The Butterfly Effect can be seen in the Time Series of two pendulums whose initial conditions vary by a small degree.  This applet allows the user to change the initial conditions of the second pendulum and observe the divergence over time.

        

Omega   =           Theta   =           Phi   =  

g   =         q   =        

Reinitialize

Observations:

            Below are some Time Series for pendula whose initial conditions vary by a small degree.

Fig. 1:  Time Series for two damped, driven pendulums when ωD = 2/3, q = 2, and g = 1.15.  When the initial conditions for the two pendulums are different in ω by 0.01, they diverge exponentially after a short time.