Add Gray-Scott model implementations and update documentation

- Introduced `gray_scott.py` for 2D Gray-Scott model simulation with interactive visualization using Matplotlib.
- Added `gray_scott_art.py` for an artistic version of the Gray-Scott model that utilizes an image mask for simulation.
- Updated references in documentation to point to the new file structure for the Gray-Scott and Gierer-Meinhardt models.
- Adjusted import paths in various `.qmd` files to reflect the new module organization.

Author: Daniel Precioso, PhD

amlab/pdes/__init__.py

@@ -1,15 +1,19 @@
-"""Shared PDE models and interactive demos for the Applied Math Lab package."""
+"""Backward-compatible re-exports from amlab.pdes_1d and amlab.pdes_2d."""
 
-from .gierer_meinhardt_1d import (
+from amlab.pdes_1d.gierer_meinhardt_1d import (
     find_unstable_spatial_modes as find_unstable_spatial_modes_1d,
 )
-from .gierer_meinhardt_1d import gierer_meinhardt_pde as gierer_meinhardt_pde_1d
-from .gierer_meinhardt_1d import is_turing_instability
-from .gierer_meinhardt_2d import (
+from amlab.pdes_1d.gierer_meinhardt_1d import (
+    gierer_meinhardt_pde as gierer_meinhardt_pde_1d,
+)
+from amlab.pdes_1d.gierer_meinhardt_1d import is_turing_instability
+from amlab.pdes_2d.gierer_meinhardt_2d import (
     find_unstable_spatial_modes as find_unstable_spatial_modes_2d,
 )
-from .gierer_meinhardt_2d import gierer_meinhardt_pde as gierer_meinhardt_pde_2d
-from .gray_scott import gray_scott_pde
+from amlab.pdes_2d.gierer_meinhardt_2d import (
+    gierer_meinhardt_pde as gierer_meinhardt_pde_2d,
+)
+from amlab.pdes_2d.gray_scott import gray_scott_pde
 
 __all__ = [
     "find_unstable_spatial_modes_1d",

amlab/pdes_1d/__init__.py

@@ -0,0 +1,13 @@
+"""1D PDE models for the Applied Math Lab package."""
+
+from .gierer_meinhardt_1d import (
+    find_unstable_spatial_modes,
+    gierer_meinhardt_pde,
+    is_turing_instability,
+)
+
+__all__ = [
+    "find_unstable_spatial_modes",
+    "gierer_meinhardt_pde",
+    "is_turing_instability",
+]

amlab/pdes/gierer_meinhardt_1d.py amlab/pdes_1d/gierer_meinhardt_1d.pyamlab/pdes/gierer_meinhardt_1d.py renamed to amlab/pdes_1d/gierer_meinhardt_1d.py

@@ -0,0 +1,10 @@
+"""2D PDE models and interactive demos for the Applied Math Lab package."""
+
+from .gierer_meinhardt_2d import find_unstable_spatial_modes, gierer_meinhardt_pde
+from .gray_scott import gray_scott_pde
+
+__all__ = [
+    "find_unstable_spatial_modes",
+    "gierer_meinhardt_pde",
+    "gray_scott_pde",
+]

amlab/pdes_2d/__init__.py

@@ -31,7 +31,7 @@ where $u(x,t)$ is the activator, $v(x,t)$ is the inhibitor, and $d$ is the diffu
 import matplotlib.pyplot as plt
 import numpy as np
 
-from amlab.pdes.gierer_meinhardt_1d import gierer_meinhardt_pde
+from amlab.pdes_1d.gierer_meinhardt_1d import gierer_meinhardt_pde
 
 np.random.seed(3)
 
@@ -390,7 +390,7 @@ You now have a working 1D solver. The next question is theoretical: for which pa
 [Turing Instability](turing-instability.qmd){.btn .btn-primary}
 
 ::: {.callout-tip}
-Reference code is available in [amlab/pdes/gierer_meinhardt_1d.py](https://github.com/daniprec/BAM-Applied-Math-Lab/blob/main/amlab/pdes/gierer_meinhardt_1d.py).
+Reference code is available in [amlab/pdes_1d/gierer_meinhardt_1d.py](https://github.com/daniprec/BAM-Applied-Math-Lab/blob/main/amlab/pdes_1d/gierer_meinhardt_1d.py).
 
 The hosted Streamlit version is available at [bam-applied-math-lab.streamlit.app](https://bam-applied-math-lab.streamlit.app/).
 :::

amlab/pdes/gierer_meinhardt_2d.py amlab/pdes_2d/gierer_meinhardt_2d.pyamlab/pdes/gierer_meinhardt_2d.py renamed to amlab/pdes_2d/gierer_meinhardt_2d.py

@@ -26,7 +26,7 @@ You can follow the theory on this page while running the [interactive 1D Gierer-
 import matplotlib.pyplot as plt
 import numpy as np
 
-from amlab.pdes.gierer_meinhardt_1d import is_turing_instability
+from amlab.pdes_1d.gierer_meinhardt_1d import is_turing_instability
 
 arr_a = np.linspace(0, 1, 400)
 arr_d = np.linspace(0, 100, 400)
@@ -308,5 +308,5 @@ Now that you know how to predict pattern-forming parameter regimes, close the 1D
 [PDEs in 2D](../pde-2d/index.qmd){.btn .btn-primary}
 
 ::: {.callout-tip}
-Reference code is available in [amlab/pdes/gierer_meinhardt_1d.py](https://github.com/daniprec/BAM-Applied-Math-Lab/blob/main/amlab/pdes/gierer_meinhardt_1d.py).
+Reference code is available in [amlab/pdes_1d/gierer_meinhardt_1d.py](https://github.com/daniprec/BAM-Applied-Math-Lab/blob/main/amlab/pdes_1d/gierer_meinhardt_1d.py).
 :::