Basically, this means that simple models of animals brains, even applied to relatively simple scenarios, don't work very well. Assuming that an animal brain will produce behaviors that consist of the combination of some deterministic behavior with some simple random input is, apparently, incorrect. The behavior of an animal is more complicated than that. How complicated? We're not sure. The basic simple models of randomness - gaussian systems, power-law systems, non-linear chaotic systems - all do not produce a behavior with the complex traits that we see in the data collected for this experiment. But the data is also not consistent with any simple deterministic system. So there's something complex going on.When the models fail to fit the data, it does not indicate that the data cannot be fitted to any model. It simply proves that we haven't yet found one that works. Period. End of story.
This does not mean that the fly has some kind of "spirit" which is deciding "Hey, I think I'll twitch now". Nor does it mean that the behavior of the fly cannot be modeled by any deterministic process with some kind of random input. In fact, the data suggests exactly the opposite: the strong fractal structure shown for the data suggests that there is some combination of complex deterministic structure and randomness. Just that it's not the kind of very simple one that we might have expected from something as a simple as a fly.
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