import numpy as np
import matplotlib.pyplot as plt

# Generate a height map using Perlin noise
def generate_perlin_noise(size, scale, seed=None):
    if seed:
        np.random.seed(seed)

    def fade(t):
        return 6 * t**5 - 15 * t**4 + 10 * t**3

    def lerp(a, b, t):
        return a + t * (b - a)

    def gradient(h, x, y):
        vectors = np.array([[0, 1], [0, -1], [1, 0], [-1, 0]])
        g = vectors[h % 4]
        return g[:, :, 0] * x + g[:, :, 1] * y

    lin = np.linspace(0, scale, size, endpoint=False)
    x, y = np.meshgrid(lin, lin)

    p = np.arange(256, dtype=int)
    np.random.shuffle(p)
    p = np.stack([p, p]).flatten()

    xi = x.astype(int) & 255
    yi = y.astype(int) & 255

    xf = x - xi
    yf = y - yi

    u = fade(xf)
    v = fade(yf)

    n00 = gradient(p[p[xi] + yi], xf, yf)
    n01 = gradient(p[p[xi] + yi + 1], xf, yf - 1)
    n11 = gradient(p[p[xi + 1] + yi + 1], xf - 1, yf - 1)
    n10 = gradient(p[p[xi + 1] + yi], xf - 1, yf)

    x1 = lerp(n00, n10, u)
    x2 = lerp(n01, n11, u)

    return lerp(x1, x2, v)

# Parameters for the height map
size = 512
scale = 100

# Generate the height map
height_map = generate_perlin_noise(size, scale, seed=42)

# Plot the height map
plt.imshow(height_map, cmap='gray')
plt.axis('off')
plt.savefig('heightmap.png', bbox_inches='tight', pad_inches=0)
plt.show()