Multi-saddle checkerboard

The slider selects the exponent m in the generalized Enneper family, g(w)=wᵐ. Order 1 is the classical Enneper surface. Increasing m produces a higher-order saddle with m+1 rising and m+1 falling height sectors.

For w=u+iv:
x=Re[w−w²ᵐ⁺¹/(2m+1)]
y=−Im[w+w²ᵐ⁺¹/(2m+1)]
z=2 Re[wᵐ⁺¹]/(m+1).

This is one connected surface, not multiple separate saddles. Checkerboard cells follow its parameter grid; their edges are generally curved. Large patches can self-intersect.