Math Art
Enneper with n Catenoids

Enneper with n Catenoids

Enneper with n Catenoids is a minimal surface, given by a Weierstrass representation, immersed.

Open Enneper with n Catenoids in the interactive viewer →

aperiodic def-weierstrass immersed implemented minimal tradition-classical

Formula

Gauss map g
z−1+n⁢(bn−zn)an−zn\frac{z^{-1 + n} \left(b^{n} - z^{n}\right)}{a^{n} - z^{n}}
Height differential dh
z−1+n⁢(an−zn)⁢(bn−zn)(−1+zn)2\frac{z^{-1 + n} \left(a^{n} - z^{n}\right) \left(b^{n} - z^{n}\right)}{\left(-1 + z^{n}\right)^{2}}

Properties

Family
minimal
Given by
a Weierstrass representation
Curvature
zero mean curvature
Periodicity
not periodic
Ends
0
Embedding
immersed
Fidelity
exact
Exactness
numerical-integral

Definition

Extracted from the shipped row's source by AST (complete multi-line lambdas, phi triple (dh = phi3, g = phi3/(phi1 - i*phi2), a Weierstrass-representation identity)) and reproduced numerically against the shipped callables over the complex plane, exactly -- no scalar slack.

Sources

Weierstrass data reproduced numerically against the shipped implementation (math_art/minsurf/zoo.py, row ENNEPER_NCAT) by sampling g and dh over rings in the complex plane at the row's default parameters: g: matches over 144 complex samples (worst 2.62e-16); dh: matches over 144 complex samples (worst 2.98e-15).