Vicsek Lab: Sliders

Module 2: Synchronization and Collective Behaviour

Optional extension

This page is optional. It continues Interactive Animation, where you created the $2 \times 2$ figure, the order-parameter plot and the noise diagnostic plot. Here you write the update function and create the sliders (Hunter 2007).

Write the Animation Update Function

The core loop is expanded to include updates for the order parameter plot and noise diagnostic plot. The pipeline is as follows:

advance the Vicsek dynamics by one step (vicsek_equations).
update xy_tail.
update the particle artists.
update order-parameter history ls_order_param and its plot.
update the noise diagnostic dict_noise and its plot.

As you can see, steps 1-3 remain the same as in Animation Loop. Use this checklist:

call vicsek_equations(...)
update xy_tail with np.roll(...)
plt_particles.set_data(...) and plt_current.set_data(...)
append vicsek_order_parameter(theta) to the window list
set line data for the order parameter plot
compute a recent average
update dict_noise[noise_eta] and redraw the noise curve

Exercise

Complete update_animation(), following the comments for each step. Keep the function inside run_simulation so it can access the state variables with nonlocal.

def update_animation(frame: int):
    nonlocal xy, xy_tail, theta, noise_eta, v0, radius_interaction, box_size, dict_noise, ls_order_param

    # TODO: advance the Vicsek equations

    # TODO: update the tail tensor
    # TODO: update the particle artists with set_data

    # TODO: update the order parameter history and plot

    # TODO: compute a recent average and update dict_noise

    # TODO: update the noise diagnostic plot with set_data


    return (plt_particles, plt_current, line_order_param, line_noise)

Hint

Keep only the last ORDER_WINDOW values with ls_order_param[-ORDER_WINDOW:]. For the recent average, take the mean of the last third of that window. line_noise.set_data(*zip(*dict_noise.items())) turns the dictionary into x and y lists.

Solution

def update_animation(frame: int):
    nonlocal \
        xy, \
        xy_tail, \
        theta, \
        noise_eta, \
        v0, \
        radius_interaction, \
        box_size, \
        dict_noise, \
        ls_order_param
    xy, theta = vicsek_equations(
        xy,
        theta,
        v0=v0,
        dt=dt,
        radius_interaction=radius_interaction,
        box_size=box_size,
        noise=noise_eta,
    )

    # Update tails
    xy_tail = np.roll(xy_tail, shift=-1, axis=2)
    xy_tail[:, :, -1] = xy
    plt_particles.set_data(xy_tail[0].flatten(), xy_tail[1].flatten())
    plt_current.set_data(xy[0], xy[1])

    # Update order parameter
    ls_order_param.append(vicsek_order_parameter(theta))
    ls_order_param = ls_order_param[-ORDER_WINDOW:]
    x_vals = np.arange(len(ls_order_param))
    line_order_param.set_data(x_vals, ls_order_param)

    # Average the last ORDER_WINDOW//3 values to get the order parameter (similar to Couzin)
    order_param = np.mean(ls_order_param[-ORDER_WINDOW // 3 :])
    dict_noise[noise_eta] = order_param
    dict_noise = dict(sorted(dict_noise.items()))
    if dict_noise:
        line_noise.set_data(*zip(*dict_noise.items()))
    else:
        line_noise.set_data([], [])
    return (plt_particles, plt_current, line_order_param, line_noise)

Create the Animation Object

This stays the same as before:

ani = animation.FuncAnimation(fig, update_animation, interval=0, blit=True)

Add Sliders

You want sliders for:

Number of boids $N$ (special: requires reinitializing particles).
Interaction radius $r$.
Noise $\eta$.
Speed $v_0$.
Box size $L$.

Create Slider Axes

Create small inset axes inside ax_sliders:

def make_slider_axes(ax_sliders: Axes):
    ax_sliders.axis("off")

    ax_num_boids = ax_sliders.inset_axes([0.0, 1.2, 0.8, 0.1])
    ax_radius_interaction = ax_sliders.inset_axes([0.0, 1.0, 0.8, 0.1])
    ax_noise_eta = ax_sliders.inset_axes([0.0, 0.8, 0.8, 0.1])
    ax_v0 = ax_sliders.inset_axes([0.0, 0.6, 0.8, 0.1])
    ax_box_size = ax_sliders.inset_axes([0.0, 0.4, 0.8, 0.1])

    return ax_num_boids, ax_radius_interaction, ax_noise_eta, ax_v0, ax_box_size

Create the Slider Widgets

Matplotlib’s Slider lives in matplotlib.widgets. Its signature is Slider(ax, label, valmin, valmax, valinit=..., valstep=...).

