demos/neural_ca_loschmidt_echo.py

"""neural_ca  --  a Loschmidt echo in a reversible cellular automaton.

The Margolus block rule is a bijection, so a gas of ~2,000 particles mixed for
500 steps can be un-mixed by iterating the same rule backward: the initial
configuration returns cell-for-cell (particle number conserved throughout). Yet
flipping a single cell of the mixed state before reversing corrupts roughly half
the reconstructed past -- exact reversibility and sensitive dependence in the
same automaton.

    python demos/neural_ca_loschmidt_echo.py
"""
import os, sys, time, random, statistics
HERE = os.path.dirname(os.path.abspath(__file__))
REPO = os.path.dirname(HERE)
sys.path.insert(0, os.path.join(REPO, "src"))
import ca


def coarse(g, H, W, k=8):
    out = []
    for by in range(0, H, k):
        for bx in range(0, W, k):
            out.append(sum(g[y][x] for y in range(by, by + k) for x in range(bx, bx + k)))
    return out


if __name__ == "__main__":
    H = W = 64
    rng = random.Random(2026)
    grid = [[1 if rng.random() < 0.5 else 0 for _ in range(W)] for _ in range(H)]
    n0 = sum(map(sum, grid))
    STEPS = 500

    print("neural_ca: Loschmidt echo (mix, then run time backward)")
    print("=" * 56)
    t0 = time.perf_counter()
    fwd = ca.run(grid, STEPS, 0)
    n1 = sum(map(sum, fwd))
    back = ca.run_back(fwd, STEPS, 0)
    echo = back == grid
    dt = time.perf_counter() - t0

    print(f"particles: {n0} at t=0, {n1} at t={STEPS} "
          f"({'conserved' if n0 == n1 else 'NOT CONSERVED'})")
    print(f"coarse 8x8 occupancy stdev: t=0 {statistics.pstdev(coarse(grid, H, W)):.2f} "
          f"-> t={STEPS} {statistics.pstdev(coarse(fwd, H, W)):.2f} (mixed)")
    print(f"{STEPS} steps forward + {STEPS} reversed in {dt:.1f}s: "
          f"t=0 recovered {'EXACTLY' if echo else 'FAILED'}")

    flip = [row[:] for row in fwd]
    flip[0][0] ^= 1
    back2 = ca.run_back(flip, STEPS, 0)
    ham = sum(back2[y][x] != grid[y][x] for y in range(H) for x in range(W))
    print(f"butterfly: flip ONE cell at t={STEPS}, reverse again -> reconstructed "
          f"past wrong in {ham}/{H * W} cells")