Fixes, still not quite there but does produce a butterfly

CLAUDE.md

@@ -23,18 +23,24 @@ The 3D surface is swept over the control parameter space (a, b), with x (the sta
 
 ### Butterfly Catastrophe
 
-- **Potential:** V(x) = x⁶ + ax⁴ + bx³ (with c=0, d=0 fixed)
+- **Potential:** V(x) = x⁶ + ax⁴ + cx² + dx  (a = −3 fixed, b = 0)
-- **Equilibrium condition:** dV/dx = 6x⁵ + 4ax³ + 3bx² = 0
+- **Equilibrium condition:** dV/dx = 6x⁵ − 12x³ + 2cx + d = 0
-- **Control space:** (a, b) swept over a 2D grid
+- **Control space:** (c, d) swept over a 2D grid
-- **State space:** up to 5 real roots x at any given (a, b)
+- **State space:** up to 5 real roots x at any given (c, d)
-- **Characteristic feature:** nested "butterfly wing" fold structure — more complex than the cusp, with additional inner fold lobes
+- **Characteristic feature:** nested "butterfly wing" fold structure — a self-intersecting bifurcation curve in the (c, d) plane enclosing a 5-root "pocket" (c∈[0,3], d≈0), surrounded by a 3-root wing region, with a single-root region outside
+
+> **Why not vary (a, b) with c=d=0?**  With c=d=0, the equilibrium equation factors as
+> x²(6x³ + 4ax + 3b) = 0 — x=0 is always a double root and the remaining roots come
+> from a cubic, which is structurally identical to the **cusp** catastrophe.  The butterfly
+> structure only appears when d ≠ 0 generically, which requires d (or an equivalent odd
+> perturbation) to be varied as a control parameter.
 
 ---
 
 ## Files
 
 - `butterfly_catastrophe.py` — generates the butterfly surface STL
-- `butterfly_catastrophe.stl` — ready-to-slice output (ASCII STL, ~7,300 triangles)
+- `butterfly_catastrophe.stl` — ready-to-slice output (ASCII STL)
 - `CLAUDE.md` — this file
 
 > A cusp catastrophe script also exists and was the starting point for this project.
@@ -63,10 +69,11 @@ Output: `butterfly_catastrophe.stl`
 
 | Parameter | Default | Effect |
 |-----------|---------|--------|
-| `grid` | `40` | Resolution of the (a,b) control grid — increase for finer mesh |
+| `GRID` | `50` | Resolution of the (c,d) control grid — increase to 80–100 for final print |
-| `a_vals` range | `(-2.5, 1.2)` | Range of control parameter a |
+| `C_RANGE` | `(-2.0, 7.0)` | Range of control parameter c |
-| `b_vals` range | `(-2.5, 2.5)` | Range of control parameter b |
+| `D_RANGE` | `(-6.0, 6.0)` | Range of control parameter d |
-| `x_range` | `2.2` | Search window for equilibrium roots |
+| `X_RANGE` | `2.5` | Search window for equilibrium roots |
+| `MAX_EDGE_DZ` | `0.6` | Z-jump threshold for rejecting branch-mismatch triangles at fold edges |
 
 For a final high-quality print, increase `grid` to `80`–`100`. The default of `40` is optimised for STL viewer compatibility.
 

butterfly_catastrophe.py

@@ -1,121 +1,140 @@
 """
-Butterfly Catastrophe Surface - ASCII STL Generator
+Butterfly Catastrophe Surface — ASCII STL Generator
-Potential: V(x) = x^6 + a*x^4 + b*x^3
+
-Equilibrium surface: dV/dx = 6x^5 + 4a*x^3 + 3b*x^2 = 0
+Potential:   V(x) = x^6 + a*x^4 + c*x^2 + d*x   (a = -3 fixed, b = 0)
+Equilibrium: dV/dx = 6x^5 - 12x^3 + 2c*x + d = 0
+
+Control parameters (print base): c (horizontal), d (depth)
+State variable (print height):    x
+
+With a = -3, the bifurcation set in the (c, d) plane forms the characteristic
+butterfly shape: a self-intersecting loop passing through (c=3, d=0), enclosing
+a region with 5 equilibria ("butterfly pocket"), surrounded by a 3-root region
+with outer fold wings, and a single-root region outside.  This is structurally
+different from the cusp catastrophe and cannot be seen with c = d = 0 fixed.
 """
 
 import numpy as np
 import os
 
-# ---------------------------------------------------------------------------
+A_FIXED = -3.0      # butterfly unfolding parameter (must be negative)
-# 1. Find equilibrium roots of dV/dx = 0
-# ---------------------------------------------------------------------------
 
