import numpy as np
import matplotlib.pyplot as plt

def chirikov_standard_map(x, y, K):
    """Compute one iteration of the Chirikov standard map."""
    x_next = (x + y + K * np.sin(x)) % (2 * np.pi)
    y_next = (y + K * np.sin(x)) % (2 * np.pi)
    return x_next, y_next

def generate_points(N, K, iterations):
    """Generate points for the Chirikov standard map."""
    x = np.random.uniform(0, 2 * np.pi, N)
    y = np.random.uniform(0, 2 * np.pi, N)
    points = np.zeros((iterations, N, 2))

    for i in range(iterations):
        x, y = chirikov_standard_map(x, y, K)
        points[i, :, 0] = x
        points[i, :, 1] = y

    return points

def plot_chirikov_map(points, iterations):
    """Plot the Chirikov standard map points."""
    plt.figure(figsize=(8, 8))
    for i in range(iterations):
        plt.scatter(points[i, :, 0], points[i, :, 1], s=0.1, color='blue')
    plt.title('Chirikov Standard Map; K = 1.5, 90 seeds')
    plt.show()

# Parameters
N = 90        # Number of initial points
K = 1.5         # Chirikov standard map parameter
iterations = 100 # Number of iterations of map

# Generate and plot points
points = generate_points(N, K, iterations)
plot_chirikov_map(points, iterations)