Pseudosphere Tractrix

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

# Pseudosphere (tractricoid) parametrization
u = np.linspace(-3, 3, 100)
v = np.linspace(0, 2*np.pi, 60)
u, v = np.meshgrid(u, v)

x = 1 / np.cosh(u) * np.cos(v)
y = 1 / np.cosh(u) * np.sin(v)
z = u - np.tanh(u)

# Custom colormap
colors = ['#0a0a0f', '#4a1942', '#F5276C', '#ec4899', '#fda4af']
cmap = LinearSegmentedColormap.from_list('coral_magenta', colors, N=256)

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

surf = ax.plot_surface(x, y, z, cmap=cmap, alpha=0.9, linewidth=0.1, edgecolor='#ffffff15')

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("Pseudosphere Tractrix", 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=15, azim=45)
plt.tight_layout()
plt.show()