> A small change in the parameter a can lead to vastly different particle trajectories and the overall shape of the attractor. Change this value in the control panel and observe the butterfly effect in action.

I think this is slightly inaccurate. The butterfly effect is about the evolution of two nearby states in phase space into well-separated states. But the parameter a is not a state. To see the butterfly effect by changing a we would need to let the system settle down, give the parameter a small change, and then change it back. The evolution during the changed time acts as a perturbation on states.

Instead, showing that the attractor changes qualitatively as a function of the parameter is more akin to a phase transition.