For the first time, fractal analysis techniques are implemented to study the correlations present in sleep actigraphy for individuals suffering from acute insomnia with comparisons made against healthy subjects. Analysis was carried out for 21 healthy individuals with no diagnosed sleep disorders and 26 subjects diagnosed with acute insomnia during night-time hours. Detrended fluctuation analysis was applied in order to look for 1/f-fluctuations indicative of high complexity. The aim is to investigate whether complexity analysis can differentiate between people who sleep normally and people who suffer from acute insomnia. We hypothesize that the complexity will be higher in subjects who suffer from acute insomnia owing to increased night-time arousals. This hypothesis, although contrary to much of the literature surrounding complexity in physiology, was found to be correct—for our study. The complexity results for nearly all of the subjects fell within a 1/f-range, indicating the presence of underlying control mechanisms. The subjects with acute insomnia displayed significantly higher correlations, confirmed by significance testing—possibly a result of too much activity in the underlying regulatory systems. Moreover, we found a linear relationship between complexity and variability, both of which increased with the onset of insomnia. Complexity analysis is very promising and could prove to be a useful non-invasive identifier for people who suffer from sleep disorders such as insomnia.