Animal welfare assessment commonly involves behavioural and physiological measurements. Physiological measures have become increasingly sophisticated over the years, while behavioural measurements, for example duration or frequency, have changed little. Although these measures can undoubtedly contribute to our assessment of an animal's welfare status, a more complex analysis of behavioural sequences could potentially reveal additional and valuable information. One emerging methodology that could provide such information is fractal analysis, which calculates measures of complexity in continuous time series. Its previous application in medical physiology suggested that it could reveal ‘hidden’ information in a dataset beyond that identified by traditional analyses. Consequently, we asked if fractal analysis of behaviour might be a useful non-invasive measure of acute and chronic stress in laying hens and in pigs. Herein, we outline our work and briefly review some previous applications of fractal analysis to animal behaviour patterns. We successfully measured novel aspects of complexity in the behavioural organisation of hens and pigs and found that these were stress-sensitive in some circumstances. Although data collection is time consuming, the benefit of fractal analysis is that it can be applied to simple behavioural transitions, thereby reducing subjective interpretation to a minimum. Collectively, the work to date suggests that fractal analysis — by providing a novel measure of behavioural organisation — could have a role in animal welfare assessment. As a method for extracting extra information from behavioural data, fractal analysis should be more widely examined in animal welfare science.