Multi-Frequency Parametric Helix

import matplotlib.pyplot as plt
import numpy as np

# Multi-frequency parametric curve
n = 300
t = np.linspace(0, 6 * np.pi, n)

# Combine multiple frequencies
x = np.sin(t) + 0.3 * np.sin(5 * t)
y = np.cos(t) + 0.3 * np.cos(5 * t)
z = t / (2 * np.pi)

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

# Plot with glow
ax.plot(x, y, z, color='#8b5cf6', linewidth=4, alpha=0.25)
ax.plot(x, y, z, color='#a78bfa', linewidth=2)
ax.plot(x, y, z, color='#c4b5fd', linewidth=0.8)

# Add scatter points at intervals
scatter_idx = np.arange(0, n, 15)
ax.scatter(x[scatter_idx], y[scatter_idx], z[scatter_idx], 
           c='#f472b6', s=30, alpha=0.8)

ax.set_xlim(-2, 2)
ax.set_ylim(-2, 2)
ax.set_zlim(0, 3)

ax.set_xlabel('X', color='white', fontsize=10)
ax.set_ylabel('Y', color='white', fontsize=10)
ax.set_zlabel('Z', color='white', fontsize=10)
ax.set_title('Multi-Frequency Parametric Helix', color='white', fontsize=14, 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.grid(True, alpha=0.2, color='#334155')

ax.view_init(elev=25, azim=30)
plt.tight_layout()
plt.show()