The common misconception

Our mental model about CAS in nature was wrong

Many people are enamored by the flocking behavior of animals like fish or birds. However, it is a common misconception that such flocks are led by a leader fish or bird that orchestrate the flock (Potts, 1984). In this short interactive lesson, we will discover that no such leader exists. Flocks, herds, or schools, in fact, are the result of emergent behavior that often occurs when the individual animals follow simple rules.

As the headline suggests, this lesson utilizes the flocking behavior of animals to introduce the concept of complex adaptive systems (CAS). Before we begin, let's lets define what CAS are:

CAS are systems that have a large numbers of components, often called agents, that interact and adapt or learn. - John H. Holland

Holland posits that although many CAS show differences in the details, they all share four major features: (i) parallelism, (ii) conditional action, (iii) modularity, (iv) adaptation and evolution.

Put another way, CAS are comprised of many parts (i) whose interactions (ii & iii) lead to complex outcomes (iv) when exercised as a collective. Specifically, in CAS, their many parts are usually local agents that follow simple rules concerning their neighbors. This set of simple behaviors followed by a collective may ultimately lead to an emergent outcome.

CAS in Nature

How agent-based models can help us simulate emergent behavior

It turns out that we are able to simulate such behavior with an approach called agent-based modeling (ABM). In ABM, a collection of individual agents obeying simple rules is modeled as a system that evolves over time. With every timestep, each agent acts upon the rules it obeys constrained by its immediate surroundings.

In the late 1980s, Craig Reynolds introduced an algorithm that he called the Boids Algorithm that is based on the ABM approach (Reynolds, 1987). His algorithm proposes to model the individuals agents as so-called boids, that possess a certain field of vision within which they are able to respond to their surroundings and follow simple rules. Hence, the agents' individual perspective is local, they are not aware that they are part of a global system, neither are they aware of all of their neighbors.

When translating the concept of CAS to nature, we can imagine that different CASs have individual characteristics, depending of whether we think of schools of fish, insects, or flocks of birds. Let's explore a set of possible characteristics in the interactive simulations below.

Rules

The three rules for the agents to follow are simple

The agents or boids in our simulation will start moving from a random location starting from the center of a canvas. While doing that, they will follow three rules with respect to their neighbors in their local vicinity. Their local vicinitry is given by a radius that we call field of vision.

 

 

Cohesion

If agents are within the field of perception, steer towards the center of all neighbors.

 

Separation

Agents that are too close to each other will try to maintain a safe distance from each other.

 

Alignment

If agents approach each other within their field of vision, they will align their trajectories.

Interrogating the rules

Dissecting the model into its constituent parts builds intuition

Cohesion

Under this rule, boids are steering toward the center of mass of all boids in their vicinity. However, that merely leads to one or possibly several individual clusters of boids across the canvas.

 

Separation

Under this rule, the boids will avoid each other and try to keep a safe distance. As a result, we merely see dispersed boids across the canvas.

 

Alignment

Under this rule, the boids will try to align their steering angle with the average steering angle of all the boids in their vicinity. Now, we see flocking behavior starting to form, however, it is not as sophisticated as expected.

 

Putting it all together

Cohesion, Separation & Alignment in one simulation

In our final simulation, the boids will obey all three rules that we introduced above. The individual strength of compliance with each rule is exposed to you by sliders. That means that you can dynamically interact with the simulation and change the rules on the fly. In its initial state, all three rules are neglected by the boids.

Alignment
Cohesion
Separation

 

Exercise

Try to find a combination of rules that will lead to emergent behavior such as what can be observed from bird flocking behavior. Once you are happy with your attempt, have a look at a possible solution by clicking the button below.

References

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