The Tent Map is one of the
simplest nonlinear functions. It consists of two linear functions: 
T(x) = s⋅x 
for x ≤ 1/2 
T(x) = s⋅(1x) 
for x ≥ 1/2 

For small x, the Tent Map represents growth; for larger x decline,
perhaps an effect of competition for limited resources. 

Note the maximum value occurs at x = 1/2, and that
maximum value is s/2. 
We shall see the graph should
stay inside the unit square. Consequently, we restrict the number s to the range 
0 ≤ s ≤ 2. 
We shall see that as
s varies, the structure of the orbit x_{0}, x_{1} = T(x_{0}),
x_{2} = T(x_{1}), ... varies in a very complicated way, but not as
complicated as that of the logistic map. 
Nevertheless, the iterates of the tent map exhibit rich behavior, including chaos. 