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kuramotoMandelbrot.py
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kuramotoMandelbrot.py
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import numpy as np
import matplotlib.pyplot as plt
def kuramoto_oscillators(N, K, dt, theta):
# Kuramoto model dynamics
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 mandelbrot(size=(800, 600), maxiter=50, theta=None):
xmin, xmax, ymin, ymax = -2.5, 1.5, -1.5, 1.5
dx = (xmax - xmin) / size[0]
dy = (ymax - ymin) / size[1]
x, y = np.meshgrid(np.linspace(xmin, xmax, size[0]), np.linspace(ymin, ymax, size[1]))
c = x + 1j * y
z = np.zeros_like(c, dtype=np.complex128)
divtime = np.zeros(z.shape, dtype=int)
for i in range(maxiter):
z = z**2 + c
diverge = np.abs(z) > 2
div_now = diverge & (divtime == 0)
divtime[div_now] = i + theta[i % len(theta)] # Kuramoto phase influences divergence time
z[diverge] = 2
return x, y, divtime
# 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 Mandelbrot set influenced by Kuramoto model
x, y, divtime = mandelbrot(size=(800, 600), maxiter=50, theta=theta)
# Plotting
plt.imshow(divtime, extent=(-2.5, 1.5, -1.5, 1.5))
plt.colorbar()
plt.title('Mandelbrot Set with Kuramoto Model Integration')
plt.show()