This study investigated the level of chaos and the existence of fractal patterns in the heart rate variability (HRV) signal prior to meditation and during meditation using two quantifiers adapted from non-linear dynamics and deterministic chaos theory: (1) component central tendency measures (CCTMs) and (2) Higuchi fractal dimension (HFD). CCTM quantifies degree of variability/chaos in the specified quadrant of the second-order difference plot for HRV time series, while HFD quantifies dimensional complexity of the HRV series. Both the quantifiers yielded excellent results in discriminating the different psychophysiological states. The study found (1) significantly higher first quadrant CCTM values and (2) significantly lower HFD values during meditation state compared to pre-meditation state. Both of these can be attributed to the respiratory-modulated oscillations shifting to the lower frequency region by parasympathetic tone during meditation. It is thought that these quantifiers are most promising in providing new insight into the evolution of complexity of underlying dynamics in different physiological states.