Stairstep Diagram Applet

This applet graphically explores first order difference equations using a stairstep diagram, or as it is sometimes known, a cobweb plot.

Examples

Logistic Equation

u(n+1) = p*u(n)*[1-u(n)]

Try p=3.2 to get a two-cycle

Try p=3.5 to get a four-cycle

Calculating the Sqrt(a)

Iterating the difference equation x = 0.5*(x + a/x) can be seen as an application of Newton's method to find the zeros of the equation x^2 = a. In other words, the fixed points of the difference equation with be the square roots of a. To find the sqrt(2), take a=2 and an initial value of 3 and observe converge to x = 1.4121...