matplotlib 4d pca demo code

honey4d.py

import numpy as np
import matplotlib.pyplot as plt
from sklearn.decomposition import PCA
from itertools import product

def generate_4d_honeycomb(grid_size=4, spacing=2.0):
    """Generate a 4D hexagonal-like lattice (offset in x/y, uniform in z/w)."""
    points = []
    edges = []
    point_index = {}
    idx = 0

    for ix, iy, iz, iw in product(range(grid_size), repeat=4):
        # Hexagonal offset in 2D plane (x/y)
        x = ix * spacing * 0.866  # cos(30°)
        y = iy * spacing + (ix % 2) * (spacing / 2)
        z = iz * spacing
        w = iw * spacing
        pt = (x, y, z, w)
        point_index[(ix, iy, iz, iw)] = idx
        points.append(pt)
        idx += 1

    # 4D neighborhood (adjacent cells in 4D grid)
    offsets = [
        (1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1),
        (-1, 0, 0, 0), (0, -1, 0, 0), (0, 0, -1, 0), (0, 0, 0, -1),
    ]

    for key, idx1 in point_index.items():
        for dx, dy, dz, dw in offsets:
            neighbor = (key[0] + dx, key[1] + dy, key[2] + dz, key[3] + dw)
            if neighbor in point_index:
                idx2 = point_index[neighbor]
                if idx1 < idx2:
                    edges.append((idx1, idx2))

    return np.array(points), edges

# Generate 4D honeycomb structure
points_4d, edges = generate_4d_honeycomb(grid_size=4)

# Project to 3D using PCA
pca = PCA(n_components=3)
points_3d = pca.fit_transform(points_4d)

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

# Draw edges with white lines
for start_idx, end_idx in edges:
    start, end = points_3d[start_idx], points_3d[end_idx]
    ax.plot(*zip(start, end), color='white', linewidth=0.5)

# Equal aspect ratio
max_range = (points_3d.max(axis=0) - points_3d.min(axis=0)).max() / 2
mid_coords = (points_3d.max(axis=0) + points_3d.min(axis=0)) / 2
ax.set_xlim(mid_coords[0] - max_range, mid_coords[0] + max_range)
ax.set_ylim(mid_coords[1] - max_range, mid_coords[1] + max_range)
ax.set_zlim(mid_coords[2] - max_range, mid_coords[2] + max_range)

ax.axis('off')
ax.set_title("4D Honeycomb Projected to 3D", color='white')
plt.tight_layout()
plt.show()