For values of r below approximately 3.0, x is a relatively monotonic function. FIG. 3A shows the function x_n+1, for a range of values n, in a case in which the coefficient r is 1.5. As shown, the function quickly reaches a value of approximately 2.7 and stays at that value. The outcome of the function is monotonic at that value for values of n above approximately 9 or 10. In this state produced by the low value of r, variation as a function of n is minimal and damps out quickly.

Returning to FIG. 2, in the range of r from approximately 3.0 to 3.4 for the value of the coefficient of r, there are essentially two possible outcomes for x. In this coefficient range, the function of x tends to be bi-stable. By way of an illustrative example of a bi-stable state of the function of equation (1), FIG. 3B depicts the function x_n+1, for a range of values n, in a case in which the coefficient r is 3.2.

Returning to FIG. 2, in the range of r from approximately 3.4 to 3.6 for the value of the coefficient of r, there are essentially four possible outcomes for x. In this coefficient range, the function of x tends to be quad-stable, i.e. a function that exhibits essentially four regularly repeating outcomes. By way of an illustrative example of a quad-stable state of the function of equation (1), FIG. 3C depicts the function x_n+1, for a range of values n, in a case in which the coefficient r is 3.5.