Morse Theory
Surface:
Torus (height function)
Sphere
Double well
Monkey saddle
Critical level:
0.0
Gradient flow step:
0.05
N flow lines:
30
Reset flow lines
Toggle sublevel sets
Critical points:
Morse theory: topology of sublevel sets f⁻¹(-∞,t] changes only at critical points (where ∇f=0). At index-k critical point: k-handle attached. Euler char = Σ (-1)^k.