Flocking model

The flock model illustrates how flocking behavior can emerge when each bird follows three simple rules:

  • maintain a minimum distance from other birds to avoid collision
  • fly towards the average position of neighbors
  • fly in the average direction of neighbors

It is also available from the Models module as Models.flocking.

Defining the core structures

We begin by calling the required packages and defining an agent type representing a bird.

using Agents
using Random, LinearAlgebra

@agent Bird ContinuousAgent{2} begin

The fields id and pos, which are required for agents on ContinuousSpace, are part of the struct. The field vel, which is also added by using ContinuousAgent is required for using move_agent! in ContinuousSpace with a time-stepping method. speed defines how far the bird travels in the direction defined by vel per step. separation defines the minimum distance a bird must maintain from its neighbors. visual_distance refers to the distance a bird can see and defines a radius of neighboring birds. The contribution of each rule defined above receives an importance weight: cohere_factor is the importance of maintaining the average position of neighbors, match_factor is the importance of matching the average trajectory of neighboring birds, and separate_factor is the importance of maintaining the minimum distance from neighboring birds.

The function initialize_model generates birds and returns a model object using default values.

function initialize_model(;
    n_birds = 100,
    speed = 1.0,
    cohere_factor = 0.25,
    separation = 4.0,
    separate_factor = 0.25,
    match_factor = 0.01,
    visual_distance = 5.0,
    extent = (100, 100),
    seed = 42,
    space2d = ContinuousSpace(extent; spacing = visual_distance/1.5)
    rng = Random.MersenneTwister(seed)

    model = ABM(Bird, space2d; rng, scheduler = Schedulers.Randomly())
    for _ in 1:n_birds
        vel = Tuple(rand(model.rng, 2) * 2 .- 1)
    return model

model = initialize_model()
StandardABM with 100 agents of type Bird
 space: periodic continuous space with (100.0, 100.0) extent and spacing=3.3333333333333335
 scheduler: Agents.Schedulers.Randomly

Defining the agent_step!

agent_step! is the primary function called for each step and computes velocity according to the three rules defined above.

function agent_step!(bird, model)
    # Obtain the ids of neighbors within the bird's visual distance
    neighbor_ids = nearby_ids(bird, model, bird.visual_distance)
    N = 0
    match = separate = cohere = (0.0, 0.0)
    # Calculate behaviour properties based on neighbors
    for id in neighbor_ids
        N += 1
        neighbor = model[id].pos
        heading = neighbor .- bird.pos

        # `cohere` computes the average position of neighboring birds
        cohere = cohere .+ heading
        if euclidean_distance(bird.pos, neighbor, model) < bird.separation
            # `separate` repels the bird away from neighboring birds
            separate = separate .- heading
        # `match` computes the average trajectory of neighboring birds
        match = match .+ model[id].vel
    N = max(N, 1)
    # Normalise results based on model input and neighbor count
    cohere = cohere ./ N .* bird.cohere_factor
    separate = separate ./ N .* bird.separate_factor
    match = match ./ N .* bird.match_factor
    # Compute velocity based on rules defined above
    bird.vel = (bird.vel .+ cohere .+ separate .+ match) ./ 2
    bird.vel = bird.vel ./ norm(bird.vel)
    # Move bird according to new velocity and speed
    move_agent!(bird, model, bird.speed)
agent_step! (generic function with 1 method)

Plotting the flock

using InteractiveDynamics
using CairoMakie

The great thing about abmplot is its flexibility. We can incorporate the direction of the birds when plotting them, by making the "marker" function am create a Polygon: a triangle with same orientation as the bird's velocity. It is as simple as defining the following function:

const bird_polygon = Polygon(Point2f[(-0.5, -0.5), (1, 0), (-0.5, 0.5)])
function bird_marker(b::Bird)
    φ = atan(b.vel[2], b.vel[1]) #+ π/2 + π
    scale(rotate2D(bird_polygon, φ), 2)
bird_marker (generic function with 1 method)

Where we have used the utility functions scale and rotate2D to act on a predefined polygon. We now give bird_marker to abmplot, and notice how the as keyword is meaningless when using polygons as markers.

model = initialize_model()
figure, = abmplot(model; am = bird_marker)

And let's also do a nice little video for it:

    "flocking.mp4", model, agent_step!;
    am = bird_marker,
    framerate = 20, frames = 100,
    title = "Flocking"