Exercise

Import Slider and create the five sliders with appropriate ranges and initial values.

from matplotlib.widgets import Slider

def make_sliders(
    *,
    ax_num_boids,
    ax_radius_interaction,
    ax_noise_eta,
    ax_v0,
    ax_box_size,
    num_boids: int,
    radius_interaction: float,
    noise_eta: float,
    v0: float,
    box_size: float,
):
    # TODO: define the sliders with appropriate ranges and initial values

    return slider_num_boids, slider_radius_interaction, slider_noise_eta, slider_v0, slider_box_size

Solution

These are the ranges used in amlab/collective_motion/vicsek_animation.py. The noise range $[0, 5]$ matches the x-limits of the noise plot.

from matplotlib.widgets import Slider

def make_sliders(
    *,
    ax_num_boids,
    ax_radius_interaction,
    ax_noise_eta,
    ax_v0,
    ax_box_size,
    num_boids: int,
    radius_interaction: float,
    noise_eta: float,
    v0: float,
    box_size: float,
):
    slider_num_boids = Slider(ax_num_boids, "Number of boids", 100, 1000, valinit=num_boids, valstep=100)
    slider_radius_interaction = Slider(
        ax_radius_interaction, "Interaction radius", 0, 50, valinit=radius_interaction, valstep=1
    )
    slider_noise_eta = Slider(ax_noise_eta, "Noise", 0.0, 5.0, valinit=noise_eta, valstep=0.01)
    slider_v0 = Slider(ax_v0, "Speed", 0.0, 0.1, valinit=v0, valstep=0.01)
    slider_box_size = Slider(ax_box_size, "Dimension", 1, 50, valinit=box_size, valstep=1)

    return slider_num_boids, slider_radius_interaction, slider_noise_eta, slider_v0, slider_box_size

Call it with keyword arguments, because of the * in the signature.

References

Hunter, John D. 2007. “Matplotlib: A 2D Graphics Environment.” Computing in Science & Engineering 9 (3): 90–95. https://doi.org/10.1109/MCSE.2007.55.

