I have a 3D scene created with Matplotlib and I would like to apply a chessboard like pattern on the bottom plane in the image below. Do you have any idea how to achieve this?

Here is the code to create this image:
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
# Create figure
plt.style.use('dark_background') # Dark theme
fig = plt.figure(frameon=False)
ax = fig.add_subplot(111, projection='3d')
# Make panes transparent
ax.xaxis.pane.fill = False # Left pane
ax.yaxis.pane.fill = False # Right pane
# ax.zaxis.pane.fill = False # Bottom pane
# Remove grid lines
ax.grid(False)
# Remove tick labels
ax.set_xticklabels([])
ax.set_yticklabels([])
ax.set_zticklabels([])
# Random data to illustrate
zdata = 15 * np.random.random(100)
xdata = np.sin(zdata) + 0.1 * np.random.randn(100)
ydata = np.cos(zdata) + 0.1 * np.random.randn(100)
ax.scatter3D(xdata, ydata, zdata, c=zdata, cmap='Greens')
# Print chart
file_path = 'charts/3d.png'
fig.savefig(file_path, bbox_inches='tight', pad_inches=0.05, transparent=True)
                You can generate a grid of rectangles and use pathpatch_2d_to_3d function from  mpl_toolkits.mplot3d.art3d to insert then into the 3d scene:
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.patches import Rectangle
import mpl_toolkits.mplot3d.art3d as art3d
# Create figure
plt.style.use('dark_background') # Dark theme
fig = plt.figure(frameon=False)
ax = fig.add_subplot(111, projection='3d')
# Make planes transparent
ax.xaxis.pane.fill = False # Left plane
ax.yaxis.pane.fill = False # Right plane
# ax.zaxis.pane.fill = False # Horizontal plane
# Remove grid lines
ax.grid(False)
# Remove tick labels
ax.set_xticklabels([])
ax.set_yticklabels([])
ax.set_zticklabels([])
# Draw chessboard on hortizontal plane
for x_index, x in enumerate(np.arange(-1, 1.1, 0.2)):
    for y_index, y in enumerate(np.arange(-1, 1.1, 0.2)):
        if (x_index+y_index)%2:
            p = Rectangle([x,y], 0.2, 0.2)
            ax.add_patch(p)
            art3d.pathpatch_2d_to_3d(p, z=0, zdir="z")
ax.set(xlim=(-1,1.1), ylim=(-1,1.2), zlim=(0,15))
# Random data to illustrate
zdata = 15 * np.random.random(100)
xdata = np.sin(zdata) + 0.1 * np.random.randn(100)
ydata = np.cos(zdata) + 0.1 * np.random.randn(100)
ax.scatter3D(xdata, ydata, zdata, c=zdata, cmap='Greens')
# Print chart
file_path = 'charts/3d.png'
fig.savefig(file_path, bbox_inches='tight', pad_inches=0.05, transparent=True)

EDIT: cleaner version
RECT_SIZE_X = 0.2
RECT_SIZE_Y = 0.2
xlims = (-1, 1)
ylims = (-1, 1)
for x_index, x_pos in enumerate(np.arange(xlims[0], xlims[1], RECT_SIZE_X)):
    for y_index, y_pos in enumerate(np.arange(ylims[0], ylims[1], RECT_SIZE_Y)):
        if (x_index+y_index)%2:
            p = Rectangle([x_pos, y_pos], RECT_SIZE_X, RECT_SIZE_Y, color='orange')
        else:
            p = Rectangle([x_pos, y_pos], RECT_SIZE_X, RECT_SIZE_Y, color='gray')
        ax.add_patch(p)
        art3d.pathpatch_2d_to_3d(p, z=0, zdir="z")
ax.set(xlim=xlims, ylim=ylims, zlim=(0,15))
# Transparent spines
ax.w_xaxis.line.set_color((1.0, 1.0, 1.0, 0.0))
ax.w_yaxis.line.set_color((1.0, 1.0, 1.0, 0.0))
ax.w_zaxis.line.set_color((1.0, 1.0, 1.0, 0.0))
# Transparent panes
ax.w_xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
ax.w_yaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
ax.w_zaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
# No ticks
ax.set_xticks([]) 
ax.set_yticks([]) 
ax.set_zticks([])

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