rule110

rule110

import numpy as np
import matplotlib.pyplot as plt
import torch
from torch.autograd import Variable
def triangle(x,y,z,v0):
    v=(y + y * y + y * y * y - 3. * (1. + x) * y * z + z * (1. + z + z * z)) / 3.
    return (v-v0)*(v-v0)
W=15
cnt=0
def eval():
    global cnt
    s = 0.
    for i in range(W - 1):
        for j in range(1, W + 1):
            xx = x[i, (j - 1) % W]
            yy = x[i, j % W]
            zz = x[i, (j + 1) % W]
            r = x[i + 1, j % W]
            s += triangle(xx, yy, zz, r)
    for j in range(W - 1): s += x[0, j] * x[0, j]
    s += (1 - x[0, W - 1]) * (1 - x[0, W - 1])
    cnt=cnt+1
    if (cnt%100==1):
        plt.ion()
        plt.imshow(np.array(x.data.numpy()))
        if (cnt==1):plt.show()
        plt.pause(0.0001)
        print(cnt,"  s=", s)
    return torch.sqrt(s)
x = Variable(torch.DoubleTensor(W,W).zero_(), requires_grad=True)
opt = torch.optim.LBFGS([x],lr=.1)
for i in range(15500):
    def closure():
        opt.zero_grad()
        s=eval()
        s.backward()
        return s
    opt.step(closure)