Superellipsoid Surface

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

# Superellipsoid with exponents
n1, n2 = 0.5, 0.5  # Creates pillow shape
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, n):
    return np.sign(x) * np.abs(x)**n

x = signed_pow(np.cos(v), n1) * signed_pow(np.cos(u), n2)
y = signed_pow(np.cos(v), n1) * signed_pow(np.sin(u), n2)
z = signed_pow(np.sin(v), n1)

# Custom colormap
colors = ['#0a0a0f', '#1a2e05', '#D3F527', '#6CF527', '#d9f99d']
cmap = LinearSegmentedColormap.from_list('yellow_green', 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='#ffffff12')

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("Superellipsoid 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()