import numpy as np
from collections import defaultdict
rng=np.random.default_rng(83)
def fiber(cp,T,K):
    p=len(cp); d=[cp[t%p] for t in range(T+K+3)]
    e=[(1^d[t+1]) if d[t]==1 else int(rng.integers(2)) for t in range(T+K+2)]
    cols={0:d,1:e}
    for k in range(1,K+1):
        x,y=cols[k],cols[k-1]; cols[k+1]=[x[t+1]^(x[t]|y[t]) for t in range(len(x)-1)]
    return cols
for cp in ((0,1,1),(0,1,1,1),(0,1,1,1,1),(0,1,1,1,1,1)):
    p=len(cp); K=20; T=60
    table=defaultdict(set)
    for _ in range(600):
        c=fiber(cp,T,K)
        for k in range(2,19):
            for t in range(5,T-p):
                a=lambda kk,tt: c[kk][tt]
                Dk=a(k,t)^a(k,t+p); Dk1=a(k-1,t)^a(k-1,t+p)
                corr=(a(k,t)|a(k-1,t))^(a(k,t+p)|a(k-1,t+p))
                table[(k,t%p,Dk1,Dk)].add(corr)
    pinned={}
    for k in range(2,19):
        cells=[key for key in table if key[0]==k and (key[2] or key[3])]      # only situations where a difference is present
        det=[key for key in cells if len(table[key])==1]
        pinned[k]=f"{len(det)}/{len(cells)}"
    print(f"Mia {''.join(map(str,cp)):5s}: creation pinned (fixed by local differences, for every survivor), situations per lantern:")
    print("    "+"  ".join(f"L{k}:{v}" for k,v in pinned.items()))