Chaos: The Logistic Map

The logistic map equation is:

x(t+1) = k * x(t) * [1 - x(t) ]     OR    x(t+1) = k * sin[x(t)]

This gives rise to a parabola or sine curve intersected by a straight line y = x, between 0 and 1 (or -pi and +pi for the sine curve). The factor k determines the "depth" of the curve.

Choose any value 0 < k < 4. For each value of k you will see widely different solutions, varying from steady convergence to zero, to completely random oscillations.

The Trig Sine case is by far the more interesting. For k > pi (3.1415...) some negative behaviour is evident.

The logistic graph has been scaled to suitable audio frequencies so that each point of the graph can be heard as a sound! Listen on your headphones!