neural_ca: demonstrate gate composition. A third particle at (0,9) collides with the A&B output particle, so cell (3,5) carries A&B&C, verified over all 8 inputs; chained collisions build larger circuits from the interaction gate. README updated.

README.md

@@ -693,7 +693,10 @@ reversibly (verified as a genuine interaction, distinct from independent motion)
 A collision computes logic directly: with input particles at (2,2) and (7,7),
 three output cells at step 4 carry A AND B (the deflected paths (3,6) and (6,3)),
 A AND NOT B ((6,6)), and NOT A AND B ((3,3)), the billiard-ball interaction
-gate, verified over all four inputs. That gate with mirror routing is
+gate, verified over all four inputs. The gates compose: launching a third
+particle at (0,9) to collide with the A AND B output makes cell (3,5) carry
+A AND B AND C, verified over all eight inputs, so chained collisions build larger
+circuits. With mirror routing and a constant-particle source the construction is
 functionally complete (Margolus 1984).
 
 ```bash

src/ca.py

@@ -192,6 +192,30 @@ def _test_gate():
     return ok
 
 
+def and3(a: int, b: int, c: int) -> int:
+    """Two composed collisions. A at (2,2) and B at (7,7) collide into an A&B
+    particle, which then collides with C launched at (0,9); the output cell
+    (3,5) at step 4 is occupied iff a, b and c. Composing gates this way builds
+    arbitrary circuits from the interaction gate."""
+    H = W = 16
+    g = [[0] * W for _ in range(H)]
+    if a:
+        g[2][2] = 1
+    if b:
+        g[7][7] = 1
+    if c:
+        g[0][9] = 1
+    return run(g, 4)[3][5]
+
+
+def _test_compose():
+    ok = all(and3(a, b, c) == (a & b & c)
+             for a in (0, 1) for b in (0, 1) for c in (0, 1))
+    print(f"  composed 3-input AND (two chained collisions) over all 8 inputs: "
+          f"{'OK' if ok else 'FAIL'}")
+    return ok
+
+
 def _test_collision():
     # Two particles interact (the joint evolution differs from independent
     # motion) and the collision stays reversible: the physics that logic needs.
@@ -233,4 +257,5 @@ if __name__ == "__main__":
     c = _test_ballistic()
     d = _test_collision()
     e = _test_gate()
-    print("PASS" if (a and g and b and c and d and e) else "FAIL")
+    f = _test_compose()
+    print("PASS" if (a and g and b and c and d and e and f) else "FAIL")