Logistic map x_{t+1} = a x_t (1-x_t).

The Cobweb diagram on the left shows you the trajectory of the map, and the graph on the right hand side shows the value of x_t at each iteration.

Choose a value of a, an initial condition and the number of iterations to plot. Then press "Draw".

The values given show a fixed point of this map (recall that x* = 1 - 1/a).