When animals get together in large numbers,  they often move in a very weird way.

Starlings might be the most famous for it. Their individual swoops translate to  massive undulations across the entire flock,   making the whole thing look  choreographed and hypnotic.

But birds aren’t the only  animals that move in this way. Schools of fish, swarms of insects,   and dense crowds of people can  display impressive coordination, too. Which makes these mesmerizing patterns  a tantalizing topic for the scientists   trying to figure out exactly how they work.

And not just so they can explain  why animal swarms look like that,   or help design buildings with safer layouts. Some of this research has even wound  up in a famous Hollywood movie! [♪ INTRO] When starlings move in those weird  flocks, it’s called a murmuration. And murmurations are just one  example of an emergent behavior.

Where each individual in a flock acts according  to its own motivations, there’s also an entirely   different collective behavior that arises  in response to all those individual actions. You're an emergent system, turns out,   just a bunch of cells working  together… and you have “thoughts”... “but I have to pee” “and are stressed” "I have to get up tomorrow." Now, since the movements of any one bird are  fairly predictable, you might think scientists   can just extrapolate to predict what shape the  overall murmuration will be at any given moment. But no.

There’s a bunch of unpredictable chaos  mixed in with all that determinism. As such, physicists have become  obsessed with emergent behavior,   and have created an entire subfield  devoted to it, called active matter. It’s clear that individual birds are communicating  with each other somehow to coordinate the motion.

Although exactly how is left for the biologists  to figure out, so we’ll set that aside for now. Don’t worry, bio fans, we will be back for you. Kind of like a like a game of Telephone,   the starlings seem like they only  communicate with their direct neighbors.

But unlike you experienced back in grade school,   the message they’re passing along can make it  across the entire flock without getting garbled. But what kind of messages are being sent, and  how far can they travel between individual birds? It’s time to break out the mathematical models.

So, let’s start with some basic behavioral  rules based on real-world observations:   First, individual birds avoid  crowding their neighbors. And second, an individual doesn’t  want to be separated from its flock. And third, individuals tend to end up facing  the same direction as their neighbors.

Each bird also has a limited range of visibility,   so let’s assume each individual in the  flock can only see its neighbors within   a couple of body-lengths of itself,  and within a specific angular range. Back in the 1980s, a computer scientist  named Craig Reynolds used a similar   set of rules to model what he called  bird-oid objects…or “boids” for short. Although technically, it wasn’t  just meant to model birds.

I love this, boids… They’re boids! The resulting algorithm was initially developed  for use in computer animation, and by 1992, it was   ready for its silver screen debut: modeling flocks  of penguins and bats in the movie Batman Returns. I told you it’s a famous hollywood movie.

The boids algorithm has been pretty successful  at replicating emergent behavior in flocks,   such as how small flocks of boids  merge to form larger flocks,   and how a flock can split to avoid an  obstacle like a tree or a predator. And for more accuracy, you can even program  your boids with a migratory urge, an ingrained   preferred direction inspired by a real life bird’s  biological urge to fly south for the winter. And I’m going to tell you more about this but much   like a basic cable showing of Batman  Returns, we do have to take a break.

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It’s a purposefully  oversimplified version of reality. You can tune the rules and parameters within  the algorithm, like the visibility range,   or “repulsion” and “attraction”  forces between the individual boids. Eventually, you’ll get simulation results that   mimic different animal swarms in the  real world and their emergent behavior.

And by tweaking the model properties,  scientists can inch toward figuring out   how individuals might sense and respond  to their flockmates and environment. But at the end of the day, they’re really  just inferring rules that seem to work and   recreate the emergent properties of a real flock. There could be lots of other parameters  physicists aren’t accounting for, and there are   often multiple combinations of input parameters  that lead to really similar simulation outputs.

But let’s give the physicists some  credit: they aren’t only guessing. They’ve taken measurements of birds, fish, and  insects to see how individuals influence each   other, allowing them to identify and  tune flocking simulation parameters. For example, analyses of starling murmurations  revealed that while the birds only interact   with their nearby neighbors, information  still makes it across the entire flock.

So if simulated flocks can also  communicate across the whole group,   then the model is on the right track. Meanwhile, studies on groups of three fish versus  shoals of 30 fish have found that the fish likely   receive signals from their closest neighbors  and their flockmates that are farther away. So adding more complicated terms to flocking   models like the boids algorithm  could improve simulation results.

But despite all these insights,   they’re still just simplified rules that  describe and reproduce flock phenomena. They can’t account for all the  complexities of animal behavior,   like individual motivations or decision making. And we do have to be careful not to  anthropomorphize these animals by assigning   them “goals” or “hopes” or “dreams”...unless  they’re the ones in Batman Returns.

Clearly, did have goals... So on the other side of the  emergent behavior problem,   biologists are considering the  neurobiology of how animals navigate. Instead of defining “rules” that the animals  follow, biologists have successfully simulated   flocking behaviors by modeling how animals  encode spatial information in their brains.

Physics models like the boids algorithm assume   actions depend on where an individual  is positioned relative to its neighbors. That’s considered an egocentric way to navigate. But biology studies have shown that,  basically across the board, animals   also navigate in allocentric ways, meaning  guided by external things in the landscape.

Egocentric and allocentric navigation  are stored differently inside the brain. And the allocentric flocking model  suggests that when some animals swarm,   they are rapidly switching between  egocentric and allocentric methods. This means animals can probably  sense where their flockmates are   relative to themselves and relative to  the landscape and any nearby predators.

This combination of self-centered  and landmark-oriented navigation   could be the biological key to  producing emergent swarm behaviors. One paper from 2025 has shown  that models of this random,   rapid neurobiological perspective-switching  can successfully recreate swarming behaviors   without needing to infer rules, like  what happens in the boids algorithm. These two different perspectives have brought  us closer to understanding animal swarms,   but physicists and biologists will need to keep  working together to understand active matter.

Because animal swarms aren’t the only  systems governed by active matter principles. Self-propelled robots, though not alive,  act individually according to fixed rules. And, much like starlings, they can display  completely different collective behavior.

For example, these tiny hexbug  robots that can turn a gear! On the living side of things, cells collectively   migrate during biological processes, like  embryonic development or wound healing. This emergent motion is completely different  from the motion of individual cells.

And don’t forget, humans are animals, too, but  with even more complicated decisions to make. Like whether or not to go see the Batman  movie marathon at your local theater. So active matter has also been  useful for modeling human crowds.

Using similar rules as the boids algorithm,   physicists have created models to describe  how people cross a crosswalk, form a mosh pit,   move through an exit, and create dangerous  crowd crushes during moments of panic. If we can design around that, we can  prevent unnecessary injuries or worse. Turns out those boids are pretty flocking useful. [♪ OUTRO]