Recurrence Table Attractors

A recurrence equation such as generates a sequence of terms based on an initial condition. For example, with , the Fibonacci sequence 1, 1, 2, 3, 5, 8, … is generated. A recurrence table can generate a multidimensional list of values. In this Demonstration, a range of two-variable recurrence equations is explored. When plotted, a variety of behaviors can be seen. The points may scatter randomly, or quickly converge to a set of values. About one time out of 50, a strange attractor is generated.