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Recordings of spontaneous activity of in vitro neuronal networks reveal various phenomena on different time scales. These include synchronized firing of neurons, bursting events of firing on both cell and network levels, hierarchies of bursting events, etc. These findings suggest that networks' natural dynamics are self-regulated to facilitate different processes on intervals in orders of magnitude ranging from fractions of seconds to hours. Observing these unique structures of recorded time-series give rise to questions regarding the diversity of the basic elements of the sequences, the information storage capacity of a network and the means of implementing calculations.Due to the complex temporal nature of the recordings, the proper methods of characterizing and quantifying these dynamics are on the time---frequency plane. We thus introduce time-series analysis of neuronal network's synchronized bursting events applying the wavelet packet decomposition based on the Haar mother-wavelet. We utilize algorithms for optimal tiling of the time---frequency plane to signify the local and global variations within the sequence. New quantifying observables of regularity and complexity are identified based on both the homogeneity and diversity of the tiling (Hulata et al., 2004, Physical Review Letters 92: 198181---198104 ). These observables are demonstrated while exploring the regularity---complexity plane to fulfill the accepted criteria (yet lacking an operational definition) of Effective Complexity. The presented question regarding the sequences' capacity of information is addressed through applying our observables on recorded sequences, scrambled sequences, artificial sequences produced with similar long-range statistical distributions and on outputs of neuronal models devised to simulate the unique networks' dynamics.