As shown in FIG. 2 the number and variances of the function x for values of the coefficient r increase significantly for higher values of r, say above 3.6 or 3.7. In the early part of this range, the function x is somewhat unstable but tends to be attracted to return in somewhat irregular manner to or near a number of recurring values, referred to as attractors. FIG. 3D illustrates an example of the function of equation (1) in which a coefficient value for r is 4.0, which produces outcomes for xn+1 that vary in a somewhat unstable manner but with attractors. For a higher coefficient value, say 5.0 by way of an example, the function becomes completely unstable as shown by way of example in FIG. 3E.