Gray-Scott: Interaction

Drawing, Sliders, and Pause

This page adds interaction to the Gray-Scott simulation: draw sources of \(v\), pause/resume, and adjust parameters with sliders. The reference implementation is in amlab/pdes_2d/gray_scott.py.

Draw on the plot

Left click adds a small perturbation near \((u,v)=(0.5,0.5)\), right click resets to \((1,0)\). Implement an update function and wire the events.

from matplotlib.backend_bases import MouseEvent

def update_uv(event: MouseEvent, r: int = 3):
    # TODO: check if event is inside the axes
    # TODO: compute (x, y) indices
    # TODO: left click adds noise around (0.5, 0.5)
    # TODO: right click resets to (1, 0)
    # TODO: update a (2r x 2r) patch in uv
    # TODO: refresh the image

Hint: update_uv (click to expand)

def update_uv(event: MouseEvent, r: int = 3):
    if event.inaxes != ax_uv:
        return
    if event.xdata is None or event.ydata is None:
        return
    x = int(event.xdata)
    y = int(event.ydata)

    if event.button == 1:
        u_new = 0.5 * (1 + 0.1 * np.random.randn())
        v_new = 0.5 * (1 + 0.1 * np.random.randn())
    elif event.button == 3:
        u_new = 1.0
        v_new = 0.0
    else:
        return

    uv[0, y - r : y + r, x - r : x + r] = u_new
    uv[1, y - r : y + r, x - r : x + r] = v_new
    im.set_array(uv[1])

Now allow continuous drawing while the mouse button is pressed.

def on_click(event: MouseEvent):
    # TODO: enable drawing and update_uv(event)

def on_release(event: MouseEvent):
    # TODO: disable drawing

def on_motion(event: MouseEvent):
    # TODO: if drawing, call update_uv(event)

fig.canvas.mpl_connect("button_press_event", on_click)
fig.canvas.mpl_connect("button_release_event", on_release)
fig.canvas.mpl_connect("motion_notify_event", on_motion)

Hint: mouse handlers (click to expand)

def on_click(event: MouseEvent):
    if event.inaxes != ax_uv:
        return
    if event.xdata is None or event.ydata is None:
        return
    nonlocal drawing
    drawing = True
    update_uv(event)


def on_release(event: MouseEvent):
    nonlocal drawing
    drawing = False


def on_motion(event: MouseEvent):
    if drawing:
        update_uv(event)

Pause and resume

Use the space bar to pause/resume the simulation.

from matplotlib.backend_bases import KeyEvent

pause = False

def on_keypress(event: KeyEvent):
    # TODO: toggle pause when space bar is pressed

fig.canvas.mpl_connect("key_press_event", on_keypress)

Hint: pause handler (click to expand)

def on_keypress(event: KeyEvent):
    nonlocal pause
    if event.key == " ":
        pause ^= True

Sliders

Create sliders to update \(d_1, d_2, f, k\) while the animation runs.

from matplotlib.widgets import Slider

# Create axes for sliders on the right
ax_d1 = ax_sliders.inset_axes([0.0, 0.8, 0.8, 0.1])
ax_d2 = ax_sliders.inset_axes([0.0, 0.6, 0.8, 0.1])
ax_f = ax_sliders.inset_axes([0.0, 0.4, 0.8, 0.1])
ax_k = ax_sliders.inset_axes([0.0, 0.2, 0.8, 0.1])

slider_d1 = Slider(ax_d1, "D1", 0.01, 0.2, valinit=d1, valstep=0.01)
slider_d2 = Slider(ax_d2, "D2", 0.01, 0.2, valinit=d2, valstep=0.01)
slider_f = Slider(ax_f, "F", 0.01, 0.09, valinit=f, valstep=0.001)
slider_k = Slider(ax_k, "k", 0.04, 0.07, valinit=k, valstep=0.001)

# TODO: update parameters when sliders change

Hint: slider update (click to expand)

def update_sliders(_):
    nonlocal d1, d2, f, k, pause
    d1 = slider_d1.val
    d2 = slider_d2.val
    f = slider_f.val
    k = slider_k.val
    pause = True

slider_d1.on_changed(update_sliders)
slider_d2.on_changed(update_sliders)
slider_f.on_changed(update_sliders)
slider_k.on_changed(update_sliders)