Visualizing the effects of filtering chaotic signals

It is well-known that filtered chaotic signals can exhibit increases in observed fractal dimension. However, there is still insufficient knowledge regarding the underlying causes of this phenomenon. We provide further insight into this problem through the use of computer animations and three-dimensional ray-tracings. Specifically, we show that lowpass filters can induce a non-uniform convergence to a dynamical system’s mean state-space location. With chaotic attractors, this convergence distorts the attractor’s normal geometrical configuration such that the observed system acquires increased dimensionality.