Fractals within practical uses: Satellite tagged Narwhals. Let's ponder the data.

Recently, biologists published an extensive study in PLOS Computational Biology. A team of biologists tracked the behaviour of narwhals with satellite tagged narwhals. To ponder this, we'll de-complex the study into plain English; they used chaos theory, what appears chaotic behaviour is actually not chaotic at all. I find this amazing because it illustrates that what appears to be irregularity is actually a pattern - fractal behaviour of the narwals! So, today, we'll be landing the space whale to ponder the oceans.


Under the Arctic Sea ice, narwhals are enigmatic marine mammals that fascinate us with their unique appearance and secretive lifestyles.

In recent years, scientists have also made a few key discoveries about narwhals, including how to save some endangered populations.


The narwhal's movements through the oceans are complicated by their deep dives to nearly 1.2 miles beneath the surface and dependence on sea ice for their life cycle.


The movement of narwhals off the coast of East Greenland seemed to be irregular every day, but, with the help of chaos theory, researchers have shed some light on this.


Pondering the Oceans


​​"While animal-borne ocean sensors continue to advance and collect more data, there is a lack of adequate methods to analyse records of irregular behaviour," says Evgeny A. Podolskiy, a geoscientist at Hokkaido University in Japan and first author of the new study.


By collaborating with Mads Peter Heide-Jorgensen, a marine biologist at the Greenland Institute of Natural Resources, Podolskiy aimed to find patterns in narwhals' seemingly haphazard behaviour.


Despite appearing unpredictable, chaos theory describes activity governed by strict laws.


The dependable physics pile up in ways no system can handle, like a butterfly kicking off a hurricane with a flap of its wing, the butterfly's flap, creating a hurricane is just a metaphor for chaos theory. But similarly, the narwhal's meanderings do not make sense to our human brains as they go about their daily lives.



(Video data: Nonlinear analysis of narwhal dive records (data and animation)


An adult male narwhal's movements were recorded by a satellite-linked time-depth recorder attached to its back over an 83-day period, providing new insights into narwhal behaviour.

Satellite-linked transmitter attached to a live-captured narwhal in Scoresby Sound, East Greenland. (Greenland Institute of Natural Resources)

Mathematical techniques borrowed from chaos theory were used by Podolskiy and Heide-Jrgensen to make sense of chaotic behaviour in dynamic settings.


Researchers explain that these techniques can reveal hidden states of chaotic systems, known as "attractors."

And some complex processes, such as cryptic narwhal behaviour, can be detected with the help of these techniques, therefore, using mathematics in practical uses, rather than just complex abstract equations.


The tools of chaos theory helped unveil a hidden daily pattern for this narwhal, including novel details about how those habits can be influenced by variables such as seasonal change.

As a result, they discovered that when the tagged narwhal dived, it plunged particularly deep during midday.


As the narwhal hunted for squid at twilight and at night, its dives were shallower but more intense.

The narwhal also adjusted his patterns in response to the prevalence of sea ice, the study found.

As sea ice increased, he not only reduced his surface activity but also dived more intensely.

Even though narwhals are not listed as an endangered species by the International Union for Conservation of Nature, they are still vulnerable to human activities, from ship traffic to pollution to climate change.



Narwhals live in a world where sea ice is rapidly vanishing due to global climate change, and insights about their behaviour could be valuable in protecting them, so chaos theory is now in a strange territory, potentially to protect them in the near future.


The minds behind the study conclude that chaos theory could also be useful for examining animal behaviour in a more general sense.

This approach might help us understand the challenges faced by other Arctic wildlife as a result of rising temperatures and dwindling sea ice, for example, even though it is still in its infancy and is still being explored, but this study alone is extremely detailed, and that detail can be read over at where the study was published. (PLOS Computational Biology click)


But I did warn you it's complex, I mean look at this which is included in the study:


''Using the analogy of atomic orbitals, the core can be seen as the most stable state with minimum potential energy, where the least kinetic energy is spent. Any displacement from this point of equilibrium corresponds to increasing energy and thus less stability. The inner orbits correspond to medium energy, and outer orbits to higher energy. Trajectories departing further from the characteristic outer region correspond to the highest energy, least stable states. To quantify the magnitude of departure from the core, we computed Euclidean distance, L, between the origin [0, 0, 0] and each individual trajectory point:''

It's a beautiful equation, but not entirely understandable in practical terms and to conformably ponder. But the information is there and ready to be read for those who would like to dive deeper into this interesting study. (PLOS Computational Biology click)





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