  Being able to objectively characterise the intrinsic complexity of
behavioural patterns resulting from human or animal decisions is fundamental
for deconvolving cognition and designing autonomous artificial intelligence
systems. Yet complexity is difficult in practice, particularly when strings are
short. By numerically approximating algorithmic (Kolmogorov) complexity (K), we
establish an objective tool to characterise behavioural complexity. Next, we
approximate structural (Bennett's Logical Depth) complexity (LD) to assess the
amount of computation required for generating a behavioural string. We apply
our toolbox to three landmark studies of animal behaviour of increasing
sophistication and degree of environmental influence, including studies of
foraging communication by ants, flight patterns of fruit flies, and tactical
deception and competition (e.g., predator-prey) strategies. We find that ants
harness the environmental condition in their internal decision process,
modulating their behavioural complexity accordingly. Our analysis of flight
(fruit flies) invalidated the common hypothesis that animals navigating in an
environment devoid of stimuli adopt a random strategy. Fruit flies exposed to a
featureless environment deviated the most from Levy flight, suggesting an
algorithmic bias in their attempt to devise a useful (navigation) strategy.
Similarly, a logical depth analysis of rats revealed that the structural
complexity of the rat always ends up matching the structural complexity of the
competitor, with the rats' behaviour simulating algorithmic randomness.
Finally, we discuss how experiments on how humans perceive randomness suggest
the existence of an algorithmic bias in our reasoning and decision processes,
in line with our analysis of the animal experiments.
