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The escape paths prey animals take following a predatory attack appear to be highly unpredictable - a property that has been described as 'protean behaviour'. Here, we present a method of quantifying the escape paths of individual animals using a path complexity approach. When individual fish ( Pseudomugil signifer ) were attacked, we found that a fish's movement path rapidly increased in complexity following the attack. This path complexity remained elevated (indicating a more unpredictable path) for a sustained period (at least 10 s) after the attack. The complexity of the path was context dependent: paths were more complex when attacks were made closer to the fish, suggesting that these responses are tailored to the perceived level of threat. We separated out the components of speed and turning rate changes to determine which of these components contributed to the overall increase in path complexity following an attack. We found that both speed and turning rate measures contributed similarly to an individual's path complexity in absolute terms. Overall, our work highlights the context-dependent escape responses that animals use to avoid predators, and also provides a method for quantifying the escape paths of animals., Competing Interests: Competing interestsThe authors declare no competing or financial interests., (© 2017. Published by The Company of Biologists Ltd.)