-def dV(x, a, b):
+# ── Tuning ──────────────────────────────────────────────────────────────────
-    return 6*x**5 + 4*a*x**3 + 3*b*x**2
+GRID      = 50      # control-space resolution — increase to 80–100 for print
+C_RANGE   = (-2.0, 7.0)   # range of control parameter c
+D_RANGE   = (-6.0, 6.0)   # range of control parameter d
+X_RANGE   = 2.5            # half-width of root search window
+MAX_EDGE_DZ = 0.6          # max z-jump per quad edge (filters branch mismatches)
 
-def d2V(x, a, b):
+# ── 1. Root finding ──────────────────────────────────────────────────────────
-    return 30*x**4 + 12*a*x**2 + 6*b*x
 
-def find_roots(a, b, n_starts=40, x_range=2.2):
+def dV(x, c, d):
-    xs = np.linspace(-x_range, x_range, n_starts)
+    return 6*x**5 + 4*A_FIXED*x**3 + 2*c*x + d
+
+def d2V(x, c, d):
+    return 30*x**4 + 12*A_FIXED*x**2 + 2*c
+
+def find_roots(c, d, n_starts=80):
+    """Return sorted real roots of dV/dx = 0 for the given (c, d)."""
+    xs = np.linspace(-X_RANGE, X_RANGE, n_starts)
     roots = []
     for x0 in xs:
         x = float(x0)
-        for _ in range(100):
+        for _ in range(200):
-            fx  = dV(x, a, b)
+            fx  = dV(x, c, d)
-            dfx = d2V(x, a, b)
+            if abs(fx) < 1e-12:
+                break
+            dfx = d2V(x, c, d)
             if abs(dfx) < 1e-14:
                 break
             step = fx / dfx
             x -= step
+            if abs(x) > 2.0 * X_RANGE:   # diverged — abandon
+                break
             if abs(step) < 1e-10:
                 break
-        if abs(dV(x, a, b)) < 1e-7 and abs(x) <= x_range + 0.05:
+        if abs(dV(x, c, d)) < 1e-7 and abs(x) <= X_RANGE + 0.15:
             if not any(abs(x - r) < 1e-4 for r in roots):
                 roots.append(x)
     return sorted(roots)
 
-# ---------------------------------------------------------------------------
+# ── 2. Build mesh ────────────────────────────────────────────────────────────
-# 2. Build mesh
-# ---------------------------------------------------------------------------
 
-def build_mesh(grid=40):
+def build_mesh():
-    a_vals = np.linspace(-2.5, 1.2, grid)
+    c_vals = np.linspace(*C_RANGE, GRID)
-    b_vals = np.linspace(-2.5, 2.5, grid)
+    d_vals = np.linspace(*D_RANGE, GRID)
 
-    # Pre-compute roots at every grid point
+    print(f'  Computing roots on {GRID}×{GRID} grid…')
-    roots_grid = [[find_roots(a, b) for b in b_vals] for a in a_vals]
+    roots_grid = [[find_roots(c, d) for d in d_vals] for c in c_vals]
 
     triangles = []
 
-    for i in range(grid - 1):
+    for i in range(GRID - 1):
-        for j in range(grid - 1):
+        for j in range(GRID - 1):
-            corners_roots = [
+            c0, c1 = c_vals[i], c_vals[i+1]
-                roots_grid[i  ][j  ],
+            d0, d1 = d_vals[j], d_vals[j+1]
-                roots_grid[i+1][j  ],
-                roots_grid[i+1][j+1],
-                roots_grid[i  ][j+1],
-            ]
-            a_c = [a_vals[i], a_vals[i+1], a_vals[i+1], a_vals[i  ]]
-            b_c = [b_vals[j], b_vals[j  ], b_vals[j+1], b_vals[j+1]]
 
-            max_branch = max(len(r) for r in corners_roots)
+            r00 = roots_grid[i  ][j  ]
+            r10 = roots_grid[i+1][j  ]
+            r11 = roots_grid[i+1][j+1]
+            r01 = roots_grid[i  ][j+1]
 
