import numpy as np
from gates import survive
rng=np.random.default_rng(127)
# Step 3 check: homogeneous half-line Rule 150 (dark lighthouse): Delta_1(r + 2^m) == Delta_1(r)
def evolve150(D,T):
    L=len(D)+T+4; x=np.zeros(L,dtype=np.uint8); x[:len(D)]=D; out=[]
    for t in range(T):
        out.append(int(x[0]))
        near=np.concatenate([[0],x[:-1]]); far=np.concatenate([x[1:],[0]]); x=far^x^near
    return out
ok=tot=0
for _ in range(300):
    W=int(rng.integers(1,12)); D=rng.integers(0,2,size=W).astype(np.uint8); D[-1]=1
    seq=evolve150(D,1100)
    for m in (6,7,8,9):
        for r in range(0,(1<<m)-2*W-4):
            if r+(1<<m)<1100: tot+=1; ok+=int(seq[r]==seq[r+(1<<m)])
print(f"self-similarity Delta_1(r+2^m) = Delta_1(r): {ok}/{tot}")
# theorem check: Rule 150 = far XOR (self XOR near): gate table (0,1,1,0); odd-period songs, all widths <= 12
for cp in ((0,0,1),(0,1,1),(0,0,0,0,1),(0,1,0,1,1),(0,0,0,0,0,0,1)):
    fooled=sum(survive((0,1,1,0),cp,w,90)[0] for w in range(1,13))
    print(f"   Rule 150, song {''.join(map(str,cp))} (p={len(cp)}): finite starts that fool the watchman for 90 nights: {fooled}")