--- title: "Vicsek Lab: Sliders" subtitle: "Module 2: Synchronization and Collective Behaviour" format: html --- ::: {.callout-tip} ## Optional extension This page is optional. It continues [Interactive Animation](vicsek-animation-interactive.qmd), where you created the $2 \times 2$ figure, the order-parameter plot and the noise diagnostic plot. Here you write the update function and create the sliders [@hunter2007matplotlib]. ::: ## Write the Animation Update Function The core loop is expanded to include updates for the order parameter plot and noise diagnostic plot. The pipeline is as follows: 1. advance the Vicsek dynamics by one step (`vicsek_equations`). 2. update `xy_tail`. 3. update the particle artists. 4. update order-parameter history `ls_order_param` and its plot. 5. update the noise diagnostic `dict_noise` and its plot. As you can see, steps 1-3 remain the same as in [Animation Loop](vicsek-animation-loop.qmd). Use this checklist: - [x] call `vicsek_equations(...)` - [x] update `xy_tail` with `np.roll(...)` - [x] `plt_particles.set_data(...)` and `plt_current.set_data(...)` - [ ] append `vicsek_order_parameter(theta)` to the window list - [ ] set line data for the order parameter plot - [ ] compute a *recent average* - [ ] update `dict_noise[noise_eta]` and redraw the noise curve ::: {.callout-note} ## Exercise Complete `update_animation()`, following the comments for each step. Keep the function inside `run_simulation` so it can access the state variables with `nonlocal`. ```python def update_animation(frame: int): nonlocal xy, xy_tail, theta, noise_eta, v0, radius_interaction, box_size, dict_noise, ls_order_param # TODO: advance the Vicsek equations # TODO: update the tail tensor # TODO: update the particle artists with set_data # TODO: update the order parameter history and plot # TODO: compute a recent average and update dict_noise # TODO: update the noise diagnostic plot with set_data return (plt_particles, plt_current, line_order_param, line_noise) ``` ::: ::: {.callout-tip collapse="true"} ## Hint Keep only the last `ORDER_WINDOW` values with `ls_order_param[-ORDER_WINDOW:]`. For the recent average, take the mean of the last third of that window. `line_noise.set_data(*zip(*dict_noise.items()))` turns the dictionary into x and y lists. ::: ::: {.callout-tip collapse="true"} ## Solution ```python def update_animation(frame: int): nonlocal \ xy, \ xy_tail, \ theta, \ noise_eta, \ v0, \ radius_interaction, \ box_size, \ dict_noise, \ ls_order_param xy, theta = vicsek_equations( xy, theta, v0=v0, dt=dt, radius_interaction=radius_interaction, box_size=box_size, noise=noise_eta, ) # Update tails xy_tail = np.roll(xy_tail, shift=-1, axis=2) xy_tail[:, :, -1] = xy plt_particles.set_data(xy_tail[0].flatten(), xy_tail[1].flatten()) plt_current.set_data(xy[0], xy[1]) # Update order parameter ls_order_param.append(vicsek_order_parameter(theta)) ls_order_param = ls_order_param[-ORDER_WINDOW:] x_vals = np.arange(len(ls_order_param)) line_order_param.set_data(x_vals, ls_order_param) # Average the last ORDER_WINDOW//3 values to get the order parameter (similar to Couzin) order_param = np.mean(ls_order_param[-ORDER_WINDOW // 3 :]) dict_noise[noise_eta] = order_param dict_noise = dict(sorted(dict_noise.items())) if dict_noise: line_noise.set_data(*zip(*dict_noise.items())) else: line_noise.set_data([], []) return (plt_particles, plt_current, line_order_param, line_noise) ``` ::: ## Create the Animation Object This stays the same as before: ```python ani = animation.FuncAnimation(fig, update_animation, interval=0, blit=True) ``` ## Add Sliders You want sliders for: - Number of boids $N$ (special: requires reinitializing particles). - Interaction radius $r$. - Noise $\eta$. - Speed $v_0$. - Box size $L$. ### Create Slider Axes Create small inset axes inside `ax_sliders`: ```python def make_slider_axes(ax_sliders: Axes): ax_sliders.axis("off") ax_num_boids = ax_sliders.inset_axes([0.0, 1.2, 0.8, 0.1]) ax_radius_interaction = ax_sliders.inset_axes([0.0, 1.0, 0.8, 0.1]) ax_noise_eta = ax_sliders.inset_axes([0.0, 0.8, 0.8, 0.1]) ax_v0 = ax_sliders.inset_axes([0.0, 0.6, 0.8, 0.1]) ax_box_size = ax_sliders.inset_axes([0.0, 0.4, 0.8, 0.1]) return ax_num_boids, ax_radius_interaction, ax_noise_eta, ax_v0, ax_box_size ``` ### Create the Slider Widgets Matplotlib's `Slider` lives in `matplotlib.widgets`. Its signature is `Slider(ax, label, valmin, valmax, valinit=..., valstep=...)`. ::: {.callout-note} ## Exercise Import `Slider` and create the five sliders with appropriate ranges and initial values. ```python from matplotlib.widgets import Slider def make_sliders( *, ax_num_boids, ax_radius_interaction, ax_noise_eta, ax_v0, ax_box_size, num_boids: int, radius_interaction: float, noise_eta: float, v0: float, box_size: float, ): # TODO: define the sliders with appropriate ranges and initial values return slider_num_boids, slider_radius_interaction, slider_noise_eta, slider_v0, slider_box_size ``` ::: ::: {.callout-tip collapse="true"} ## Solution These are the ranges used in `amlab/collective_motion/vicsek_animation.py`. The noise range $[0, 5]$ matches the x-limits of the noise plot. ```python from matplotlib.widgets import Slider def make_sliders( *, ax_num_boids, ax_radius_interaction, ax_noise_eta, ax_v0, ax_box_size, num_boids: int, radius_interaction: float, noise_eta: float, v0: float, box_size: float, ): slider_num_boids = Slider(ax_num_boids, "Number of boids", 100, 1000, valinit=num_boids, valstep=100) slider_radius_interaction = Slider( ax_radius_interaction, "Interaction radius", 0, 50, valinit=radius_interaction, valstep=1 ) slider_noise_eta = Slider(ax_noise_eta, "Noise", 0.0, 5.0, valinit=noise_eta, valstep=0.01) slider_v0 = Slider(ax_v0, "Speed", 0.0, 0.1, valinit=v0, valstep=0.01) slider_box_size = Slider(ax_box_size, "Dimension", 1, 50, valinit=box_size, valstep=1) return slider_num_boids, slider_radius_interaction, slider_noise_eta, slider_v0, slider_box_size ``` Call it with keyword arguments, because of the `*` in the signature. :::