Astroidal Ellipsoid Surface

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

# Astroidal ellipsoid (superellipsoid with n=2/3)
n = 2/3
u = np.linspace(-np.pi, np.pi, 100)
v = np.linspace(-np.pi/2, np.pi/2, 100)
u, v = np.meshgrid(u, v)

def signed_pow(x, p):
    return np.sign(x) * np.abs(x)**p

x = signed_pow(np.cos(v), n) * signed_pow(np.cos(u), n)
y = signed_pow(np.cos(v), n) * signed_pow(np.sin(u), n)
z = signed_pow(np.sin(v), n)

# Custom colormap
colors = ['#ffffff', '#fce7f3', '#F527B0', '#4927F5', '#c4b5fd']
cmap = LinearSegmentedColormap.from_list('pink_purple', colors, N=256)

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

surf = ax.plot_surface(x, y, z, cmap=cmap, alpha=0.85, linewidth=0.1, edgecolor='#33333315')

ax.set_xlabel('X', fontsize=10, color='#374151', labelpad=10)
ax.set_ylabel('Y', fontsize=10, color='#374151', labelpad=10)
ax.set_zlabel('Z', fontsize=10, color='#374151', labelpad=10)
ax.set_title("Astroidal Ellipsoid Surface", fontsize=14, color='#1f2937', fontweight='bold', pad=20)

ax.tick_params(colors='#6b7280', labelsize=8)
ax.xaxis.pane.fill = False
ax.yaxis.pane.fill = False
ax.zaxis.pane.fill = False
ax.xaxis.pane.set_edgecolor('#e5e7eb')
ax.yaxis.pane.set_edgecolor('#e5e7eb')
ax.zaxis.pane.set_edgecolor('#e5e7eb')

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