Saddle Point Surface

import matplotlib.pyplot as plt
import numpy as np
from matplotlib.colors import LinearSegmentedColormap

# Scattered points
np.random.seed(77)
n_points = 500
x = np.random.uniform(-2, 2, n_points)
y = np.random.uniform(-2, 2, n_points)
z = x**2 - y**2

# Custom colormap
colors = ['#0a0a0f', '#2d1b4e', '#4927F5', '#27D3F5', '#a5f3fc']
cmap = LinearSegmentedColormap.from_list('purple_cyan', colors, N=256)

fig = plt.figure(figsize=(10, 8), facecolor='#0a0a0f')
ax = fig.add_subplot(111, projection='3d', facecolor='#0a0a0f')

surf = ax.plot_trisurf(x, y, z, cmap=cmap, alpha=0.9, linewidth=0.1, edgecolor='#ffffff10')

ax.set_xlabel('X', fontsize=10, color='#94a3b8', labelpad=10)
ax.set_ylabel('Y', fontsize=10, color='#94a3b8', labelpad=10)
ax.set_zlabel('Z', fontsize=10, color='#94a3b8', labelpad=10)
ax.set_title("Saddle Point Surface", fontsize=14, color='white', fontweight='bold', pad=20)

ax.tick_params(colors='#64748b', labelsize=8)
ax.xaxis.pane.fill = False
ax.yaxis.pane.fill = False
ax.zaxis.pane.fill = False
ax.xaxis.pane.set_edgecolor('#1e293b')
ax.yaxis.pane.set_edgecolor('#1e293b')
ax.zaxis.pane.set_edgecolor('#1e293b')

ax.view_init(elev=25, azim=45)
plt.tight_layout()
plt.show()