Gray-Scott: Sliders

Module 4: Space and Pattern Formation

This page finishes the interactive simulator of Gray-Scott: Interaction. You add sliders for $d_1$, $d_2$, $f$, and $k$, and make the animation respect the pause flag. As before, the handlers use nonlocal, so they live inside one function that owns uv, pause, and the parameters. This page is an optional extension.

Add Sliders for the Parameters

Exercise

Read the slider values into the model parameters and pause the simulation.

from matplotlib.widgets import Slider

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)

def update_sliders(_):
    # TODO: read the slider values into d1, d2, f, and k
    # TODO: pause the simulation so the new pattern is easier to inspect

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

Solution

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

Put It Together

Inside your animation callback, respect the pause flag before advancing the PDE.

def update_frame(_):
    nonlocal uv
    if pause:
        return [im]

    for _ in range(anim_speed):
        uv = uv + gray_scott_pde(0, uv, d1=d1, d2=d2, f=f, k=k) * dt

    im.set_array(uv[1])
    return [im]

This setup is enough to create your own Gray-Scott experiments. Try drawing thin lines, large blobs, or repeated point sources and see which parameter sets erase the perturbation and which ones amplify it.

Tip

Reference code is available in amlab/pdes_2d/gray_scott.py. Run it with python -m amlab.pdes_2d.gray_scott.

Return to the assignment to complete Parts 3 and 4.

Exit question

Exercise

You move the slider for $d_1$ from $0.1$ to $0.2$ while keeping $dx = 1$ and $dt = 2$. What happens to the simulation, and why?

Solution

It blows up. The 2D explicit Euler bound is $dt \le dx^2/(4 d_1)$, which drops from $2.5$ to $1.25$, so $dt = 2$ is now unstable and a grid-scale checkerboard grows. Reduce $dt$ below $1.25$ when you increase $d_1$ (Time-Step Stability).

--- title: "Gray-Scott: Sliders" subtitle: "Module 4: Space and Pattern Formation" format: html --- This page finishes the interactive simulator of [Gray-Scott: Interaction](gray-scott-art.qmd). You add sliders for $d_1$, $d_2$, $f$, and $k$, and make the animation respect the `pause` flag. As before, the handlers use `nonlocal`, so they live inside one function that owns `uv`, `pause`, and the parameters. This page is an optional extension. ## Add Sliders for the Parameters ::: {.callout-note} ## Exercise Read the slider values into the model parameters and pause the simulation. ```python from matplotlib.widgets import Slider 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) def update_sliders(_): # TODO: read the slider values into d1, d2, f, and k # TODO: pause the simulation so the new pattern is easier to inspect slider_d1.on_changed(update_sliders) slider_d2.on_changed(update_sliders) slider_f.on_changed(update_sliders) slider_k.on_changed(update_sliders) ``` ::: ::: {.callout-tip collapse="true"} ## Solution ```python 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 ``` ::: ## Put It Together Inside your animation callback, respect the `pause` flag before advancing the PDE. ```python def update_frame(_): nonlocal uv if pause: return [im] for _ in range(anim_speed): uv = uv + gray_scott_pde(0, uv, d1=d1, d2=d2, f=f, k=k) * dt im.set_array(uv[1]) return [im] ``` This setup is enough to create your own Gray-Scott experiments. Try drawing thin lines, large blobs, or repeated point sources and see which parameter sets erase the perturbation and which ones amplify it. ::: {.callout-tip} Reference code is available in [amlab/pdes_2d/gray_scott.py](https://github.com/daniprec/BAM-Applied-Math-Lab/blob/main/amlab/pdes_2d/gray_scott.py). Run it with `python -m amlab.pdes_2d.gray_scott`. ::: Return to the [assignment](assignment-patterns.qmd) to complete Parts 3 and 4. ## Exit question ::: {.callout-note} ## Exercise You move the slider for $d_1$ from $0.1$ to $0.2$ while keeping $dx = 1$ and $dt = 2$. What happens to the simulation, and why? ::: ::: {.callout-tip collapse="true"} ## Solution It blows up. The 2D explicit Euler bound is $dt \le dx^2/(4 d_1)$, which drops from $2.5$ to $1.25$, so $dt = 2$ is now unstable and a grid-scale checkerboard grows. Reduce $dt$ below $1.25$ when you increase $d_1$ ([Time-Step Stability](time-step-stability.qmd)). :::