#Library import
import numpy as np
import matplotlib.pyplot as plt

#Children who produce linear interpolation and continuity
def fade(t):return 6*t**5-15*t**4+10*t**3
def lerp(a,b,t):return a+fade(t)*(b-a)

#Body
def perlin(r,seed=np.random.randint(0,100)):
    np.random.seed(seed)

    ri = np.floor(r).astype(int) #Integer part, used as an index
    ri[0] -= ri[0].min()         #
    ri[1] -= ri[1].min()         #Ready to use as an index
    rf = np.array(r) % 1         #Decimal part
    g = 2 * np.random.rand(ri[0].max()+2,ri[1].max()+2,2) - 1 #Gradient of grid points
    e = np.array([[[[0,0],[0,1],[1,0],[1,1]]]])                       #four corners
    er = (np.array([rf]).transpose(2,3,0,1) - e).reshape(r.shape[1],r.shape[2],4,1,2) #Position vector seen from each point of the four corners
    gr = np.r_["3,4,0",g[ri[0],ri[1]],g[ri[0],ri[1]+1],g[ri[0]+1,ri[1]],g[ri[0]+1,ri[1]+1]].transpose(0,1,3,2).reshape(r.shape[1],r.shape[2],4,2,1) #Processed into a shape that can calculate the inner product by collecting the gradients of the four corners with the familiar fancy sort
    p = (er@gr).reshape(r.shape[1],r.shape[2],4).transpose(2,0,1) #Dot product calculation with gradient for all points
    
    return lerp(lerp(p[0],p[2],rf[0]),lerp(p[1],p[3],rf[0]),rf[1]) #Interpolate and return

N = 512
y = np.zeros((N,N))
for i in np.random.rand(1):         #Perlin noise seems to show its true potential when you change the frequency and stack several sheets, so loop and add (please do as much as you like)
    x = np.linspace(0,8*i,N)
    r = np.array(np.meshgrid(x,x))
    y += perlin(r)                  #shape of meshgrid(2,N,N)Pass by

plt.imshow(y)
plt.show()

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