Charles Darwin noted that natural selection applies even to the hourly organization of daily life. Indeed, in many species, the day is segmented into active periods when the animal searches for food, and inactive periods when the animal digests and rests. This episodic temporal patterning is conventionally referred to as ultradian (<24 hours) rhythmicity. The average time between ultradian events is approximately 1–2 hours, but the interval is highly variable. The ultradian pattern is stochastic, jaggy rather than smooth, so that although the next event is likely to occur within 1–2 hours, it is not possible to predict the precise timing. When models of circadian timing are applied to the ultradian temporal pattern, the underlying assumption of true periodicity (stationarity) has distorted the analyses, so that the ultradian pattern is frequently averaged away and ignored. Each active ultradian episode commences with an increase in hippocampal theta rhythm, indicating the switch of attention to the external environment. During each active episode, behavioral and physiological processes, including changes in body and brain temperature, occur in an integrated temporal order, confirming organization by programs endogenous to the central nervous system. We describe methods for analyzing episodic ultradian events, including the use of wavelet mathematics to determine their timing and amplitude, and the use of fractal-based procedures to determine their complexity.