The algorithm works as follows:
Beginning with a certain x value, find the point on the parabola that corresponds to it. Then move horizontally to a point on the line y=x with the same y coordinate. Let f(x)=rx(1-x).
Point n+1: (x, f(x))
Point n+2: (f(x), f(x))
Replace x with f(x)
Enter values for x0 and r and a number of iterations of the logistic map to use. The cobweb diagram will show whether the (non-zero, if there is one) fixed point of the logistic equation is attractive or repulsive. An attractive fixed point draws the values of successive iterations of the map closer to the fixed point, while a repulsive fixed point pushes those values away from the fixed point. There is also the possibility that the fixed point will neither attract nor repel successive iterations and instead produce a periodic orbit.
n=200, x0=0.2, r=2 (x=1/2 is an attractive fixed point)
n=200, x0=0.2, r=3.9 (x=29/39 is a repulsive fixed point)
n=200, x0=0.2, r=3.2 (x=22/32 has a 2-periodic orbit)