Pecora and Carroll’s study of the synchronization of this property has been applied to sending secret messages. Cobweb plots can visualize why this property appears intermittently near “windows” in parameter space where it vanishes. As r approaches 3.57, this property arises as increasing 2-to-the-n (15[1])cycles appear in a recurrence relation that Robert May used to study population growth. 1D discrete maps that gain this property via the (*) period-doubling route, like the logistic map, have cascading forks on their bifurcation diagrams. In phase space, systems with this property trace out fractals called strange attractors, like one named for Edward Lorenz. The double pendulum displays this property of extreme sensitivity to initial conditions. For 10 points, name this difficult-to-predict behavior demonstrated by the butterfly effect. ■END■