which can be given a very technical meaning.