import numpy as np


def perlin(x, y, seed=0):
    # permutation table
    np.random.seed(seed)
    p = np.arange(256, dtype=int)
    np.random.shuffle(p)
    p = np.stack([p, p]).flatten()
    # coordinates of the top-left
    xi, yi = x.astype(int), y.astype(int)
    # internal coordinates
    xf, yf = x - xi, y - yi
    # fade factors
    u, v = fade(xf), fade(yf)
    # noise components
    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)
    # combine noises
    x1 = lerp(n00, n10, u)
    x2 = lerp(n01, n11, u)  # FIX1: I was using n10 instead of n01
    return lerp(x1, x2, v)  # FIX2: I also had to reverse x1 and x2 here


def lerp(a, b, x):
    "linear interpolation"
    return a + x * (b - a)


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


def gradient(h, x, y):
    "grad converts h to the right gradient vector and return the dot product with (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, 5, 100, endpoint=False)
x, y = np.meshgrid(lin, lin)


def perlinNoise(height, width, octavesx=5, octavesy=5, seed=None):
    linx = np.linspace(0, octavesx, width, endpoint=False)
    liny = np.linspace(0, octavesy, height, endpoint=False)
    x, y = np.meshgrid(linx, liny)
    return perlin(x, y, seed=seed)