Three-dimensional trajectory time series from a radioactive solid tracer freely moving in a 3-D conical-base spouted-bed reactor were analyzed using standard statistical and qualitative dynamics tools. The wanderings of the tagged tracer, sharing the same characteristics as the bed inventory particles, were monitored non-invasively by means of a radioactive particle tracking technique in flow conditions of developed, under-, and over-developed fountains. Strong periodic components in the motion have been diagnosed for all experimental conditions. In addition, state-space reconstruction by embedding time-delay vectors from the tracer trajectory indicated an embedding dimension range [2-5] and positive Kolmogorov entropies, thereby giving prima facie indication of the existence of chaotic signatures in the solid motion in spouted beds. An increase in gas velocity introduced order in the chaotic motion by giving rise to low-dimensionality attractors. This was also confirmed by return map plots and mutual information function which showed a preeminence of periodic behavior in the tracer trajectory with increasing gas velocity.