A “landscape of fear” (LOF) is a map that describes continuous spatial variation in an animal's perception of predation risk. The relief on this map reflects, for example, places that an animal avoids to minimize risk. Although the LOF concept is a potentially unifying theme in ecology that is often invoked to explain the ecological and conservation significance of fear, little is known about the daily dynamics of an LOF. Despite theory and data to the contrary, investigators often assume, implicitly or explicitly, that an LOF is a static consequence of a predator's mere presence within an ecosystem. We tested the prediction that an LOF in a large‐scale, free‐living system is a highly dynamic map with “peaks” and “valleys” that alternate across the diel (24‐h) cycle in response to daily lulls in predator activity. We did so with extensive data from the case study of Yellowstone elk (Cervus elaphus) and wolves (Canis lupus) that was the original basis for the LOF concept. We quantified the elk LOF, defined here as spatial allocation of time away from risky places and times, across nearly 1,000‐km² of northern Yellowstone National Park and found that it fluctuated with the crepuscular activity pattern of wolves, enabling elk to use risky places during wolf downtimes. This may help explain evidence that wolf predation risk has no effect on elk stress levels, body condition, pregnancy, or herbivory. The ability of free‐living animals to adaptively allocate habitat use across periods of high and low predator activity within the diel cycle is an underappreciated aspect of animal behavior that helps explain why strong antipredator responses may trigger weak ecological effects, and why an LOF may have less conceptual and practical importance than direct killing.