keybd INPUT yes screen home lf swiss13 on %x 10 fmtlist fmt \n\N:=\F yes 1 yes fixed 3 degrees home The emergence of chaotic dynamics from simpler behavior may be observed in this example called the logistic map. The iterative equation: x:=r*x*(1-x) exhibits a variety of behaviors, depending upon its initial value, and the value of the parameter r. To explore the behavior of this equation, set values for r and x, go to cell x, and select Evaluate from the Special menu. For a value of the parameter r of 0.4, and an initial x value of 0.7, successive values of x approach zero and stay there. For an r value of 2.4, and initial x value 0f 0.7, successive values of x approach a constant 0.583. For r=3.0, and an initial x, of 0.5; an extended damped oscillation takes place between between two numbers. For r=3.5, initial x=0.7; an extended oscillation among four numbers takes place. For r=3.8, initial x=0.7; a chaotic sequence of numbers is the result. For more information on the period doubling approach to chaos, see the book: Creating Artificial Life, by Edward Rietman; from which this example was taken. 0.525 r 3.8 x 0.230