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kuramotoKochSnowDynamicSync.py
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kuramotoKochSnowDynamicSync.py
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import numpy as np
import matplotlib.pyplot as plt
def kuramoto_oscillators(N, K, dt, theta):
omega = np.random.normal(0, 1, N)
sin_diff = np.sin(theta[:, None] - theta)
theta += dt * (omega + (K/N) * np.sum(sin_diff, axis=1))
return theta
def koch_snowflake(order, scale=10, theta=None):
def koch_curve(points, order, theta, depth):
if order == 0:
return points
else:
new_points = []
for i in range(0, len(points) - 1, 2):
start, end = np.array(points[i], dtype=np.float64), np.array(points[i+1], dtype=np.float64)
vec = (end - start) / 3.0
angle = np.pi / 3 * np.sin(theta[depth % len(theta)]) # Vary angle based on Kuramoto phase
# Calculate the three new points
p1 = start + vec
p2 = start + vec / 2.0 + np.array([np.cos(angle), np.sin(angle)]) * np.linalg.norm(vec) / np.sqrt(3)
p3 = start + vec * 2.0
new_points.extend([start.tolist(), p1.tolist(), p2.tolist(), p3.tolist(), end.tolist()])
return koch_curve(new_points, order - 1, theta, depth + 1)
# Initial triangle points
points = [[0, 0], [scale / 2, scale * np.sqrt(3) / 2], [scale, 0], [0, 0]]
points = koch_curve(points, order, theta, 0)
# Plot each line segment with color based on Kuramoto phase
for i in range(0, len(points) - 1, 2):
start, end = points[i], points[i+1]
plt.plot([start[0], end[0]], [start[1], end[1]], color=plt.cm.viridis(theta[(i//2) % len(theta)] / (2*np.pi)))
# Parameters for Kuramoto model
N = 50
K = 2
dt = 0.01
theta = np.random.uniform(0, 2*np.pi, N)
# Simulate Kuramoto model for a few steps
for _ in range(100):
theta = kuramoto_oscillators(N, K, dt, theta)
# Generate and plot Koch snowflake
plt.figure(figsize=(8, 8))
koch_snowflake(order=5, scale=10, theta=theta)
plt.axis('equal')
plt.axis('off')
plt.show()