The quantification of subtle patterns in sequential data, and their changes, has considerable potential utility both in analysis of hormonal secretory dynamics, and of fetal heart rate rhythms. Approximate entropy, a recently developed statistic quantifying serial irregularity, has been applied in both these settings, and has yielded a number of new findings. Among endocrine applications, approximate entropy increases with increasing age for luteinizing hormone and follicle stimulating hormone, for both women and men, indicating greater irregularity (more apparently random dynamics) in the older groups; for the luteinizing hormone-testosterone axis, both irregularity and asynchrony increases accompany advancing age for men. These findings produce a means to potentially predict time until menopause onset, the efficacy of infertility drugs, and also provide firm quantitative support of a partial male menopause. In fetal monitoring, antepartum, and postnatal heart rate studies, approximate entropy consistently detected subtle shifts in heart rate rhythmicity, with greater regularity clinically corresponding to compromised physiology in all settings. Both the capability of approximate entropy to quantify rhythm changes undiscernible by auscultation, and a continuum interpretation linking per-individual antepartum, perinatal, and postnatal heart rate analyses provide considerable potential enhancement to the present clinical utility of fetal monitoring.