Just Lévy Things

Lévy patterns are one of the craziest things there is; proof that free will is an illusion, and one of those typically invisible patterns that can be used to predict our behavior (and to mimic our behavior, for those of us making artificial humans).

It happens all over the place, from the way animals forage, to the way our eyes move across a computer screen. It's one of those universal laws that happens in biology and in physics too (called Brownian walk, or Brownian motion). But you might remember it more easily by calling it simply "foraging behavior", a mixture of small random movements with less frequent larger movements.

It's no secret that we do this; our eyes get mapped when we look at websites to figure out how to make us click-buy uncontrollably. Hidden cameras in retail shops do the same thing. Pedestrian traffic, vehicle traffic, pandemics even, you name it. 

What we don't know is the full "why" of Lévy walks. Why use such a chaotic approach; wouldn't a more rational approach get better results? Researchers at RIKEN made a simulation that found Lévy patterns popping up spontaneously at critical moments such as the edge between Exploitation vs Exploration -- for example when an animal has to decide whether to exploit areas that are already known to be beneficial, versus exploring for new areas.

You know exploit/explore, it's how you decide where to eat dinner -- on those nights when Old Trusty just isn't cutting it, then it's time to explore. But at the same time, you can't "explore" every night, or going out to eat would be exhausting, and less rewarding in general. So the next time you're at that critical juncture, just let the chaos take over. Or, soon enough, let the Lévy algorithm do it for you.

 

Chaotic Lévy walks are a good strategy for animals

Sep 2020, phys.org

https://phys.org/news/2020-09-chaotic-lvy-good-strategy-animals.html

via the RIKEN Center: Masato S. Abe. Functional advantages of Lévy walks emerging near a critical point, Proceedings of the National Academy of Sciences (2020). DOI: 10.1073/pnas.2001548117

See Also:

Pedestrians at crosswalks found to follow the Lévy walk process

Apr 2019, phys.org

https://phys.org/news/2019-04-pedestrians-crosswalks-levy.html

Musical melodies obey same laws as foraging animals

Jan 2016, phys.org

http://phys.org/news/2016-01-musical-melodies-laws-foraging-animals.html

Post Script:

When you see RIKEN Center being involved, you know you're in for some cool stuff. 

Nature Nature Everywhere

Van Gogh's starry swirls are generally known to be formed according to Levy distributions, which are mathematical formulae, and can be found in turbulent water and other natural phenomena

Musical melodies obey same laws as foraging animals
phys.org, Jan 2016

"The researchers found that the distribution of melodic intervals in two classical concertos and two folk songs can be modeled by a Lévy distribution... [which] describes many other diverse scenarios, such as the turbulent motion of a particle in a liquid or gas, the changes in the price of a stock, earthquake activity, and the foraging paths of wild animals."

It really makes you wonder natural vs artificial, and free will etc.

Did Van Gogh really put those lines there, or was he just following his animal instinct. Debussy?

POST SCRIPT

Music, the Arts and Ideas
Leonard B. Meyer, U. of Chicago, 1967

“It is impossible to stand outside of culture, for the models and categories we use on conceptualizing and ordering the world are necessarily limited to, if not determined by, those which are provided by our particular culture.” (viii)

“A culture, like a musical style, is a learned probability system.” (p17, footnote 21)

Culture as Learned Probability System
Network Address, 2012