PyVicsek

This is a Python library used to simulate systems using the Vicsek model. It currently has support for non periodic-boundary conditions, $N$-dimensional space, as well as particle heterogeneity.

Dependencies and Installation

VicsekPy is best run on Python 3.9+ and is supported by numpy, scipy, matplotlib, and tqdm. Additionally, unit tests are made with pytest. These packages are automatically included in requirements.txt.

To download VicsekPy, run the following commands in a UNIX terminal:

pip install pyvicsek

Examples

Here is a basic script to initialize and create a 2-D homogenous Vicsek system.

import vicsek as vs

N = 1024
L = 16
v = 0.03

particles = vs.initialize_random_particles(
    n_particles=N,
    box_length=L,
    speed=v,
    n_dimensions=2,
    particle_type='standard'
)

vicsek = vs.Vicsek(
    particles=particles,
    length=L,
    interaction_range=1.0,
    speed=v,
    base_noise=0.5,
)

anim = vicsek.animate(frames=200)
anim.save(filename='example.gif')

Here is another example to initialize a 2-D heterogeneous Vicsek system.

import vicsek as vs

N = 1024
L = 16
v = 0.03

particles_A = vs.initialize_random_particles(
    n_particles=round(N * 0.5),
    box_length=L,
    speed=v,
    n_dimensions=2,
    particle_type='A'
)

particles_B = vs.initialize_random_particles(
    n_particles=round(N * 0.5),
    box_length=L,
    speed=v,
    n_dimensions=2,
    particle_type='B'
)

particles = particles_A + particles_B

alignment_weights = {
    ('A', 'A'): 1.0,
    ('B', 'B'): 1.0,
    ('A', 'B'): -1.0,
    ('B', 'A'): -1.0,
}

noise_weights = {
    ('A', 'A'): 0.5,  # low noise within groups
    ('B', 'B'): 0.5,
    ('A', 'B'): 2.0,  # high noise between groups
    ('B', 'A'): 2.0,
}

legend = {
    'A': 'red',
    'B': 'blue',
}


vicsek = vs.HeterogeneousVicsek(
    particles=particles,
    length=L,
    interaction_range=1.0,
    speed=v,
    base_noise=0.5,
    alignment_weights=alignment_weights,
    noise_weights=noise_weights
)

anim = vicsek.animate(frames=200, legend=legend)
anim.save(filename='hetero_example.gif')

You can find more information on the Vicsek class as well as other classes in the doc-strings located in the files of the vicsek directory. You can also find further examples in the scripts directory, where they are organized by system type.

Roadmap

If given more time, we would like to spend some time working on the following things for this library:

• Higher dimensional testing.
• Lyapunov analysis of phase dimensions (based on this paper).
• Geometry support for particles and boundaries using shapely.