A marker of engaging in compassion meditation and related processes is an increase in heart-rate variability (HRV), typically interpreted as a marker of parasympathetic nervous system response. While insightful, open questions remain. For example, which timescale is best to examine the effects of meditation and related practices on HRV? Furthermore, how might advanced time-series analyses--such as stationarity--be able to examine dynamic changes in the mean and variance of the HRV signal across time? Here we apply such methods to previously published data, which measured HRV pre- and post- a two-week compassionate mind training (CMT) intervention. Inspection of these data reveals that a visualization of HRV correlations across resting and compassion meditation states, pre- and post-two-week training, is retained across numerous recording timescales. Here, the fractal-like nature of our data indicates that the accuracy of representing HRV data can exist across timescales, albeit with greater or lesser granularity. Interestingly, inspection of the HRV signal at Time 2 compassion meditation versus Time 1 revealed a more highly correlated (i.e. potentially more stable) signal. We followed up these results with tests of stationarity, which revealed Time 2 had a less stochastic (variable) signal than Time 1, and a measure of distance in the time series, which showed that Time 2 had less of an average difference between rest and meditation than at Time 1. Our results provide novel assessment of visual and statistical markers of HRV change across distinct experimental states.