Entailment Cone Structure

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

# Create the figure and a 3D axis
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

# Define points at different levels of the cone
base = [0, 0, 0]  # Base axiom
level_1 = [[1, 0, 1], [-1, 0, 1]]  # First set of derived statements
level_2 = [[2, 1, 2], [-2, 1, 2], [1.5, -1, 2], [-1.5, -1, 2]]  # Next derivations

# Function to generate points in a circular (conical) pattern
def generate_cone_points(level, num_points, radius):
    # Z-coordinate is fixed to the level number (height)
    z = level
    points = []
    # Angle between points (in radians) to distribute them evenly in a circle
    angle_increment = 2 * np.pi / num_points
    for i in range(num_points):
        angle = i * angle_increment
        x = radius * np.cos(angle)
        y = radius * np.sin(angle)
        points.append([x, y, z])
    return points

# Generate points for level 3 and onward with conical spread
level_3 = generate_cone_points(3, 6, 3)  # 6 points at level 3 with radius 3
level_4 = generate_cone_points(4, 8, 4)  # 8 points at level 4 with radius 4
level_5= generate_cone_points(5, 10, 5)  # 10 points at level 5 with radius 5
# Plot the base
ax.scatter(base[0], base[1], base[2], c='red', s=100, label='Axiom')

# Plot level 1 points
for point in level_1:
    ax.scatter(point[0], point[1], point[2], c='blue', s=60)
    ax.plot([base[0], point[0]], [base[1], point[1]], [base[2], point[2]], color='black')

# Plot level 2 points
for point in level_2:
    ax.scatter(point[0], point[1], point[2], c='green', s=60)
    for l1_point in level_1:
        ax.plot([l1_point[0], point[0]], [l1_point[1], point[1]], [l1_point[2], point[2]], color='black')

# Plot level 3 points (cone pattern)
for point in level_3:
    ax.scatter(point[0], point[1], point[2], c='orange', s=60)
    for l2_point in level_2:
        ax.plot([l2_point[0], point[0]], [l2_point[1], point[1]], [l2_point[2], point[2]], color='black')

# Plot level 4 points (cone pattern)
for point in level_4:
    ax.scatter(point[0], point[1], point[2], c='purple', s=60)
    for l3_point in level_3:
        ax.plot([l3_point[0], point[0]], [l3_point[1], point[1]], [l3_point[2], point[2]], color='black')

# Plot level 5 points (cone pattern)
for point in level_5:
    ax.scatter(point[0], point[1], point[2], c='yellow', s=60)
    for l4_point in level_4:
        ax.plot([l4_point[0], point[0]], [l4_point[1], point[1]], [l4_point[2], point[2]], color='black')

# Labels and legend
ax.set_title('Entailment Cone')
ax.set_xlabel('X Axis')
ax.set_ylabel('Y Axis')
ax.set_zlabel('Z Axis')
plt.legend()
plt.show()