Update app.py

app.py

@@ -85,29 +85,40 @@ def black_hole_advanced(mass):
     # ===============================
     # LIGHT BENDING
     # ===============================
-    y_vals = np.linspace(-4*rs, 4*rs, 7)
+    # ===============================
+    # CORRECTED GRAVITATIONAL LENSING
+    # ===============================
+    y_vals = np.linspace(-4*rs, 4*rs, 9)
 
     for y0 in y_vals:
-        x_ray = np.linspace(-7*rs, 7*rs, 350)
+        x_ray = np.linspace(-8*rs, 8*rs, 500)
         y_ray, z_ray = [], []
 
         for x0 in x_ray:
             r = np.sqrt(x0**2 + y0**2)
-            if r < 1.05 * rs:
+
+            if r <= 1.02 * rs:
                 y_ray.append(np.nan)
                 z_ray.append(np.nan)
-            else:
-                bend = rs / (r - rs)
-                bend = np.clip(bend, 0, 1.4)
-                y_ray.append(y0 - bend * y0 * 0.1)
-                z_ray.append(bend * rs * 0.12)
+                continue
+
+            # Strong relativistic-style bending
+            b = abs(y0) + 0.2 * rs              # impact parameter
+            bend_strength = (rs / r) * (rs / b)
+
+            y_deflect = bend_strength * y0 * 0.9
+            z_deflect = bend_strength * rs * 0.7
+
+            y_ray.append(y0 - y_deflect)
+            z_ray.append(z_deflect)
 
         fig.add_trace(go.Scatter3d(
             x=x_ray,
             y=y_ray,
             z=z_ray,
             mode="lines",
-            opacity=0.35,
+            line=dict(width=2),
+            opacity=0.5,
             showlegend=False
         ))