and behave in ways that map strongly to the periodicity of the circadian clock, then which is a sign of better health and improved overall wellness [5].  
One approach to detecting recurrences in data streams is visualising them via recurrence plots (RPs) [6]. These are visualisations of a matrix in which elements of the matrix correspond to instances at which there is a recurrence in a dynamic system. RPs operate by first performing a cluster analysis on the data and then building graphical patterns to illustrate recurrences in the data. RPs have been used in many applications, for example, fault diagnosis in machinery [7] and image transformations [8].  
Recurrence plots are useful for providing analysis of short sequences with a limited amount of recurrence, but for longer time series with many iterations of recurrences, they are designed to hide the volume of iterations and to mask variations that may occur among the iterations. Sometimes when we look for and find patterns in time series data, we want to measure those patterns and compare the patterns over time or even compare them to other recurring patterns. This goes far beyond just using the patterns to detect outliers. If we could measure the patterns and how strong their recurrence is at different points throughout a dataset, then this might reveal insights into the patterns and deeper insights into the data.  
In previous work, we developed a technique for calculating and visualising the strength of periodicity at a given frequency throughout a time series. The technique was applied to the sleeping patterns of US war veterans who continuously wore wrist-worn accelerometers for 90 consecutive days each, and we found that the 24 h periodicity strength varied significantly across participants [9]. That work also found that high levels of periodicity indicating regular sleep and movement patterns, were associated with lower measures of LDL-cholesterol, triglycerides and hs-CRP, as well as improved health-related quality of life measures [9]. The same technique for visualising periodicity strength over time was used in an analysis of lifelong data defined as the automatic digital recording of everyday activities, and it provided insights into shifts in the underlying behaviour of the subjects [10].  
While [PERSON] et al. [11] used the same term, \"periodicity intensity\", in their work on the diagnosis of faults in machine bearings, their work defines periodicity intensity as the ratio of the energy of the local maxima to the total energy in the autocorrelation of vibration signals in faulty machinery and that is very different to the definition of periodicity used here.  
Our research hypothesis is that computing a visualisation of the strength of 24-h periodicity for a range of longitudinal time series data will reveal insights into the data that are not visible using other forms of analysis. In this paper, we apply the calculation of periodicity strength to three different use cases and show how, in each case, deeper insights into the data are revealed by the analysis. The paper's importance lies in the relative simplicity of the technique and of the computation and the powerful insights into time series data that it provides. The technique can be used on any data series where underlying temporal patterns reoccur and where the strength of those patterns throughout the data is important to determine.