A quick project inspired by this tweet by @story645 referencing Jacques Bertin's Semiology of Graphics.

The function plotted is the sum of a random selection of two-dimensional Gaussian functions, with filled and line contours indicated using Matplotlib's `contourf`

and `contour`

' methods. They are animated by changing the Gaussians' parameters in random steps.

The plot is constrained to the region defined by a mask array, read in as a PNG image file. Examples files are us_100.png and france_100.png. Mask images are assumed to be have RGB and alpha channels.

```
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation
from PIL import Image
SAVE_ANIMATION = False
# The mask image to use: only plot contours on the black area.
img = Image.open('us_100.png')
mask = np.array(img)[::-1,:,:].mean(axis=2) < 128
# Number of 2D Gaussian functions to use, size of the plot array.
ng = 80
nx, ny = 100, 100
arr = np.zeros((nx, ny))
# Scaling factors for random initialization of Gaussian parameters.
sigma = 20
A = 1
g_prms = np.array(
(np.random.random(ng) * nx,
np.random.random(ng) * ny,
sigma * (np.random.random(ng) + 0.2),
sigma * (np.random.random(ng) + 0.2),
A * np.random.random(ng))
)
# Meshgrid of 2D coordinates.
x, y = np.arange(0, nx), np.arange(0, ny)
X, Y = np.meshgrid(x, y)
def gaussian(prms):
"""Return the 2D Gaussian function defined by prms."""
x0, y0, sig_x, sig_y, A = prms
return A[:,None,None] * np.exp(
- ((X-x0[:,None,None]) / sig_x[:,None,None])**2
- ((Y-y0[:,None,None]) / sig_y[:,None,None])**2
)
# Initialize the array with the initial Gaussian parameters.
arr = np.sum(gaussian(g_prms), axis=0)
# Start the figure, make sure it's square and turn off the Axes labels.
fig, ax = plt.subplots()
ax.axis('equal')
ax.axis('off')
# Plot the filled and line contours, and the outline of the mask.
cf = ax.contourf(arr, cmap='RdYlBu')
c = ax.contour(arr, colors='k')
ax.contour(mask, colors='k')
# These parameters determine how fast the Gaussian parameters change.
vx, vy = 4, 4
vsig_x, vsig_y = 0.2, 0.2
vA = 0.05
sc = np.array((vx, vy, vsig_x, vsig_y, vA)).reshape(5, 1)
def animate(i):
"""Set the data for the ith iteration of the animation."""
global c, cf, arr, g_prms
# Advance the parameters, update the array, and apply the mask.
g_prms += sc * (1 - 2*np.random.random((5, ng)))
arr = np.sum(gaussian(g_prms), axis=0)
arr[~mask] = np.nan
# Update the plot objects: remove the previous collections to save memory.
for coll in cf.collections:
coll.remove()
cf = ax.contourf(arr, cmap='RdYlBu')
for coll in c.collections:
coll.remove()
c = ax.contour(arr, colors='k')
return c, cf
if SAVE_ANIMATION:
anim = animation.FuncAnimation(fig, animate, frames=100, repeat=False)
anim.save('us.gif', writer='imagemagick', fps=5)
else:
anim = animation.FuncAnimation(fig, animate, frames=100)
plt.show()
```

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