-            for branch in range(max_branch):
+            # Only draw branch k when ALL four corners have it.
-                pts = []
+            # The rs[-1] fallback used previously created false triangles at
-                for k in range(4):
+            # fold edges by connecting unrelated branches — this is the main
-                    rs = corners_roots[k]
+            # cause of the messy, self-intersecting geometry.
-                    if rs:
+            n = min(len(r00), len(r10), len(r11), len(r01))
-                        x = rs[branch] if branch < len(rs) else rs[-1]
+
-                    else:
+            for k in range(n):
-                        pts = None
+                p0 = (c0, d0, r00[k])
-                        break
+                p1 = (c1, d0, r10[k])
-                    pts.append((a_c[k], b_c[k], x))
+                p2 = (c1, d1, r11[k])
+                p3 = (c0, d1, r01[k])
+
+                # Reject quads where any edge has a large z-jump.  A large
+                # jump indicates a branch-index mismatch near a fold line
+                # (sorted order is preserved within a branch but can
+                # "swap" across folds where adjacent branches coalesce).
+                if any(abs(a[2] - b[2]) > MAX_EDGE_DZ
+                       for a, b in [(p0,p1),(p1,p2),(p2,p3),(p3,p0)]):
+                    continue
 
-                if pts and len(pts) == 4:
-                    p0, p1, p2, p3 = pts
                 triangles.append((p0, p1, p2))
                 triangles.append((p0, p2, p3))
 
     return triangles
 
-# ---------------------------------------------------------------------------
+# ── 3. Flat base ─────────────────────────────────────────────────────────────
-# 3. Add flat base
-# ---------------------------------------------------------------------------
 
-def add_base(triangles, z_base=-2.4):
+def add_base(triangles, z_base=-2.8):
-    a0, a1 = -2.5, 1.2
+    c0, c1 = C_RANGE
-    b0, b1 = -2.5, 2.5
+    d0, d1 = D_RANGE
     zb, zt = z_base, z_base + 0.15
 
     triangles += [
-        ((a0,b0,zt),(a1,b0,zt),(a1,b1,zt)),
+        ((c0,d0,zt),(c1,d0,zt),(c1,d1,zt)),
-        ((a0,b0,zt),(a1,b1,zt),(a0,b1,zt)),
+        ((c0,d0,zt),(c1,d1,zt),(c0,d1,zt)),
-        ((a0,b0,zb),(a1,b1,zb),(a1,b0,zb)),
+        ((c0,d0,zb),(c1,d1,zb),(c1,d0,zb)),
-        ((a0,b0,zb),(a0,b1,zb),(a1,b1,zb)),
+        ((c0,d0,zb),(c0,d1,zb),(c1,d1,zb)),
     ]
-    walls = [
+    for (x0,y0),(x1,y1) in [
-        ((a0,b0),(a1,b0)), ((a1,b0),(a1,b1)),
+        ((c0,d0),(c1,d0)), ((c1,d0),(c1,d1)),
-        ((a1,b1),(a0,b1)), ((a0,b1),(a0,b0)),
+        ((c1,d1),(c0,d1)), ((c0,d1),(c0,d0)),
-    ]
+    ]:
-    for (x0,y0),(x1,y1) in walls:
         triangles += [
             ((x0,y0,zb),(x1,y1,zb),(x1,y1,zt)),
             ((x0,y0,zb),(x1,y1,zt),(x0,y0,zt)),
         ]
     return triangles
 
-# ---------------------------------------------------------------------------
+# ── 4. ASCII STL output ───────────────────────────────────────────────────────
-# 4. Write ASCII STL
-# ---------------------------------------------------------------------------
 
 def normal(v0, v1, v2):
     a = np.subtract(v1, v0)
     b = np.subtract(v2, v0)
     n = np.cross(a, b)
     length = np.linalg.norm(n)
-    return n / length if length > 1e-14 else np.array([0, 0, 1])
+    return n / length if length > 1e-14 else np.array([0.0, 0.0, 1.0])
 
 def write_ascii_stl(triangles, filename):
     with open(filename, 'w') as f:
@@ -134,13 +153,11 @@ def write_ascii_stl(triangles, filename):
     print(f'  Triangles : {len(triangles):,}')
     print(f'  File size : {size_kb:.0f} KB  →  {filename}')
 
-# ---------------------------------------------------------------------------
+# ── 5. Main ───────────────────────────────────────────────────────────────────
-# 5. Main
-# ---------------------------------------------------------------------------
 
 if __name__ == '__main__':
-    print('Building butterfly catastrophe mesh (grid=40)…')
+    print(f'Building butterfly catastrophe mesh (grid={GRID})…')
-    tris = build_mesh(grid=40)
+    tris = build_mesh()
     tris = add_base(tris)
     print('Writing ASCII STL…')
     write_ascii_stl(tris, 'butterfly_catastrophe.stl')